guessing cards

[Mr. Ratface]

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

[Gullanian]

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.

[Lester B]

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.

[rufus]

[ 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.

[starchyy]

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.

[rufus]

[ 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.

[starchyy]

Where did he say he knew the cards were unpaired? It is possible that the card holder had a pair...

[elitegimp]

[ 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.

[geoncic]

the chance is 0.00364%

(4/52*4/51)^2

or if it's pocket pairs

(4/52*3/51)^2 = .002%

[rufus]

[ 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.