Is this a useful visualisation/analysis of hand drain/draw

[Busling]

Are the attached charts and analysis useful for discussing crew selection? 

NOTE: These are statistical APPROXIMATIONs they are not spot on, there are way too many variables to calculate to get the real stats. These are intended for comparing one crew vs another more than using the numbers as exact predictions on what will/could happen.

 

 

HandEconomy_v6.xlsx

Edited December 25, 2020 by Busling
Attach v6 of spreadsheet

[Maniacal_cackle]

I manually (roughly) calculate this all the time when creating crews. It is my basis for rejecting many of the popular models I reject.

So... I think this is awesomely useful  

Of course, you have to go much deeper with analysis, but this is a great start. For example, failing Lampad's TN is probably bad enough that you're willing to skip the model if you can't make the TN, but failing P&N's TN isn't terribly relevant most of the time.

One issue, though, is that it shows averages. So if you craft a crew that in the average case is going to have enough cards, 50% of the time you're not going to have the correct cards. So something to be aware of when crafting something like this.

EDIT: To steal a rough guess from some pro-magic players, I'd probably aim for having at least 90% consistency on getting my TNs off - at least the ones I care about.

[Busling]

Thank you, glad to know it will be helpful 😃

The images just show the summary that comes at the end of many calculations (none of which use the average formula). 

I have attached the spreadsheet that does the calculations; feel free to try it out. 

Are you able to elaborate on what deeper analysis would be useful?

[Maniacal_cackle]

23 minutes ago, Busling said:

Thank you, glad to know it will be helpful 😃

The images just show the summary that comes at the end of many calculations (none of which use the average formula). 

I have attached the spreadsheet that does the calculations; feel free to try it out. 

Are you able to elaborate on what deeper analysis would be useful?

I think most of the deeper analysis starts after having this very useful starter! I'll try to remember to have a look at the excel sheet!

[Adran]

I've only had a quick glimpse, so I may have missed some bits, and I can't quite work out how you got the numbers you got. 

The idea is a good one for planning your crew and considering what you are likely to achieve, but I think it requires more thought for analysis in depth as it is based only on simple duels and its probably the case that most people don't use the majority of their cards on simple duels.

 

[Maniacal_cackle]

2 hours ago, Adran said:

I've only had a quick glimpse, so I may have missed some bits, and I can't quite work out how you got the numbers you got. 

The idea is a good one for planning your crew and considering what you are likely to achieve, but I think it requires more thought for analysis in depth as it is based only on simple duels and its probably the case that most people don't use the majority of their cards on simple duels.

 

They do if they build their crew to be too card hungry 😜

A useful trick here might be 'average cards needed to hit all their TNs'.

So then if you make one crew that needs 5 cards on average (accounting for duds), and another crew that needs 8 on average, you can tell there is a difference there.

Of course that doesn't cover the more edge cases. I would want to know something like "how many cards will be enough 80-90% of the time".

[Maniacal_cackle]

One way I would love to use this information:

On the Ressers forum, we talk a lot about some models being tricky to use because of TN requirements. Being able to have a raw statistic to compare (this version of the crew takes 7 cards, this one 5, and this one 3 for important TNs) would aid those discussions.

[Adran]

48 minutes ago, Maniacal_cackle said:

They do if they build their crew to be too card hungry 😜

A useful trick here might be 'average cards needed to hit all their TNs'.

So then if you make one crew that needs 5 cards on average (accounting for duds), and another crew that needs 8 on average, you can tell there is a difference there.

Of course that doesn't cover the more edge cases. I would want to know something like "how many cards will be enough 80-90% of the time".

I think mentally we think a simple duel requires cards, but opposed duels don't. Or at least we very rarely " count" them in our requirements.

Knowing your crews card wants is good. Building a Cree that relies on you getting 3 severe cards to cheat for tns, duels and damage ( I'm thinking Seamus as a good case where you want to allow 2 severe cards to make your opposed duel work as planned). 

Just analysing the TN will help in some cases, and give you a good idea about crews that won't work, but you either need a strong will or an idea of opposed duels to really perform good analysis. ( that might be just assuming you get 2 attacks and they are against average df 5, that flips a 7 as its card for simplicity).

You also need to look at desired triggers on cards to get a full picture of how card hungry the crew is.

 But this is a good start at looking at those things, and probably more than most people formally do.

I think I'm saying your looking at more than a paper cut into the subject, but you've barely reached flesh wound depth for analysis.

So it depends on what you are after. I know some people like to try and get a good mix of suits across the TNs and triggers, as its easier than if all models want the same suit. I can't see if this gets to that level of detail or not whilst on my phone. Three 5+is much harder on your hand than one 5+ of each suit for example. 

[Maniacal_cackle]

I think the best such a project could hope for is providing a starting point for discussing and comparing options.

It'd be impossible (ish) to calculate the best list.

[Hermit]

This looks like a great project. Interesting analysis. If there's any way the database at biggerhat.net can help just let me know. Would you mind if we linked to your project as a resource from the site?

[Busling]

17 hours ago, Adran said:

I've only had a quick glimpse, so I may have missed some bits, and I can't quite work out how you got the numbers you got. 

The idea is a good one for planning your crew and considering what you are likely to achieve, but I think it requires more thought for analysis in depth as it is based only on simple duels and its probably the case that most people don't use the majority of their cards on simple duels.

 

Hi Adran, I see you point about most people using some of their cards for contested duels. So in v6 that I am about to upload I added a "Cards to reserve for contested duels" field to reflect that. 

Also I intend to edit the original post and provide some explanation for how the figures are calculated.

[Busling]

14 hours ago, Maniacal_cackle said:

They do if they build their crew to be too card hungry 😜

A useful trick here might be 'average cards needed to hit all their TNs'.

So then if you make one crew that needs 5 cards on average (accounting for duds), and another crew that needs 8 on average, you can tell there is a difference there.

Of course that doesn't cover the more edge cases. I would want to know something like "how many cards will be enough 80-90% of the time".

Maniacal_cackle to know  "how many cards will be enough 80-90% of the time" I would need to run a monte carlo simulation, which is not something I currently have time to develop. I do agree that would be great outcome if we could get there.

[Busling]

13 hours ago, Adran said:

I think mentally we think a simple duel requires cards, but opposed duels don't. Or at least we very rarely " count" them in our requirements.

Knowing your crews card wants is good. Building a Cree that relies on you getting 3 severe cards to cheat for tns, duels and damage ( I'm thinking Seamus as a good case where you want to allow 2 severe cards to make your opposed duel work as planned). 

Just analysing the TN will help in some cases, and give you a good idea about crews that won't work, but you either need a strong will or an idea of opposed duels to really perform good analysis. ( that might be just assuming you get 2 attacks and they are against average df 5, that flips a 7 as its card for simplicity).

You also need to look at desired triggers on cards to get a full picture of how card hungry the crew is.

 But this is a good start at looking at those things, and probably more than most people formally do.

I think I'm saying your looking at more than a paper cut into the subject, but you've barely reached flesh wound depth for analysis.

So it depends on what you are after. I know some people like to try and get a good mix of suits across the TNs and triggers, as its easier than if all models want the same suit. I can't see if this gets to that level of detail or not whilst on my phone. Three 5+is much harder on your hand than one 5+ of each suit for example. 

Unfortunately your last paragraph has pointed out one of several weaknesses this simple spreadsheet has. In the spreadsheet the chance of drawing two "Masks of 5 or higher" is presented the same as drawing a "Mask of five or higher" AND a "Crow of five or higher" (or any other suit for that matter). I agree that the chance of drawing multiple cards of the same suit is lower than drawing across multiple suits (that is just very hard to represent in this simple spreadsheet).

The other big weakness of the spreadsheet is that each "draw" assumes a full deck of cards. This assumption is of course invalid and skews the results. Again this is difficult to represent in this simple spreadsheet. 

The two weakness above would be nicely addresses by a Monte Carlo simluation however I don't want to go that far at the moment.

[Busling]

8 hours ago, Hermit said:

This looks like a great project. Interesting analysis. If there's any way the database at biggerhat.net can help just let me know. Would you mind if we linked to your project as a resource from the site?

Hi Hermit, please go ahead and link to it as a resource.

Thank you for the offer regarding the database; at the moment I don't think I want to go as far as integrating to your database. However if I do push on to look at Monte Carlo simulations I should also link to your database and go all the way

[Adran]

13 hours ago, Busling said:

Unfortunately your last paragraph has pointed out one of several weaknesses this simple spreadsheet has. In the spreadsheet the chance of drawing two "Masks of 5 or higher" is presented the same as drawing a "Mask of five or higher" AND a "Crow of five or higher" (or any other suit for that matter). I agree that the chance of drawing multiple cards of the same suit is lower than drawing across multiple suits (that is just very hard to represent in this simple spreadsheet).

The other big weakness of the spreadsheet is that each "draw" assumes a full deck of cards. This assumption is of course invalid and skews the results. Again this is difficult to represent in this simple spreadsheet. 

The two weakness above would be nicely addresses by a Monte Carlo simluation however I don't want to go that far at the moment.

I would have thought you could relatively easily set the spread sheet up to do each suit seperatly, although I'd need to think about the right way to sum them. 

The approximation of a new deck is generally fine, as you go through the deck you'll always alter the odds, but sometimes in your favour and others against you, to sort of average out. If you need that suited5 then you have 10 cards out of 54. If you have flipped 20 cards already, the chances are you have flipped 4 or 5 of the cards you need, leading to roughly the same odds. It gets a bit less useful as you need rarer cards, if you only have 2 cards in the deck that meet your needs then you probably will count cards to know if they have Come up yet. 

But then I don't know how to set up Monte Carlo simulations so I always work in probabilities. 

[Maniacal_cackle]

I agree for crew selection, knowing what cards have been flipped is not generally important.

The only time when it matters is if your decision is going to be made based on cards flipped (this is common for Dreamer, for example, since if you flip 5 weak cards that might be all the weak cards left in the deck). But that's a 'while playing, calculate on the fly' sort of thing than something you can put into a scenario like this.

Although I guess one way it does matter here is if one model uses a severe, that severe shouldn't be 'in the deck'. So the simulation breaks down at the extreme level (if you need five 13+s to get your TNs, then your odds of getting it are going to be wayyyy worse than the spreadsheet indicates).

[Busling]

In that case I will see if I can figure out a way for the spreadsheet to better account for the lowering probability of drawing multiple of the same suit. Not sure how but I will have a go...

[Maniacal_cackle]

18 minutes ago, Busling said:

In that case I will see if I can figure out a way for the spreadsheet to better account for the lowering probability of drawing multiple of the same suit. Not sure how but I will have a go...

If not, it is already at a pretty awesome level