A hypothetical, 2 cards vs. 3

This discussion came up at the poker table last night. I thought it was interesting enough to get others thoughts on.


What if you played hold'em 2 cards vs. 3. You get AA every time for your 2 cards. The other guy can use all three of his cards if he wants, not just 2 like pineapple. Both hands are face up and go all the way to the river.


First question, if you can pick any 3 cards for your opponent, what do you pick and who has the advantage? I decided I'd give the other guy an ace along with a pocket pair between 66 and 99 so he can't make a straight with the ace. The suits of the pair would be the same as my AA. I think my AA would be a big winner in the long run. Can anyone figure out how big a winner? Can you pick a hand for your opponent that gives you an even bigger advantage?


Now, assume your opponent holds 3 random cards. Does AA still have the edge? How much?

> First question, if you can pick any 3 cards for your opponent, what do you pick and who has the advantage?


I'd pick AsAc for me and Ad6s2c for him, making me a 11:2 favorite w/ 84.83% equity. It is better to give him 2 cards to a str8 (note that the 6 is utterly redundant in this respect), than 2 single-card outs to beat you (Ad6s6c would give me only 76.69% equity).


> Now, assume your opponent holds 3 random cards. Does AA still have the edge? How much?


AA would still be a 11:5 favorite (68.8% equity).


These asymmetric holdem games would make for a nice quiz ...


cu


Ignatius

I'm a little surprised that AA is still such a big favorite over 3 random cards.


How many random cards do you have to have to be a favorite over AA? I'm guessing 4 cards makes a big jump. Is it enough to be a favorite?

How many random cards do you have to have to be a favorite over AA? I'm guessing 4 cards makes a big jump. Is it enough to be a favorite?


I want to take a guess at answering this. I've got a freeware hold 'em simulator. I loaded AcAs into one hand and then played it against an increasing number of opponents playing random hands. When the number of opponents was 5, the AA's win rate approached %50. With a three-card hand, you have the equivelent of three 2-card hands, and with a four-card hand you have the equivilent of six 2-card hands. So I'd suppose that a four-card hand might be a favorite.


I see a couple of problems with my reasoning, how ever. One is that the six 2-card hands derived from the one four-card hand are not discrete. I'm not sure if this weakens it (as a player of pineapple and the old game of three-card hold 'em, I feel it might). Another factor is that the four-card hand also contains three 3-card hands and, of course, one four-card hand which increase its value since, unlike in omaha, any number can be played.