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April 20th, 2021 at 2:08:27 AM
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Hi! Could anybody calculate this odds in three card poker?

1- odds of be dealt Q64 or better?

2-odds of be dealt Q64 or better, and be beaten by the dealer?

I cant find the correct way to calculate these odds.

Thanks a lot in advance!👏👏

1- odds of be dealt Q64 or better?

2-odds of be dealt Q64 or better, and be beaten by the dealer?

I cant find the correct way to calculate these odds.

Thanks a lot in advance!👏👏

April 20th, 2021 at 8:42:24 AM
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I don't think there's an "easy" way to do it; you may have to just count all of the hands (there are 22,100 of them, and for each one, there are 18,424 possible dealer hands).

Somebody check my numbers, but I get this:

The 22,100 possible deals of your cards includes:

48 straight flushes

52 threes of a kind

1,096 flushes

720 straights

3,744 pairs

4,096 Ace high

3,456 King high

2,784 Queen high (Q64 or better)

This is a total of 14,900 hands of Q64 or better (67.4%).

Of these hands, the results are:

85,493,652 dealer folds (31.14%)

97,327,228 wins (35.45%)

91,374,160 losses (33.29%)

322,560 pushes (0.12%)

Somebody check my numbers, but I get this:

The 22,100 possible deals of your cards includes:

48 straight flushes

52 threes of a kind

1,096 flushes

720 straights

3,744 pairs

4,096 Ace high

3,456 King high

2,784 Queen high (Q64 or better)

This is a total of 14,900 hands of Q64 or better (67.4%).

Of these hands, the results are:

85,493,652 dealer folds (31.14%)

97,327,228 wins (35.45%)

91,374,160 losses (33.29%)

322,560 pushes (0.12%)

Last edited by: ThatDonGuy on Apr 20, 2021

April 20th, 2021 at 3:44:03 PM
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Oh, thanks a lot!👏👏

April 21st, 2021 at 2:06:04 PM
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Yes you work out all the player hands, sometimes it's quicker to work out all the types of hands and multiply up (e.g. AAA has four ways, AKQ straight has 4*4*4-4(sf) ways). Then the easiest way is to work out what cards are left in the deck and cycle through them all tallying the result. In this case you don't need to do this for Q63 or less, but it's easier coding to do it and work out the EV is less than -1, so you fold.