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#1
08-08-2005, 05:11 AM
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No two poker games the same have ever been played?
Lets assume a full table, 9 seater game of hold em. The cards are shuffled, and only the top (lets ignore burn cards, etc) 23 cards are significant (9x2 holecards, and 5 flop cards).
Since there are 23! ways to arrange these cards, we could say that there are 23! unique games - is that correct? If so, that's a huge number, probably around the age of the universe in seconds. So, even with the hundreds of online tables rattling out hands 24/7 at an incredible speed, would I be correct in saying that for all intents and purposes, there's probably never been 2 poker games the same? (And by "the same", I mean the same holecards and flop - ignore the way the betting and folding goes, etc). Am I thinking in the right ballpark at least for this type of thought? Ringo 
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#2
08-08-2005, 05:21 AM
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Re: No two poker games the same have ever been played?
What about the fact that a hand can be played out in many different ways?
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#3
08-08-2005, 05:24 AM
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Re: No two poker games the same have ever been played?
[ QUOTE ]
What about the fact that a hand can be played out in many different ways? [/ QUOTE ] I realise thats possible, yea.. what I was meaning were the initial conditions - ie, only hole cards and the board. Betting, etc, doesn't count [img]/images/graemlins/tongue.gif[/img] Ringo
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#4
08-08-2005, 05:52 AM
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Re: No two poker games the same have ever been played?
[ QUOTE ]
If so, that's a huge number, probably around the age of the universe in seconds. So, even with the hundreds of online tables rattling out hands 24/7 at an incredible speed, would I be correct in saying that for all intents and purposes, there's probably never been 2 poker games the same? (And by "the same", I mean the same holecards and flop - ignore the way the betting and folding goes, etc). [/ QUOTE ] Seems so - but it shouldn't be too surprising; it's just another "combinatorial explosion", like the oft-quoted statistic about how the number of possible permutations of brain-states (i.e. configurations of neurons) is greater than the number of atoms in the entire universe. It sounds amazing and a bit paradoxical at first, but if you think about it it's only amazing because we're comparing apples and oranges. We're taking the number of possible states of some combinatorial scenario (states of the brain, states of nine-handed holdem, etc) and comparing that with only one of the possible states of the universe. In other words, it's like saying "there are more ways you can deal out two hole cards in holdem than there are cards in a standard deck!" It would be very different (and a true paradox, provided it weren't false) to say that the number of connections in Person X's brain were greater than the number of atoms in the universe, since X's neural connections are made up of the very atoms they supposedly outnumber. Do you see what I mean?
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#5
08-08-2005, 05:54 AM
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Re: No two poker games the same have ever been played?
[ QUOTE ]
Lets assume a full table, 9 seater game of hold em. The cards are shuffled, and only the top (lets ignore burn cards, etc) 23 cards are significant (9x2 holecards, and 5 flop cards). Since there are 23! ways to arrange these cards, we could say that there are 23! unique games - is that correct? [/ QUOTE ] No, you want to ignore the order of the 2 cards for each player, and the order of the 3 flop cards. You also want to consider all 52 cards since any of these can contribute to the top 23. I assume by "flop" you mean all 5 board cards, since you said 23. P(52,18)/2^9 * C(34,3)*31*30 =~ 3.0 x 10^33. Where P(52,18) = 52*51*50*49*...*35 = 52!/(52-18)! This is the number of permutations of the 18 player cards. Then we divide by 2 for each player to ignore the order of each pair of hole cards. This gives us the number of ways the players can hold 9 hands. C(34,3) = 34*33*32/3! is the number of flops that can be made out of the remaining 34 cards. Then there are 31 ways to choose the turn card, and 30 ways to choose the river. I just computed something similar here. [ QUOTE ] If so, that's a huge number, probably around the age of the universe in seconds. So, even with the hundreds of online tables rattling out hands 24/7 at an incredible speed, would I be correct in saying that for all intents and purposes, there's probably never been 2 poker games the same? (And by "the same", I mean the same holecards and flop - ignore the way the betting and folding goes, etc). Am I thinking in the right ballpark at least for this type of thought? [/ QUOTE ] That's certainly true if all P(52,23) permutations of the first 23 cards can be generated. Some random number generators may only generate a subset of these, but the same conclusion should still hold.
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#6
08-08-2005, 11:14 AM
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Re: No two poker games the same have ever been played?
[ QUOTE ]
Lets assume a full table, 9 seater game of hold em. The cards are shuffled, and only the top (lets ignore burn cards, etc) 23 cards are significant (9x2 holecards, and 5 flop cards). Since there are 23! ways to arrange these cards, we could say that there are 23! unique games - is that correct? If so, that's a huge number, probably around the age of the universe in seconds. So, even with the hundreds of online tables rattling out hands 24/7 at an incredible speed, would I be correct in saying that for all intents and purposes, there's probably never been 2 poker games the same? (And by "the same", I mean the same holecards and flop - ignore the way the betting and folding goes, etc). Am I thinking in the right ballpark at least for this type of thought? Ringo [/ QUOTE ] It seems to me that you are significantly UNDERestimating the number of unique hands by using 23!. After all, 23! equals only 1*2*3...22*23, however I believe the correct formula should be 52*51*50...31*30. This gives a bit over 9.12*10^36th power. This does count variations in order as different hands though. (For example, A [img]/images/graemlins/diamond.gif[/img] A [img]/images/graemlins/spade.gif[/img] would be considered a different hand than A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/diamond.gif[/img])
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#7
08-08-2005, 12:15 PM
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Re: No two poker games the same have ever been played?
I also remember reading somewhere that two completely randomized decks of cards have almost certainly never been in the same order. 52! is like, a really big number, man.
Pretty crazy stuff.
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#8
08-08-2005, 01:40 PM
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Re: No two poker games the same have ever been played?
I have heard that once the RNG of an online room messed up, and dealt the same hand twice two a table.
Can anyone confirm this?
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#9
08-08-2005, 04:51 PM
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Re: No two poker games the same have ever been played?
[ QUOTE ]
I have heard that once the RNG of an online room messed up, and dealt the same hand twice two a table. Can anyone confirm this? [/ QUOTE ] once i saw it goto showdown when only the turn had been delt. I still have no idea what happend.
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