Joined: Jun 17, 2011
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August 21st, 2020 at 4:26:56 PM permalink
Just out of interest, as I've yet to go down to my local casino, I'm wondering how they'll deal games like 3-card Poker, where Players cannot touch the cards.

So I was wondering if they played it face up, how much of a problem it would be, if you knew all other people's cards (say 6 to a table, so you'd know 15 more cards than usual). How might this affect the House Edge. (btw I'm not intending to take advantage, it's just a mathematical challenge.)

Has anyone else tried to work this out without running billions of simulations and analysing every hand.

After a bit of playing around it seems you probably always call Kxx and better. If you had full knowledge of the other players' hands you should call most low hands about 19% of the time, presumably this is because you see enough high cards to make it more likely the dealer will not qualify. Occasionally you sometimes fold good Qxx hands.

In summary this means, rather than folding 32.6% (i.e. every hand Q63 or lower), you only fold 27.9% of the time; and the House Edge is reduced from 3.37% to 2.62% (EOR from 2.01% to 1.52%.)

If this was true, wouldn't it be easier to play the game face up and perhaps allow people to play two hands (although many are happy to play the second hand blind or just the sidebets on it.)

Many thanks

NB As I'm based in the UK I was assuming 1 4 5 bonus payments, but that doesn't affect which hands you call or fold, just the base House Edge.
Joined: Feb 18, 2015
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August 21st, 2020 at 8:48:11 PM permalink
Charlie, I have worked it out in my distant past. I listed all the possible hi-card hands that were K-Q-T or lower - that's all you need.

In fact, I have worked out strategies for what to do in normal 3CP as a function of the number of people who fold (because you know they do not have an Ace or King and probably not a queen), versus the number of people who bet.

You are correct that the most important strategy for a face up game would be to bet your low hands when you see a lot of A,K Q because the dealer is less likely to qualify. The 2 is a pathological card when you are trying to decide whether the dealer will qualify -it can only form one straight 4-3-2 (because the 3-2-A has an Ace and thus the dealer would have qualified with an Ace-high anyway) so the removal of a 2 from the deck increases the probability of a dealer straight as well as a dealer hand with Q or higher.

Of course there are also cases where you fold Q-7-X to Q-J-X but these are less important because they occur far less frequently than high-card hands that are 5-3-2 to Q-5-X.

The House Edge is too large to overcome. Especially with fewer players at the table due to covid restrictions!
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.

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