Public TN (again) and uncertainty

[LeperColony]

1 hour ago, Adran said:

And also why using ratios of AVs is a usless number. the ration of 1 to -1 is the same as 2 to-2, (ratio of -1) but because the difference is 2 units to 4 units, the effect on the game is very different.

Sorry for double posting, I forgot to include this originally and can't figure out how to add a "quote selection" to the edit.

That's why it's not the ratio of AVs in a vacuum, but set against their odds of success at different TNs.  This is another metric in measuring relative value, but not the only one.  Obviously, when looking at negative or zeros, it produces an odd results.  Though I am not sure that the ratio of 2:-2 is 1.  I believe it's a meaningless value (and a quick Google search couldn't find a value).

Also, something that only just occurred to me, but opposed flips also extends the utility of the control hand.

Consider, if you have AV 2 against TN 10, any 7 or less is worthless pre-flip (not counting that you might want to get within 5 for DF/WP, etc and assuming AV wins ties).  But against an opposed flip with AV 6, only cards less than 3 are worthless pre-flip (again, assuming low AV wins ties).

And the same 4 that was worthless in my hand against TN 10 can allow me to potentially beat AV 6.

To be honest, even if the only benefit to opposed flipping were adding uncertainty, which it isn't, it would still be worth it.  Although, as I type this, I realize that if it resolves certainty, it must necessarily resolve worthlessness, because if a value can lead to success, it isn't worthless.  And if it either can't lead to success or it automatically leads to success, then it is certain.

I should also like to say, I lay no claim to being a math wizard.  This thread is probably about the limit of my abilities, which were only involuntarily acquired from Gen Eds.  I went to law school specifically to avoid math!  Too bad I got into gaming...

[Adran]

44 minutes ago, LeperColony said:

This is true, but first of all, you can't discount the two jokers because they do impact the variance of the distribution of values.  And also, the fact that you have an equal chance of flipping 1-13 is only true at the beginning, with a fresh deck.  As the deck degrades, low AVs are disproportionately impacted in that they become worthless at lower TNs.  Being rendered worthless at TN 20 is not really a meaningful concept in the game under the vast majority of situations.  AV 2 is worthless at 17.  0 is rendered worthless at TN 15.  AV -1, 14, AV -2 13.

Except I showed it doesn't with the chart.  Of course, part of this does depend on what you mean by extremes.  It is in the mid-range that fixed TN performs best.  At lower TNs, low AVs have a much higher relative value than high AVs, and at high TNs that changes.

Now, to be sure, if you don't think relative value is an important concept, then the fact that low AV overperforms at low TNs doesn't matter.  

This is because as a ratio, a higher number divides into the total chances and results in a lesser apparent improvement.  But this is a statistical artifice.  For each point of improvement, it blocks out a set of four cards from the range at which you can win, which is a fixed rate of advancement.

In other words, as the difference in values increases, the percent of total value each AV is responsible for decreases.  But until you reach a 14 point difference in AV, each point of AV increases the range.

Because you are most likely to flip the same value, that means that each point of AV you have in excess of your opponent removes four cards from the available total number they need to match you.  Hence the 7.5% straight advantage per point (in a fresh deck).

This is a simple, consistent metric between two AV values that simply does not change until you get to the transition from 13-14 point difference. And at a 13 or 14 point AV difference, really, what's the point?

The reason this is not the same at fixed TN is because against low TNs, low AVs can provide a high reliability of success, and at high TNs can be rendered worthless.

Part of the issue we're seeing is that there are many different metrics by which we can ascribe value to the mechanics.  That's why I've clearly labeled what it is I think is valuable, and why opposed flipping supports those valuations.

You've yet to indicate any sense of what value you think fixed TNs have.  I'm not saying there aren't any, in fact there are (simplicity and speed namely).  But if you don't identify what you think is valuable, it's hard to determine which figures support those claims.

Again, this is another statistical artifice we see because the variance is not even.  Not all results are equally likely because there are only 2 jokers, 1 BJ (0) and 1 RJ (14).  When looked at as a range of cards, the advantage is a flat.  The relative value between 6 and 2 is always going to be the 16 cards (or 20 if ties go to high) between them.

The reason this is not true of fixed TN is because low AVs peter out and become worthless.

 

 

I've not argued saying that one form is better than another because it's personal preference and I don't care what other people use. 

 I am arguing to say some of the facts on the maths you claim are wrong as far as I understand the maths. 

You claim the improvement in opposed duels is linear as you increase your stat. I think I showed it isn't for a new deck.

You claimed improvement isn't linear for fixed TNs. I showed it was on a new deck, and agree that as the deck changes, the odds of any 1 flip change, although I think that since the odds show what would happen if you go through the whole deck, doing something that makes AV2 worse at that TN, is AV2 succeeding at that TN. I know you won't have the whole deck doing the same test, so its not fully true, and players want to know the odds at that time. The memory of using a deck of cards does mean you don't always have the same probability of success for the same test. That is something that is unrelated to the type of test (fixed or opposed) so using it to claim one is worse seems flawed. 

Edit I also double posted because I couldn't work out how to add the quote, so I understand. 

[LeperColony]

8 minutes ago, Adran said:

You claim the improvement in opposed duels is linear as you increase your stat. I think I showed it isn't for a new deck.

Except you didn't.  The improvement remains a flat edge of 4 cards, or 7.5%. 

I think this is an issue with us measuring different metrics, though it's hard for me to say for sure because this thread is pretty involved and I'm not 100% sure I can be certain what I'm replying to anymore. 

9 minutes ago, Adran said:

You claimed improvement isn't linear for fixed TNs. I showed it was on a new deck

I'm not sure I said the improvement is not linear, because in either case it's always improving the cards that succeed for you by 4 (or 1 in the RJ case).

But I certainly may have, this thread is now long and confusing.

My point is that each AV you hold in advantage over someone else in opposed flips is a flat ~ 7.5% edge until you get to very high numbers.  So the relative value of the AV holds steady.

But low AV manages to perform against high AVs on low TNs at a comparatively good rate, but then low AVs lose much or all value at high TNs relative to high AVs.

And also low AVs are susceptible to card loss at a higher rate.  And they also lose value from their control hands at a higher rate.

Also, out for the weekend, so any replies will likely have to wait for Monday, but I don't want you to think I'm not responding anymore.  Few things on the internet more annoying than putting thought into a reply and having it unacknowledged.

19 minutes ago, Adran said:

I've not argued saying that one form is better than another because it's personal preference and I don't care what other people use. 

I should also say I don't care which system other people use.  But that doesn't mean they are the same.  I've identified actual differences.  You can disagree about whether they are improvements or not, but they are differences.

 

[Adran]

On ‎5‎/‎10‎/‎2019 at 7:16 PM, LeperColony said:

 

My point is that each AV you hold in advantage over someone else in opposed flips is a flat ~ 7.5% edge until you get to very high numbers.  

I've left a keyboard for the weekend and using a phone, which makes quotes much harder. 

I think I got my chart before wrong in that it is misleading.  ( the numbers are correct for fixed TN but you can't just use them like that for opposed duel it seems). 

Going from first principles. An opposed flip of 2 decks has (54*54) 2916 different outcomes, ranging from -14 to +14. 

There is 1 outcome that results in -14, black joker vs red joker. 

There are 8 outcomes that result in -13, ( black joker and the 4 13s and red joker and the 4 1s). 

There are 24 outcomes that result in -12 (  black and 12s, 1&13, 2s and red). 

There are 40 outcomes that result in -11( back and 11, 1& 12, 2&13, 3 and red) 

There are 56 outcomes that result in -10, 

72 outcomes for - 9

 And so forth leading to 210 possible outcomes that will result in the cards having the same value. ( positive difference is the same combination, just you flipped the higher card). 

This means the difference of each AV in an opposed duel isn't just 4 cards, so 7.4%. It changes so as you improve your AV to higher numbers than the opponent, each increase does help you win, but it helps you win by a lower amount than the last increase did. 

I hope this is clear. 

I think that this shows that doing opposed duels has a less linear effect on the improvement of Av than fixed TN. 

 

Edit - Back with my computer, and there is a consistent difference of 0.55% (16/2916) for most values. But that means as you get higher AVS, each point improves you chances by 0.55% less than the last point did. SO Improving from needing to flip the same card to flipping 1 worse, will improve your odds by 6.86%. The next AV improvement improves that by a further 6.31%, which is a 0.55% worse improvement than the first point. The Next improvement is by 5.76%, which is again 0.55% less of an improvement than the last improvement. Here is a chart of the numbers

Difference		Possible outcomes	Percentage chance
-14		1	0.03
-13		8	0.27
-12		24	0.82
-11		40	1.37
-10		56	1.92
-9		72	2.47
-8		88	3.02
-7		104	3.57
-6		120	4.12
-5		136	4.66
-4		152	5.21
-3		168	5.76
-2		184	6.31
-1		200	6.86
0		210	7.20

 

[LeperColony]

On 5/10/2019 at 12:58 PM, Adran said:

I think that this shows that doing opposed duels has a less linear effect on the improvement of Av than fixed TN. 

I'm going to assume your numbers are correct, because they've been generally reliable (except for the ratios) and also because I'm too lazy to calculate them myself!

It is interesting that the rate changes at a constant amount, though I suppose not to be surprised given that, excepting the jokers, each value is equally likely (though each range is not).

I do admit that your table shows that opposed flips do not maintain a flat consistent AV value, though they do provide for a more consistent AV increase that fixed TN because opposed flips require much higher numbers before they become worthless.  Therefore, I amend my argument from providing an unqualified consistent to a more consistent value.

Also, because opposed flips are based on a range, they are more resilient to card loss.  That is, they will become worthless under more rare circumstances.  

For what it's worth, these figures also make me realize that previously I had assumed the AV in question wins ties when doing calculations earlier.  

On 5/10/2019 at 12:58 PM, Adran said:

I think that this shows that doing opposed duels has a less linear effect on the improvement of Av than fixed TN. 

Again, this is not accurate because fixed TNs become worthless faster than opposed flips, and also because lower AVs overperform against higher AVs at low TNs.  All you consider, and all you've ever considered, is the rate of change.  And you just sort of handwave off the ends where values become certain.

Remember, AV 2 vs AV 6 is the same 4 point range as AV -2 vs AV 2.  In an opposed flip situation, all value differences behave in the same manner.  But in fixed TN, AVs become worthless and are susceptible to card loss at significantly different rates.

We need only look at the potential utility of the control hand to see conceptually how AV increases in a fixed TN system can be valueless in a way that isn't true in opposed flips.

Low value twist cards hold very little value to low AVs in a fixed TN system, because they will never be sufficient to succeed.  But low value twist cards in an opposed flip system retain more value because they are only worthless if their value is less than (or equal to, depending on ties) the margin of difference.

 

Finally, consider this from a gameplay standpoint.  As the deck shrinks, especially as it gets really small (say, less than 10 cards) and the players have a good sense of what remains, you can end up with the absurd situation where they take actions they know will fail just to refresh the deck.

Through the Breach has been written as a story-driven game, but it has an underlying mechanical system that leads to very "gamey" decisions. 

Oh, I know I can't fail?  I'll do it.  

Oh, I know I can't succeed?  I won't do it.

Oh, I know the deck only has bad cards?  Let's do garbage actions to refresh the deck.

Part of this is simply a side-effect of using cards.  But wouldn't you prefer a system that minimized those situations?

[Adran]

You're probably right and you can't ratio positive and negative numbers together, in which case its a useless way to evaluate a system that can contain both. Otherwise it followed the same maths as you were performing (Taking 1 number and dividing it by the other number) when you generated the 3x as much value. Either way I still say its a stat that doesn't really contain any useful information.

The rate change is constant because the are 16 new possibilities that allow the new number each time (except =14, 13 and 0 which have different numbers because of the effects of jokers)

55 minutes ago, LeperColony said:

I do admit that your table shows that opposed flips do not maintain a flat consistent AV value, though they do provide for a more consistent AV increase that fixed TN because opposed flips require much higher numbers before they become worthless.  Therefore, I amend my argument from providing an unqualified consistent to a more consistent value.

Also, because opposed flips are based on a range, they are more resilient to card loss.  That is, they will become worthless under more rare circumstances.  

For what it's worth, these figures also make me realize that previously I had assumed the AV in question wins ties when doing calculations earlier.  

Again, this is not accurate because fixed TNs become worthless faster than opposed flips, and also because lower AVs overperform against higher AVs at low TNs.  All you consider, and all you've ever considered, is the rate of change.  And you just sort of handwave off the ends where values become certain.

Remember, AV 2 vs AV 6 is the same 4 point range as AV -2 vs AV 2.  In an opposed flip situation, all value differences behave in the same manner.  But in fixed TN, AVs become worthless and are susceptible to card loss at significantly different rates.

 

All my numbers have only looked at a New deck. I really struggle when I try to show (and understand) used deck odds. You do seem fixated on them, and I honestly don't think I've followed mathematically why.

One thing I would say, in the fixed TN scenario you know exactly how many times you will succeed if that's the only challenge you do and you do it over and over again. So My AV 2 needing a TN 10 will succeed 25 times in 54 attempts. My AV 6 will succeed  41 times in 54 attempts.

If you are doing the same opposed duel you don't have that guaranteed number of successes. if you are AV 6 vs AV 5 (and winning ties) those 54 duels may cause as few as 16 successes and as many as 54, but would typically average  32.6 successes. (About the equivalent to fixed numbers needing a 6, but it is more luck dependent.)

 

All of the examples you have shown that appear to have a large change on the probability are based on you scoring your successes early on or late on it the deck. And in the game, as you count cards, this does matter if you have control over when you as a player take the vital actions. Similar things will occur in opposed duels but you need to count more cards and its less extreme.

On ‎5‎/‎8‎/‎2019 at 8:08 PM, LeperColony said:

Random elements nobody has control over is actually not true, because you do have control (also, I'm not introducing it, I'm expanding it.  There's already a random element, the Fated's flip).  You can cheat fate.  What I'm actually accomplishing, but what you entirely fail to appreciate, is the following:

1)  Eliminating (or at least vastly reducing) the loss of relative value between different AVs.

2)  Vastly reducing the situations where an AV is worthless.

3)  Vastly reducing the situations where an action is known to be automatically successful before taking it.

 

I will fully agree that using an opposed duel does reduce the situations where you know you can't win and can't lose before you start. (so 2 and 3 are true)

It does also reduce the ease at which you can calculate the relative chances of success, and hides the curve in the deck.

But I would say that opposed duels increase the loss of relative values between different AVs in that you are in a situation where they will matter less because the random number has a greater effect on the duel, and there are actually fewer "garenteed" successes and failures.

 

I have avoided adding cheating into the stats, as that sort of ignores the probability

It does increase the value of your hand (particularly looked at the scenario of 54 identical duels) because you have a greater chance of making full use of the value of the card, and they aren't just turned into Pass/fail. 

 

[LeperColony]

1 hour ago, Adran said:

You're probably right and you can't ratio positive and negative numbers together, in which case its a useless way to evaluate a system that can contain both.

It's another metric in comparing the value a player gets from one AV compared to another.  The fact that it doesn't work in all situations doesn't make it worthless, just limited.  

1 hour ago, Adran said:

All my numbers have only looked at a New deck. I really struggle when I try to show (and understand) used deck odds. You do seem fixated on them, and I honestly don't think I've followed mathematically why.

Because the fact that the deck has memory is very significant.  Cards aren't just flat paper dice.  They behave differently, and people understand those differences in different ways and to varying extents.  Frankly, I don't know how anyone who advocates for any system based on cards can't, whether fixed or opposed, can't think deck memory is an important concept.

Since you don't think AVs being rendered worthless is a problem, it's not a surprise that you don't see why I'm concerned about lower AVs degrading through card loss and control hand irrelevance.

But I consider worthless AVs and pre-ordained results as a major issue.  Again, this may simply be a philosophical difference.  People who are fine with more being consigned to automatic results, whether success or failure, are obviously not going to see the point in modifications meant to avoid them.

1 hour ago, Adran said:

One thing I would say, in the fixed TN scenario you know exactly how many times you will succeed if that's the only challenge you do and you do it over and over again. So My AV 2 needing a TN 10 will succeed 25 times in 54 attempts. My AV 6 will succeed  41 times in 54 attempts.

You also know that after X successes, there's only failures (or vice versa).  As troublesome as that is to me from a theoretical mathematical proposition, it also makes balancing varying AVs difficult.

A TN that challenges AV 6 might, perhaps, be one where they're expected to succeed about half the time.  Which is probably around TN 12/13, meaning they need to flip a 6, 7, or 8 depending on ties.  But that same TN 12/13 to an AV 2 is going to take a 10, 11 or 12, depending again on ties.  Whereas in an opposed flip, if we say AV 6 vs AV 6 is roughly even, that's still a more manageable proposition for the AV 2, even if the odds of success are similar, because it is much harder for AV 2 to get card locked out against the opposed flip versus the fixed.

1 hour ago, Adran said:

All of the examples you have shown that appear to have a large change on the probability are based on you scoring your successes early on or late on it the deck. And in the game, as you count cards, this does matter if you have control over when you as a player take the vital actions. Similar things will occur in opposed duels but you need to count more cards and its less extreme.

The fewer cards you have available, the more vulnerable you are.  A 13 is just as likely to be the top card as the bottom card, but when you encounter it is significant.  

You apparently don't mind pre-ordained results, and that's fine.  I do think certainty is a negative impact on the game.  I wouldn't want to be in a group where people do something that's supposed to be risky because they are guaranteed success, just like I don't want empty tests to reset the deck or a death spiral of certain failure.

I don't want low AVs to be spectators or high AVs to wonder why they bothered to have a better rating.  I don't want all balance to be based on everyone having the same AVs, or a very small range, like you tend to see with pre-cons.

So while you are correct to say that similar effects are possible in opposed flips, they are greatly reduced, especially with two decks.

1 hour ago, Adran said:

But I would say that opposed duels increase the loss of relative values between different AVs in that you are in a situation where they will matter less because the random number has a greater effect on the duel, and there are actually fewer "garenteed" successes and failures.

Guaranteed failure reduces the value of an AV to nothing (although that's admittedly an oversimplification because margins of success do matter), which is a pretty severe change in relative value.  While at lower TNs, low AVs offer a lot of effectiveness compared to higher AVs.  

Do those circumstances negate the reliability in the mid-range?  I'll admit at the start I felt they definitely did.  Now I'm not as sure, but I'm not at all convinced that the mid-range reliability does make the relative value more consistent than the high/low valuation situation.

Maybe you might be able to provide a mathematical breakdown for it?  It seems pretty complicated and as we've taken deeper and deeper dives in the numbers, I wouldn't be surprised if it became a matter of preference.

1 hour ago, Adran said:

I have avoided adding cheating into the stats, as that sort of ignores the probability

It does increase the value of your hand (particularly looked at the scenario of 54 identical duels) because you have a greater chance of making full use of the value of the card, and they aren't just turned into Pass/fail. 

While it does ignore probability in terms of comparing with the flip cards, it probably is possible to calculate how likely a twist card is to be useful if you know the range of TNs you might reliably encounter.  And I think players do make those kinds of calculations, even if they're on a subconscious level.

 

At this point I think we've mostly sketched out the proposition, and the question becomes whether or not you think certain things are problems or irrelevant or maybe even beneficial.  

[Adran]

12 hours ago, LeperColony said:

It's another metric in comparing the value a player gets from one AV compared to another.  The fact that it doesn't work in all situations doesn't make it worthless, just limited.  

But following it as a metric means you also compare AV3 vs AV1, as the same as AV6 vs AV2.  I think its a way of looking at the stats that only misleads and doesn't give you any real information.

12 hours ago, LeperColony said:

Because the fact that the deck has memory is very significant.  Cards aren't just flat paper dice.  They behave differently, and people understand those differences in different ways and to varying extents.  Frankly, I don't know how anyone who advocates for any system based on cards can't, whether fixed or opposed, can't think deck memory is an important concept.

Since you don't think AVs being rendered worthless is a problem, it's not a surprise that you don't see why I'm concerned about lower AVs degrading through card loss and control hand irrelevance.

But I consider worthless AVs and pre-ordained results as a major issue.  Again, this may simply be a philosophical difference.  People who are fine with more being consigned to automatic results, whether success or failure, are obviously not going to see the point in modifications meant to avoid them.

You also know that after X successes, there's only failures (or vice versa).  As troublesome as that is to me from a theoretical mathematical proposition, it also makes balancing varying AVs difficult.

A TN that challenges AV 6 might, perhaps, be one where they're expected to succeed about half the time.  Which is probably around TN 12/13, meaning they need to flip a 6, 7, or 8 depending on ties.  But that same TN 12/13 to an AV 2 is going to take a 10, 11 or 12, depending again on ties.  Whereas in an opposed flip, if we say AV 6 vs AV 6 is roughly even, that's still a more manageable proposition for the AV 2, even if the odds of success are similar, because it is much harder for AV 2 to get card locked out against the opposed flip versus the fixed.

The fewer cards you have available, the more vulnerable you are.  A 13 is just as likely to be the top card as the bottom card, but when you encounter it is significant.  

You apparently don't mind pre-ordained results, and that's fine.  I do think certainty is a negative impact on the game.  I wouldn't want to be in a group where people do something that's supposed to be risky because they are guaranteed success, just like I don't want empty tests to reset the deck or a death spiral of certain failure.

 

I agree memory is very significant, I just don't know how to show its effects in a meaningful way short of doing 1000s of simulations to give an idea of the long term effect of the memory.

You can say ""well if you need a 13 to reach the TN, and you know that your first 4 flips were the red Joker and 3*13s so you now only have a 1 in 50 chance of succeeding". Its true, but it completely ignores the likelihood of you ever being in that state. (which is something astronomically small its almost mathematically meaningless. ) So whilst I agree that you will see extreme jumps in the effectiveness of lower AV as you go through the deck, it will be just after a success that they will have that large decrease in chance of succeeding.

12 hours ago, LeperColony said:

I don't want low AVs to be spectators or high AVs to wonder why they bothered to have a better rating.  I don't want all balance to be based on everyone having the same AVs, or a very small range, like you tend to see with pre-cons.

This is almost a contradictory statement. The more value you place on the higher AV, the more like a spectator the lower AV will become. The  more you make it so that the lower AV can do something useful, the less useful the higher AV is.

A system based on Fixed TN flips does have a more linear rate of the Value of the AV.  (That does not mean AV 3 is always 3 times better than AV 1, because that's a not looking as a linear range. Because AV 4 is the same amount better than AV 2, and that's only 2 times better AV). Obviously it plateaus at the extremes when you reach automatic success/failure. Its easier to calculate the change in probabilities as the deck changes because it is more linear, but this also means that its more affected by the composition of the deck (I think. I'm, not sure how to prove it).

An opposed duel system has less emphasis on the AV. This does have advantages and disadvantages.

If you want an untrained swordsman to face Lady Justice and have a chance in a fight, then you want the opposed duel system, because at AV-2 vs AV6 the swordsman still has a chance (about 10% I think) where as in a Fixed TN system, its just going to be always impossible. (If I remember right, Justice would be setting a TN of 15 for that challenge of AV 6 + her effectively automatic flip of a 9).

 

(Of course how you change the system to use control hands would also alter this. If you haven't given the NPC any way to cheat fate, then the cheat fate mechanic would improve the odds of the fated winning the duel even more. If you do give Justice a way to cheat fate, then She is likely to do so on those really low flips that have allowed the very poor swordsman to hit her).

 

I've not really looked at many of the precons, but I expect the range of AVs of characters to be roughly -2 to 5 or 6, which is quite a large range.

 

13 hours ago, LeperColony said:

Guaranteed failure reduces the value of an AV to nothing (although that's admittedly an oversimplification because margins of success do matter), which is a pretty severe change in relative value.  While at lower TNs, low AVs offer a lot of effectiveness compared to higher AVs.  

Do those circumstances negate the reliability in the mid-range?  I'll admit at the start I felt they definitely did.  Now I'm not as sure, but I'm not at all convinced that the mid-range reliability does make the relative value more consistent than the high/low valuation situation.

Maybe you might be able to provide a mathematical breakdown for it?  It seems pretty complicated and as we've taken deeper and deeper dives in the numbers, I wouldn't be surprised if it became a matter of preference.

While it does ignore probability in terms of comparing with the flip cards, it probably is possible to calculate how likely a twist card is to be useful if you know the range of TNs you might reliably encounter.  And I think players do make those kinds of calculations, even if they're on a subconscious level.  

I don't think I can do that because a lot of it depends on the sort of challenge the party are facing. If they regularly face TN 10, then you would get 1 answer, but if they face TN 14 you would get a different answer ( I think, based on the numbers you have shown, which sound right).

Likewise on the hand, if I have AV 3 and the most common TN is 10, then I know that over half the cards in the deck are going pass that test (the mean average is 7 in a new deck), so on the same numbers over half the cards in my hand are likely to allow me to cheat to pass it(7 out of 13). If I need to get to TN 14, then slight less than 25% of the deck will be of use, and so 3/13 of my twist deck will be of use (Twist decks contain 1 or each number  but no Jokers at least at the beginning if I remember right). 

I'm not sure I can work out the odds that after you have used half of the deck that you will have Doubled your chances of success or failure (its possible to do so, but my card probabilities understanding is not good enough to be sure I'm right) for each of those AV.

[LeperColony]

6 hours ago, Adran said:

I agree memory is very significant, I just don't know how to show its effects in a meaningful way short of doing 1000s of simulations to give an idea of the long term effect of the memory.

The interesting thing about cards is that since most people will have interacted with them, we all have a "feel" for how they operate.  And that feeling may actually be largely accurate, even if it is beyond our ability to mathematically determine with precision.

But casinos prove that the margin between our general understanding and their actual operation has significant differences, even if that understanding is, for most purposes, fairly good.

6 hours ago, Adran said:

So whilst I agree that you will see extreme jumps in the effectiveness of lower AV as you go through the deck, it will be just after a success that they will have that large decrease in chance of succeeding.

Or anyone else succeeding.  That's the thing.  TtB is not Malifaux, it's not you versus someone else.  All the Fated use the deck, and so in actuality, you're not guaranteed to ever succeed.  The lower your AV, the more vulnerable you are to card loss, which includes cards lost to the pulls of your compatriots.

6 hours ago, Adran said:

This is almost a contradictory statement. The more value you place on the higher AV, the more like a spectator the lower AV will become. The  more you make it so that the lower AV can do something useful, the less useful the higher AV is.

It's not a contradictory statement, but rather they are two different concerns that each implicate the other.  Given the realities of the mechanics, there are only so many options to try to resolve the difficulties presented by each.  I feel opposed flips do a better job of alleviating the problems than fixed TNs.

6 hours ago, Adran said:

A system based on Fixed TN flips does have a more linear rate of the Value of the AV.  (That does not mean AV 3 is always 3 times better than AV 1, because that's a not looking as a linear range. Because AV 4 is the same amount better than AV 2, and that's only 2 times better AV). Obviously it plateaus at the extremes when you reach automatic success/failure. Its easier to calculate the change in probabilities as the deck changes because it is more linear, but this also means that its more affected by the composition of the deck (I think. I'm, not sure how to prove it).

Again, at the mid-range I agree it has a more linear rate of value.  But as I said, I'm not sure that means it has a more linear rate as a whole because I don't know (and you haven't shown either) if the flattening out to 0% or 100% preserves the rate of value, decreases it, or if it somehow increases it (not sure how that could be, but who knows).

Fixed TNs are almost certainly more susceptible to deck changes because the subset of qualifying cards is fixed.  But also, most Fated are going to be "competing" (for lack of a better word) for the same cards.  In a fixed TN system, very low cards (let's say less than 4), are going to be of very limited value to anyone.  Ideally, you'd like each Fated to flip exactly what they need and no more (which, again, is an oversimplification because margins can matter), so that successes occur but lower AVs still retain their best chances.  But that's not how cards work.

In an opposed flip situation, there are just as many 1-3 cards as there are 11-13, and so even the low cards are going to see real utility.

Even if you go back to when this subject came up last time on the forums, I think around late 2017, everyone agreed that fixed TNs work reasonably well when you need mid-range flips and everyone has similar AVs.

6 hours ago, Adran said:

An opposed duel system has less emphasis on the AV. This does have advantages and disadvantages.

I'm actually not sure this is true.  Or rather, it seems like a complicated prospect to figure out.  In a fixed TN system, AVs significance vis-a-vis the flipped card are going to fluctuate based on the AV in question.  Low AVs matter less, higher AVs matter more.

6 hours ago, Adran said:

If you want an untrained swordsman to face Lady Justice and have a chance in a fight, then you want the opposed duel system, because at AV-2 vs AV6 the swordsman still has a chance (about 10% I think) where as in a Fixed TN system, its just going to be always impossible. (If I remember right, Justice would be setting a TN of 15 for that challenge of AV 6 + her effectively automatic flip of a 9).

The thing is, it's possible to construct scenarios so that Fixed and Opposed have the same percent chance of success.  And yet the opposed flips still have a wider range of possible successful outcomes, meaning they won't get blocked out through card loss as easily.  Earlier in the thread, I mentioned this in reference to another topic on the forum re: retainers.

In another thread, a @oadrian is asking if retainers are balanced because they can get up to a 14 (or more) without too much difficulty.  

Now let me ask you.  Which scenario would you rather have as the AV 2 player? 

Flipping against a static 14 (or higher, depending), or flipping against someone with a AV of 9 or 10.  I'm just eyeballing it here, so I could be wrong, but I believe these are roughly similar in percentage.  But there's a wider range of scenarios in the flip.  Again, this goes to resilience from card loss.

6 hours ago, Adran said:

If I need to get to TN 14, then slight less than 25% of the deck will be of use, and so 3/13 of my twist deck will be of use (Twist decks contain 1 or each number  but no Jokers at least at the beginning if I remember right). 

Interestingly, the twist hand wasn't even part of my considerations until this discussion.  But the fact that they retain more utility in opposed flips is another reason for me to dislike fixed TNs.

Though, I should say that even if a card is worthless from a success/failure standpoint, it can still be of value to shrink margins or to discard for other effects.  So a truly worthless twist hand is probably not a meaningful concept.  But it's still fair to say that twist hands are more useful in opposed flips.

 

 

I should also say it's been great talking to you about this.  While I believe the things opposed flips addresses are real concerns, I know it's entirely possible to care more about speed and simplicity, or to just dislike modifications (because some people do just dislike changing systems), and to not think things like certainty, deck degradation, twist hand utility and AV value loss to worthless or automatic scenarios matter as much. 

[Adran]

Firstly, Thank you for the discussion. I've been playing Malifaux for 10 years, and I haven't looked at the opposed duel mechanics this closely before, its been an eye opener looking at some of the things that are implicated in working out random in this way.  

16 hours ago, LeperColony said:

Or anyone else succeeding.  That's the thing.  TtB is not Malifaux, it's not you versus someone else.  All the Fated use the deck, and so in actuality, you're not guaranteed to ever succeed. 

Thats true and its something that remains true regardless of the mechanism you use. I have phrased most of my examples as if you are the only person using the deck, because from  the terms of probability it makes no difference who flips the card. In the game it might make a huge difference if its you that flips that card, or someone else in your group. (It might make very little difference to the end result, but it certainly will affect your perception).

16 hours ago, LeperColony said:

Fixed TNs are almost certainly more susceptible to deck changes because the subset of qualifying cards is fixed.  But also, most Fated are going to be "competing" (for lack of a better word) for the same cards.  In a fixed TN system, very low cards (let's say less than 4), are going to be of very limited value to anyone.  Ideally, you'd like each Fated to flip exactly what they need and no more (which, again, is an oversimplification because margins can matter), so that successes occur but lower AVs still retain their best chances.  But that's not how cards work.

In an opposed flip situation, there are just as many 1-3 cards as there are 11-13, and so even the low cards are going to see real utility.

This is something that Is going to be really hard to work out, because the Value of the 3 card is based on 2 things - the Stat of the player, and the difficulty of the task. You may well play in a game where the players regularly need to pass a TN 5 challenge, in which case the 3 Card is still very valuable to the AV 2 player (while worthless to the AV 1 Player if thats the only tn). Or you could be facing foes who start with an AV of 6, in which case the 3 card is worthless to the AV 2 player in opposed duels. Now these are both extreme cases but they are entirely dependent on the type of game you play, which only you know.

 

Deck degradation is something I've never really looked at, I've just relied on my "knowing how cards work", so I'm expecting what I though to be surprisingly wrong.

AV 2 VS AV 10 appears to be a 10% Success rate on a new deck. (9.9%)

AV 2 vs TN 15 is about 10% success rate on a new deck. (9.3%)

 

If I do a successful hit in each case, how does it affect my chances?

This is easy in the Fixed TN, I had only 5 successful options in 54. I now only have 4 successful options in 53, so its 7.5%

In an opposed duel there are 289 possible combinations that will have given me the success. But taking 1 of those possible combinations out does not mean there are 288 possible combinations remaining.

For example I hit because I flipped a 8, and my opponent flipped the black joker. Of the 288 combinations that "are left" to succeed, 24 contained my opponent flipping the black joker, so aren't possible.

But also there are also 29 Times when they flipped the black joker, and would still win, and 53 less  times that my 8 will be a loss, so I think this has altered there to be 2809 possible options, and 264 successes. So this is then 9.3%.

If I flipped a 13 and my opponent flipped a 1 we have removed 24 successes that the 13 would have contributed, and a further 16 that involve the opponent flipping a 1.

So this is (I think) now 248 options that succeed from 2809 possible remaining outcomes, so a 8.8% chance.

 

I can't easily work out an overall probability that you will win an opposed duel after just 1 successful flip at the duel has occurred, because its a sum of 289 different chances (or really 28 different chances since we're ignoring suits). I am prepared to say that you are overall going to be more likely to win that second flip than in the fixed TN scenario, but how that changes over time is too complex for me to calculate.

 

Just to add to this, its also worth noting that Opposed duels that you lose can also decrease your chance of winning the next identical duel because there isn't a fixed number of successes, which doesn't occur in this scenario for Fixed TNs. So I'm not prepared to say that deck degradation over time favours opposed duels vs fixed TNs.

(I flip a red joker, my opponent flips a 7. I've removed 25 possible successful flips from the combinations, so despite losing I am now at 9.3% chance of winning the next flip, rather than the 10% chance I was at before I took that losing duel. This was something I hadn't realised before this)

 

17 hours ago, LeperColony said:

Interestingly, the twist hand wasn't even part of my considerations until this discussion.  But the fact that they retain more utility in opposed flips is another reason for me to dislike fixed TNs.

Though, I should say that even if a card is worthless from a success/failure standpoint, it can still be of value to shrink margins or to discard for other effects.  So a truly worthless twist hand is probably not a meaningful concept.  But it's still fair to say that twist hands are more useful in opposed flips.

My comment on the value of Twist cards was said in relation to you taking "the same duel" multiple times (So either same AV vs TN, or same AVs in opposed duels). If you typically have a wide range of Fixed TNs, then the twist cards are maintaining a similar utility. (Its probably not the same utility, but without knowing how often you need certain cards in the games you play, I have no idea how to even attempt to calculate it). If you have a FM who often likes "round" numbers then you may find that the TNs clump more around 5, 10 and 15, which will alter the value of some cards.

[LeperColony]

On 5/15/2019 at 2:49 AM, Adran said:

I have phrased most of my examples as if you are the only person using the deck, because from  the terms of probability it makes no difference who flips the card.

From a mathematical standpoint, that's certainly true.  But I more meant that we've both been talking as though the whole deck is going to be available to an individual player, but that's not true.  And there are situations like combat, that involve a lot of flips, but the Fated may have very different capabilities depending on their individual characters.  

I personally don't run fixed TN (which isn't to say there are no fixed TN checks in my games, more on that below), but I've played in Fixed TN games, particularly at conventions or the like, and I've seen the "why bother" sense when people figure out they're flipping against a TN they aren't going to overcome (even if they actually can).  I've seen it come up most in the "boss fight" stage of the scenario, where the non-combat characters with their respectable 2 AV are rendered mostly as spectators for all the impact they have on things.  

Which can happen in opposed flips too, but unless the AV difference is truly oppressive, it isn't as easy to get locked out.  Or to feel locked out.

That's another thing about uncertainty.  There's actual uncertainty, where success or failure is not pre-ordained.  But there's also subjective uncertainty, where the player's grasp of the math involved is insufficient to provide knowledge of whether or not the action is pre-ordained.  Given the discussion in this thread, I think it's pretty clear both are better preserved in opposed flips.

I've seen players keep track of used cards before.  I even once played in a con game where some guy checked off cards as they got spent.  Maybe that's against the "spirit" of TtB, but it seems pretty smart in a fixed TN game (or really any game with cards).  

On 5/15/2019 at 2:49 AM, Adran said:

You may well play in a game where the players regularly need to pass a TN 5 challenge, in which case the 3 Card is still very valuable to the AV 2 player (while worthless to the AV 1 Player if thats the only tn).

Are TN 5 flips actually done?  Genuine question.

In my own games, I do use some fixed TN flips, for things like climbing a wall, and I'm not likely to ask for a flip with such a low TN.  But rather, in most cases I'd just assume success if the task is that simple.

Maybe that's unfair.  Someone with a bad AV can actually struggle against a 5.  If you've got a -2, that's a 7 they need.

So perhaps part of my belief that low cards aren't useful in fixed TNs is due to sorts of things I flip for as opposed to just hand wave.

On 5/15/2019 at 2:49 AM, Adran said:

(I flip a red joker, my opponent flips a 7. I've removed 25 possible successful flips from the combinations, so despite losing I am now at 9.3% chance of winning the next flip, rather than the 10% chance I was at before I took that losing duel. This was something I hadn't realised before this)

It's probably even more complicated than that, because removing the 7 changes the odds on future flips too.  Is removing a mid-range card from the higher AV deck (whether two decks or one are used) good or bad for the lower AV?  

 

 

[Adran]

3 minutes ago, LeperColony said:

Are TN 5 flips actually done?  Genuine question.

In my own games, I do use some fixed TN flips, for things like climbing a wall, and I'm not likely to ask for a flip with such a low TN.  But rather, in most cases I'd just assume success if the task is that simple.

Maybe that's unfair.  Someone with a bad AV can actually struggle against a 5.  If you've got a -2, that's a 7 they need.

So perhaps part of my belief that low cards aren't useful in fixed TNs is due to sorts of things I flip for as opposed to just hand wave.

I honestly don't know, I've not played second edition, and only played a few 1st edition games. I haven't ever finished a campaign in it, I've just played a few of the world wide campaigns. It also means I haven't watched character progression and seen how that affects the different challenges.  Taking it to a different game if I play DnD (pretty much any of the versions) then the things that almost kill me at level 1 are things that its not worth rolling for by about level 5

10 minutes ago, LeperColony said:

It's probably even more complicated than that, because removing the 7 changes the odds on future flips too.  Is removing a mid-range card from the higher AV deck (whether two decks or one are used) good or bad for the lower AV?  

I think this time I've got that covered, in the example, because I worked out every possible success combination of those 2 "degraded" decks, and then divided that by the total number of possible combinations. (also made easier in this example because every time the AV 6 flipped a 7 they would win regardless of the TN -2s flip. If I picked flipping a 12 and a 5, then it is more complicated). But Its certainly not as simple as calculating 1 deck, which probably means most people can't track the changes in probability, so the perception of Uncertainty is maintained almost regardless of the actual uncertainty.

 

19 minutes ago, LeperColony said:

I personally don't run fixed TN (which isn't to say there are no fixed TN checks in my games, more on that below), but I've played in Fixed TN games, particularly at conventions or the like, and I've seen the "why bother" sense when people figure out they're flipping against a TN they aren't going to overcome (even if they actually can).  I've seen it come up most in the "boss fight" stage of the scenario, where the non-combat characters with their respectable 2 AV are rendered mostly as spectators for all the impact they have on things.  

Which can happen in opposed flips too, but unless the AV difference is truly oppressive, it isn't as easy to get locked out.  Or to feel locked out.

I don't know how much alteration you give to the fatemaster characters because you have changed the system. The printed stats in the book are based around 1 set of odds, and opposed duels give different odds. If I remember correctly, in combat you assume the FMcharacter flips a certain value every time which is why its a fixed TN.

Changing to opposed duels will increase the power of Minions, and decrease the power of masters, because part of the power the master has in the published rules is in effect always flipping a high card.

So I can't talk from a TTB perspective, but certainly in the Malifaux community, people typically think  a duel that is AV 4 vs AV 6 is a total waste of time. (I don't agree but its a well held view often expressed as "Its not worth picking that model because its only got an AV 4") Obviously goals are different, and Malifaux has the "time" aspect as well, and more choice to pick your AVs, and less attachment to the character making the duel, but players there still feel some close opposed duels are not worth taking. That, to me, is a similar feeling of locked out although in a very different context.

[LeperColony]

On 5/17/2019 at 1:24 AM, Adran said:

I honestly don't know, I've not played second edition, and only played a few 1st edition games. I haven't ever finished a campaign in it, I've just played a few of the world wide campaigns. It also means I haven't watched character progression and seen how that affects the different challenges.  Taking it to a different game if I play DnD (pretty much any of the versions) then the things that almost kill me at level 1 are things that its not worth rolling for by about level 5

This has left me wondering if I don't test often enough for low TNs.  Climbing the proverbial TN 5 fence, for instance.  I generally would only flip for something I considered so simple if the stakes were high or the situation intense (like during combat).  But what's simple or even automatic for some AVs is a real struggle for others, and in TtB you do often see groups with a wide range of scores.

Obviously I wouldn't want to bog my game down with constantly flipping for technically uncertain but relatively simple tasks, but just looking at the implications of flipping or not can be interesting.  For clarity and sake of argument, I'm defining these simple tasks as having a TN of 5, being non-trivial in that I'm not testing something whose outcome is irrelevant, but with very low stakes, such that failure doesn't incur serious harm (more like some kind of minor delay or inconvenience).

There used to be a "take 10" rule, but that was errata'ed out.  So we can no longer assume a simple task, like climbing a low fence, is automatic RAW.

When hand waving away these tasks, low AV benefits because even though I mentally regard a TN 5 as trivial, it can include a significant risk of failure all the way up to about AV 1 or 2.  At the same time, high AV is "penalized" because it is treated in the same manner as low AV, even though it represents a higher investment in the Fated's resources to have acquired the better value.

But is the solution really to flip for more things that I just allowed to pass on the wave?  I'm not sure.

On 5/17/2019 at 1:24 AM, Adran said:

I think this time I've got that covered, in the example, because I worked out every possible success combination of those 2 "degraded" decks, and then divided that by the total number of possible combinations. (also made easier in this example because every time the AV 6 flipped a 7 they would win regardless of the TN -2s flip. If I picked flipping a 12 and a 5, then it is more complicated). But Its certainly not as simple as calculating 1 deck, which probably means most people can't track the changes in probability, so the perception of Uncertainty is maintained almost regardless of the actual uncertainty.

What I more meant here was that is removing a mid card from the high AV deck good or bad from the low AV perspective?

For instance, if a 7 beats the low's RJ, then a 13 would have too.  But removing a 13 from the high deck is obviously good from the low AV perspective, because removing any card that would automatically defeat the low AV is beneficial to future flips, just like removing any low card from the low AV is beneficial to future flips.

But do mid-range cards "matter," or is it kind of like the quick-and-dirty card counting trick for Blackjack, where you track low and high, but ignore mid?

On 5/17/2019 at 1:24 AM, Adran said:

So I can't talk from a TTB perspective, but certainly in the Malifaux community, people typically think  a duel that is AV 4 vs AV 6 is a total waste of time. (I don't agree but its a well held view often expressed as "Its not worth picking that model because its only got an AV 4") Obviously goals are different, and Malifaux has the "time" aspect as well, and more choice to pick your AVs, and less attachment to the character making the duel, but players there still feel some close opposed duels are not worth taking. That, to me, is a similar feeling of locked out although in a very different context.

I've also heard similar sentiments, but never really felt the math supported it.  However, I don't really think they are comparable situations at all, even though the numbers are very similar (because the systems are similar).  Malifaux is a competitive game where you're trying to beat another player by making a team from a list of options.  So when someone says something like an "AV of 4 is not worth taking," they're doing so within a fixed universe of known AV values and relative to other options.  In other words, "why take the AV 4 for X SS when I can take the AV 6 for X+Y?"  

But also, all models in Malifaux are created to be of use in a competitive setting, and they can have a singular focus which a low AV might significantly undermine.  For instance, if Rotten Belles had a Ca of 4 for their lure, and that was the point of the model, it very well could make sense to say you wouldn't want them because the return on SS investment isn't going to be worth it compared to other options.    

TtB Fated creation can't really be compared to Malifaux crew hiring.