#1
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guessing cards
Interesting little scenario happened to me today while playing heads up agaisnt my cousin today in holdem. Very first, I look at my cards, and before any action has taken place announce he has jack 4. At the end of the hand he flips over jack,4. Very next hand, I look at my cards and say he has King, 6 and he immediately turns over king six in disbelief that I guessed it right two in a row.
So basically what are the odds of someone guessions the other person's hand two times in a row. The suit is not considered and the only information is the two cards I hold in each of the two guesses. Thank you |
#2
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Re: guessing cards
If it's completely random its approximatly:
(1/13 * 1/13)^2 If you factor in the fact that him holding the same card as you is less likely its a little more complicated. |
#3
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Re: guessing cards
There are 169 two-card combinations ignoring suits. Lets also ignore the two cards you hold for simplicity's sake.
So the odds of correctly guessing a random hand two consecutive times would be 169 * 169, or 1 in 28561. |
#4
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Re: guessing cards
[ QUOTE ]
There are 169 two-card combinations ignoring suits. Lets also ignore the two cards you hold for simplicity's sake. So the odds of correctly guessing a random hand two consecutive times would be 169 * 169, or 1 in 28561. [/ QUOTE ] Actually, pairs are less likely, so two consecutive correct guesses are a bit more likely than that... Assuming that that you guess cards that are not in your holding and don't guess a pair the chance is 16 in 50 choose 2 guessing two back to back works out to 256 in 1500625, roughly 1 in 5882. |
#5
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Re: guessing cards
I understand that pairs are less likely but how would you know not to guess a pair? I don't think you can count them out here.
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#6
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Re: guessing cards
[ QUOTE ]
I understand that pairs are less likely but how would you know not to guess a pair? I don't think you can count them out here. [/ QUOTE ] You can't, but the OP is guessing non-pair hands, and if one were to guess for optimal likelihood one would guess cards that are not in the holding. |
#7
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Re: guessing cards
Where did he say he knew the cards were unpaired? It is possible that the card holder had a pair...
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#8
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Re: guessing cards
[ QUOTE ]
Where did he say he knew the cards were unpaired? It is possible that the card holder had a pair... [/ QUOTE ] Rufus is just saying that unpaired hands are more likely than paired hands, so if that is what you are guessing you are more likely to be correct. Example: I have a weighted coin so that the odds I flip heads is 3/5 and the odds I flip tails is 2/5. If you're trying to guess two consecutive flips, the optimal strategy would be to guess heads both times (you're right 36% of the time)... whereas if you treat the coin as fair it any two guesses would come up 25% of the time. So replace "heads" with "unpaired hand" and 3/5 with the proper odds... but the point is that you want to guess out of the more likely class. |
#9
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Re: guessing cards
the chance is 0.00364%
(4/52*4/51)^2 or if it's pocket pairs (4/52*3/51)^2 = .002% |
#10
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Re: guessing cards
[ QUOTE ]
the chance is 0.00364% (4/52*4/51)^2 or if it's pocket pairs (4/52*3/51)^2 = .002% [/ QUOTE ] The OP looked at his cards before guessing, so this is incorrect. |
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