Card probability.

[WWHSD]

I was wondering how likely it is for Ramos to draw a card that would let him summon 3 spiders. I was also wondering how taking Arcane Reservoir and stoning for cards changes that. I'm also horrible at math but I do okay with Goggle. 

I found a cool hand probability calculator that was designed for games like MtG. I figured that other folks around her might find it handy.

For anyone that's curious, the odds of getting an 11+  or a Red Joker are as follows:

6 cards: 38.5%
6 cards w/stone for draw: 48.4%
7 cards: 43.6%
7 cards w/stone for draw: 52.9%

Assuming I'm using that calculator correctly, the odds are much higher than I had figured.

[DonCheadle]

Wouldn't stone for drawing have the same effect as simply drawing two more cards? 

[Rillan]

I don't know how u calculated it but in 54 card deck there are 13 cards (11+12+13*4 + Joker) with value of 11+ and chance to getting on a flip is ~25%.
Chance of not getting a single card with 6 card draw is 19% and same opposite there is a 81% chance that one of your 6 cards will have value 11+

 

[Adran]

He wants 11, so only 4 cards in the deck that work. 

Those numbers sound high, but probability can throw out seemingly strange numbers. I'm going to go and work it out myself because I think the calculator doesn't do what you want it to do. Wait on the edit with my answer...

I got the odds on your 6 card hand not having one of those 4 cards as being 61.5% of the time. So agrees with the 38.5% chance of you having at least one. 

The site does what you want, I just can't read well... (missed how to set the size of the deck)

[DonCheadle]

4 minutes ago, Adran said:

He wants 11, so only 4 cards in the deck that work. 

Those numbers sound high, but probability can throw out seemingly strange numbers. I'm going to go and work it out myself because I think the calculator doesn't do what you want it to do. Wait on the edit with my answer...

It's correct in that for 6 cards, the chance to get 0 of them is 61.5270782% and so on and so forth. 

However, it does not account for possible multiples (aka what is the chance of getting 2 or more usable cards?).

[Adran]

6 minutes ago, DonCheadle said:

It's correct in that for 6 cards, the chance to get 0 of them is 61.5270782% and so on and so forth. 

However, it does not account for possible multiples (aka what is the chance of getting 2 or more usable cards?).

For the purposes of Summon the Swarm you only want 1 or more, which this tells you. so in 38.5% of my hands I will have the ability to summon 3 Spiders. Some number of them ( 32.8%) I only have 1 of those 4 cards, and in 5.4% of my hand I have 2 of those cards. (At least according to the site, its early on a monday and I can't quite be bothered to work it out myself)

[DonCheadle]

Eh, nice to have one for next turn as well. 

On a side note, this is why I stopped playing Ramos. Overall prepwork turned very formulaic and there wasn't much reactive play (plus me being slow on 3 Spiders a turn leads to very long games). 

[Rillan]

1 hour ago, Adran said:

He wants 11, so only 4 cards in the deck that work. 

This topic come from @WWHSD complained about his results in spider summoning. And ok there is not so big chance of getting 11+ but with 81% chance + spending SS is not a problem at all.

[Adran]

10 minutes ago, Rillan said:

This topic come from @WWHSD complained about his results in spider summoning. And ok there is not so big chance of getting 11+ but with 81% chance + spending SS is not a problem at all.

But you are already spending a stone to add a suit to your duel, you can not replace the 11 with any 11 and a stone.

But to be honest, a  40% chance to get 3 each turn is probably likely enough, and without it you can still get 2 a turn almost all the time.

[WWHSD]

5 hours ago, Rillan said:

This topic come from @WWHSD complained about his results in spider summoning.

Yup, I certainly did complain about only infrequently being able to summon 3 spiders turn 1. I was looking to see if my anecdotal experience reflected the actual probability when I found this calculator. This calculator shows that my results are a likely due to having too small a sample size. 

[WWHSD]

7 hours ago, Adran said:

The site does what you want, I just can't read well... (missed how to set the size of the deck)

You don't set the size of the deck directly. 

I added 50 cards of which I required 0 and 4 cards of which I required 1. This resulted in a 54 card deck. 

[WWHSD]

7 hours ago, DonCheadle said:

Wouldn't stone for drawing have the same effect as simply drawing two more cards? 

That's how I calculated it. I calculated odds for a hand of 6, 7, 8, and 9 cards.

[WWHSD]

7 hours ago, DonCheadle said:

It's correct in that for 6 cards, the chance to get 0 of them is 61.5270782% and so on and so forth. 

However, it does not account for possible multiples (aka what is the chance of getting 2 or more usable cards?).

If you want the odds for 2 matching cards change the value in  the "need" field for the 4 cards to 2. 

[santaclaws01]

7 hours ago, Adran said:

He wants 11, so only 4 cards in the deck that work. 

Those numbers sound high, but probability can throw out seemingly strange numbers. I'm going to go and work it out myself because I think the calculator doesn't do what you want it to do. Wait on the edit with my answer...

I got the odds on your 6 card hand not having one of those 4 cards as being 61.5% of the time. So agrees with the 38.5% chance of you having at least one. 

The site does what you want, I just can't read well... (missed how to set the size of the deck)

Fun fact about probabiliy and weird numbers. It only takes 23 people for there to be a 50% chance that 2 of them share a birthday.

[Adran]

3 minutes ago, santaclaws01 said:

Fun fact about probabiliy and weird numbers. It only takes 23 people for there to be a 50% chance that 2 of them share a birthday.

I know. I had to work that one out myself to believe it. Its one of those seemingly strange numbers that probability throws out. that means I feel I need to check almost anythign regardless of how outlandish it sounds. 

[Gnomezilla]

Probability also tells us that there has been no deck of cards since their invention, including every time each of those decks was shuffled, in which every card in the deck was sorted by suit and number (citation via QI, a TV trivia program and panel show)—yet most decks printed these days are printed and packaged in order. Probability is crazy powerful, but it isn’t always the only influence.

 

For myself, I’m still not great at shuffling, but better now when making sure to move the top few and bottom few cards into the middle of the well-shuffled parts and shuffling one more time. If the deck doesn’t seem to be randomizing enough at the top and bottom (for good or ill), then my technique is getting in the way of probability, and I take time to pile shuffle into five piles. Pile shuffling doesn’t randomize well on its own but it does break any streak which shows up. I have pile shuffled between games in which Ramos simply could not get three spiders out on a single turn.

[DonCheadle]

1 hour ago, Gnomezilla said:

Probability also tells us that there has been no deck of cards since their invention, including every time each of those decks was shuffled, in which every card in the deck was sorted by suit and number (citation via QI, a TV trivia program and panel show)—yet most decks printed these days are printed and packaged in order. Probability is crazy powerful, but it isn’t always the only influence.

 

For myself, I’m still not great at shuffling, but better now when making sure to move the top few and bottom few cards into the middle of the well-shuffled parts and shuffling one more time. If the deck doesn’t seem to be randomizing enough at the top and bottom (for good or ill), then my technique is getting in the way of probability, and I take time to pile shuffle into five piles. Pile shuffling doesn’t randomize well on its own but it does break any streak which shows up. I have pile shuffled between games in which Ramos simply could not get three spiders out on a single turn.

You could argue that that's low key cheating in the same way mana weaving exists in Mtg. 

[WWHSD]

25 minutes ago, DonCheadle said:

You could argue that that's low key cheating in the same way mana weaving exists in Mtg. 

I find that pile shuffling and then riffle and/or overhand shuffling work well for people that aren't great at riffle shuffling or with cards that kind of stick together when riffled.The pile shuffling breaks up strings of cards from the last time around and then a couple of riffles and overhand shuffles randomizes those cards. With riffle shuffling alone, poor technique or difficult to work with cards can result in clumps of cards that don't ever get broken up.

During a game of Malifaux I'll typically overhand shuffle at least 5 times and riffle shuffle 2 twice. I'll do that twice and then finish up with a bit more overhand shuffling. It's quick and it seems like alternating between overhand and riffle shuffling does a good job of randomizing even if my riffle is sloppy because i'm doing it quickly.

Apparently 7 riffle shuffles is the magic number for having a thoroughly randomized deck.

[Clement]

40 minutes ago, DonCheadle said:

You could argue that that's low key cheating in the same way mana weaving exists in Mtg. 

I actually had to go look up mana weaving.  Are there people that actually "mana weave" and then just leave it that way?  Learn something new every day.  

The basic rule to shuffling is you have to make sure you actually arrive at the stated goal (that being a randomized pile of cards).  No single method of shuffling really gets the job completely done, since each method of shuffling usually has it's own particular flaws.

• Rifle shuffling will often keep the top cards on/near the top, especially if you don't pay much attention since people tend to use the same "top half on the left" pattern to the motion.
• Overhand shuffle tends to keep clumps of cards together since it doesn't really break up the deck as much as rifle shuffling does.

The trick is to use multiple shuffling types.  Throw a rifle shuffle or two, then overhand once or twice, then rifle a few more.

[solkan]

 

3 hours ago, WWHSD said:

Apparently 7 riffle shuffles is the magic number for having a thoroughly randomized deck.

For the record:  https://www.dartmouth.edu/~chance/teaching_aids/Mann.pdf

I bring up the paper because they go through the math that results in the 7 result, but then they present the arguments based on other criteria for 11 shuffles to be randomized.

And here's an article presenting a conclusion for 12:  http://www.ams.org/publicoutreach/feature-column/fcarc-shuffle

Point being that 7 is often quoted as the "good enough" point, especially if you've got a clock ticking, but it's not necessarily well shuffled.  🃏

[DonCheadle]

10 hours ago, WWHSD said:

I find that pile shuffling and then riffle and/or overhand shuffling work well for people that aren't great at riffle shuffling or with cards that kind of stick together when riffled.The pile shuffling breaks up strings of cards from the last time around and then a couple of riffles and overhand shuffles randomizes those cards. With riffle shuffling alone, poor technique or difficult to work with cards can result in clumps of cards that don't ever get broken up.

During a game of Malifaux I'll typically overhand shuffle at least 5 times and riffle shuffle 2 twice. I'll do that twice and then finish up with a bit more overhand shuffling. It's quick and it seems like alternating between overhand and riffle shuffling does a good job of randomizing even if my riffle is sloppy because i'm doing it quickly.

Apparently 7 riffle shuffles is the magic number for having a thoroughly randomized deck.

Ah no, I loved the overall point @Gnomezilla made, I was solely referring to the last part of reacting to an "unshuffled" deck with a special way to shuffle.  In true randomness, similar cards being stuck together is absolutely possible, and I'd say changing the way you shuffle mid-game is cheating, if only a very mild form. 

[Gnomezilla]

11 hours ago, DonCheadle said:

Ah no, I loved the overall point @Gnomezilla made, I was solely referring to the last part of reacting to an "unshuffled" deck with a special way to shuffle.  In true randomness, similar cards being stuck together is absolutely possible, and I'd say changing the way you shuffle mid-game is cheating, if only a very mild form. 

I believed the cards were literally stuck together, not stuck by probability, once I played enough to notice it happened mostly with the first few from the deck (more memorable—perhaps memory bias—but a newbie’s T1 elite crew doesn’t flip many cards and so there was less to remember overall).

I have to worry. In tournaments I have tried to say every round, if I am not shuffling well enough PLEASE feel free to shuffle them for me, I’ll be happy, not offended. (Early on, one opponent from a very time-efficient meta even shuffled mine every round—I thank him again here. For the shuffling. I maybe could’ve done without being tabled turn 3, but it was efficient. ) That’s also a change of shuffling technique and just as ‘mildly cheating’ to you, but now the other person is implied too.