Chess or Poker?

[Superman26gt]

I used to play chess seriously and was thinking about it in relation to poker when I came up with this question...

How many combinations of moves are possible in chess and how many in poker? (we'll assume SH limit HE for "simplicity")

I know they are both big numbers obviously but could anyone come up with exact answers, or find a study done on this?

[Superman26gt]

I did some searching and found a few things on chess...

-Chess is infinite: There are 400 different positions after each player makes one move apiece. There are 72,084 positions after two moves apiece. There are 9+ million positions after three moves apiece. There are 288+ billion different possible positions after four moves apiece. There are more 40-move games on Level-1 than the number of electrons in our universe. There are more game-trees of Chess than the number of galaxies (100+ billion), and more openings, defences, gambits, etc. than the number of quarks in our universe! --Chesmayne

-The longest Chess game theoretically possible is 5,949 moves.

(http://www.chess-poster.com/english/...d_you_know.htm)

Any ideas on SH limit HE?

[LCposter]

All right, I'll take a stab at the heads up solution. This can be extended to 3-handed, 4-handed, etc. but the complexity increases exponentially with each additional player. Assume betting is capped for all rounds at 4 bets. First we enumerate the number of possible preflop betting sequences:

1. fold
2. complete/check
3. complete/raise/fold
4. complete/raise/call
5. complete/raise/3-bet/fold
6. complete/raise/3-bet/call
7. complete/raise/3-bet/4-bet/fold
8. complete/raise/3-bet/4-bet/call
9. raise/fold
10. raise/call
11. raise/3-bet/fold
12. raise/3-bet/call
13. raise/3-bet/4-bet/fold
14. raise/3-bet/4-bet/call

Next we enumerate the number of possible betting sequences for the flop/turn/river:

1. check/check
2. check/bet/fold
3. check/bet/call
4. check/bet/raise/fold
5. check/bet/raise/call
6. check/bet/raise/3-bet/fold
7. check/bet/raise/3-bet/call
8. check/bet/raise/3-bet/4-bet/fold
9. check/bet/raise/3-bet/4-bet/call
10. bet/fold
11. bet/call
12. bet/raise/fold
13. bet/raise/call
14. bet/raise/3-bet/fold
15. bet/raise/3-bet/call
16. bet/raise/3-bet/4-bet/fold
17. bet/raise/3-bet/4-bet/call
(18). fold
(19). check/fold

Note the last two involve folding when it's free to check, but they should be counted because a player could choose to fold rather than go to showdown and reveal his/her hole cards.

In summary, we have:
C(52,2) = 1,326 possible hands for player 1
C(50,2) = 1,225 possible hands for player 2
C(48,3) = 17,296 possible flops
45 possible turns
44 possible rivers
14 possible betting sequences preflop
19 possible betting sequences flop
19 possible betting sequences turn
19 possible betting sequences river

# games = 1326 * 1225 * 17296 * 45 * 44 * 14 * 19^3 = 5.34e18 possible heads up limit hold 'em games

[Superman26gt]

Nice LC.

Has anyone found anything on the internet about this or heard of this being done, cause if not I'm going to take a shot at it.

[SumZero]

[ QUOTE ]
I did some searching and found a few things on chess...

-Chess is infinite: There are 400 different positions after each player makes one move apiece. There are 72,084 positions after two moves apiece. There are 9+ million positions after three moves apiece. There are 288+ billion different possible positions after four moves apiece. There are more 40-move games on Level-1 than the number of electrons in our universe. There are more game-trees of Chess than the number of galaxies (100+ billion), and more openings, defences, gambits, etc. than the number of quarks in our universe! --Chesmayne

-The longest Chess game theoretically possible is 5,949 moves.


[/ QUOTE ]

I do not think it means what you think it means.

Each move has at most 7*64*64*4 choices (7 types of pieces, 64 starting squares, 64 ending squares, and at most 4 choices of which piece to become [for a pawn on the end rank]. Obviously this is an outside bound as many combinations in here are invalid. Call 7*64*64*4 = M.

Therefore if the longest Chess game is 5,959 moves than I claim there are less than M**5959. That number is very large but not infinite.

[UATrewqaz]

Poker 52 cards, 10 players, 4 rounds of betting, each round each player has at most 3 options

Chess has 32 pieces, 64 squares on the board, 2 players, an infinite number of rounds (most pro games last around 60 moves), and each player had at most 100+ moves

Chess and it's not close.

[Shroomy]

[ QUOTE ]
I do not think it means what you think it means.

Each move has at most 7*64*64*4 choices (7 types of pieces, 64 starting squares, 64 ending squares, and at most 4 choices of which piece to become [for a pawn on the end rank]. Obviously this is an outside bound as many combinations in here are invalid. Call 7*64*64*4 = M.

Therefore if the longest Chess game is 5,959 moves than I claim there are less than M**5959. That number is very large but not infinite.

[/ QUOTE ]

I don't understand how it could not be infinite. Take the simple example of both players moving their queen around in circles (a triangle or square literally). Since that is a posibility why could they not do it forever.

[drbst]

After a position occurs three times with the same player to move the game is declared a draw.

[frontal]

In chess, a draw is declared if each player makes 50 consecutive moves without slaying a piece or moving a pawn. If the same position arises three times, any player has the right to declare a draw.

[rufus]

I think chess is estimated to be on the order of 10^40, and heads-up limit hold-em is on the order of 10^15 or so. Chess is much bigger.