sevenshooter
sevenshooter
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December 26th, 2009 at 7:42:46 PM permalink
Does the player have an advantage in the game of Four Card Poker when the dealer is inadvertently exposing his bottom card? Knowing two of the six dealer's cards (plus five of your own and the values of other players' cards around you), would this not result in gaining an advantage over the house?
sevenshooter
sevenshooter
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December 29th, 2009 at 1:39:49 PM permalink
Hello?

Can anyone reply to this question?

I believe it has merit.
DorothyGale
DorothyGale
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December 29th, 2009 at 2:22:13 PM permalink
Quote: sevenshooter

Hello?

Can anyone reply to this question?

I believe it has merit.


It's a big problem. A cycle is

C(52,5)*C(47,2)*C(45,4) = 418,597,840,861,200.

Unlike 3 card poker, in 4 card poker the extra flash card can be exploited only through an extremely complex optimal strategy. The strategy would have endless cases and rules about your hand taking the dealer's flush, straight and pair/trip outs, and the relative strength of your high cards to the dealer's known cards.

I have no idea if the optimal flash card strategy gives you an edge, but I imagine those who do know won't say very much about it in public. A suboptimal strategy might not be good enough.

OTOH, I think if you saw three dealer cards you could play almost any reasonable strategy and beat the game.

Good luck!

--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
Wizard
Administrator
Wizard
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December 29th, 2009 at 4:50:58 PM permalink
Sorry, I have never worked on this, nor know of anybody who has. As the above post mentioned, the number of combinations involved is prohibitive. Here is what I do know is available about hole carding by game:

Caribbean Stud Poker: Beyond Counting by James Grosjean.

Let it Ride: See Beyond Counting by James Grosjean or 'Master the Game of Let it Ride' by Stanley Ko.

Three Card Poker: See Beyond Counting by James Grosjean, 'Master the Game of Three Card Poker' by Stanley Ko, or 'Gambling 102' by yours truly.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
boymimbo
boymimbo
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December 29th, 2009 at 8:54:46 PM permalink
I agree with Dorothy.

The dealer is dealt six cards. Knowing the cards around you and seeing an extra dealer hand can definitely help you. For example, if you have a pair and you see the dealer pull a bigger pair based on two cards, you will want to fold.

If you see the dealer pull two of the same suit and you see the players around you lacking the cards and you hold less than a flush, you might want to fold if you have a low pair.

But certainly even with two known cards you can't really make any obvious strategy changes because four cards are unknown and those four cards can make a hand.

Really, you have four choices in the hand, fold, raise 1, 2 or 3 units. The basic strategy for the game says to raise 1 on 10s or less and 3 on jacks or better. Anything else you fold. Knowing two of the dealer's six cards wouldn't cause you not to fold. You would only go to a lesser strategy (fold if you see the dealer with a bigger pair, bet less if you see enough cards that make you believe the dealer has a larger plan).

But certainly I think the exceptions would be anecdotal (as above) at the best.
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