Best 3 hand hold em combo to win pots??

RiverTheNuts · #1 06-22-2005, 11:35 AM

I was thinking about this in the shower for no apparent reason... if you had 3 hands, not 6 cards, and were all in preflop, using one of the three to win with, what would be the best 3 hands?? How would this change from heads up to a table of 7 (cant do more than 7, youd run out of cards)

My first guess is something close to AdAc, 56s, JTh ... or something like that

LetYouDown · #2 06-22-2005, 12:08 PM

Well, there's all kinds of problems with putting this in practice. How can you guarantee that other people don't choose the cards that you want before you?

Based on the "nature" of the question, I'd intuitively say A-A, K-K and Q-Q...

RiverTheNuts · #3 06-22-2005, 12:38 PM

No choosing, we're talking which 3 have the most pot equity combined against any other random 3

LetYouDown · #4 06-22-2005, 01:09 PM

So everyone else is randomly dealt 3 hands? Then my confidence in A-A K-K Q-Q goes up.

RiverTheNuts · #5 06-22-2005, 01:38 PM

Correct... I dont think that AA/KK/QQ is the best combination... you will improve from AA/KK/QQ to a set about half the time, and to a full house about 25% of the time you hit a set, and if you hit a set with one, you dont need the other 2 pairs...

AA/KK/22 is about the same as AA/KK/QQ ... because you will only use the lower pairs if they hit a set, and if they hit a set then you are not only wasting your other 2 pairs, but also will not be up against a higher set almost any of the time.

Anyone else want to take some guesses at this?? I picked the hands I did because you have 2 strong and 2 weak chances for a flush, 2 strong chances for a straight, and 1 chance to improve to a set/FH, and if all of the above fail you still have AA, whereas the AA/KK/QQ you are looking for 6 outs to improve to a set, which still gets beat if one of the suited connectors hits and you dont make the boat

LetYouDown · #6 06-22-2005, 02:01 PM

If you have A-A and someone folds A-A (in theory, obviously) vs. J-10 suited, you're still a big favorite. The problem I have with connectors in this problem is that they need to catch at least two cards to win, and even then they're not guaranteed.

RiverTheNuts · #7 06-22-2005, 02:10 PM

Right, I see what you're saying, but what Im trying to get across is that if you have AA, you are safe as long as no one hits a set, and even if they do hit a set, the person with the connectors is almost the same odds to win with a straight/flush against an overpair as he is against a set. And if AA hits a set, then you are basically throwing away the other 2 pairs, and have very little room to improve from a set. If someone hits a straight or a flush when you are holding your AA/KK/QQ, you are just about dead in the water, whereas a 4th of one suit gives my aces the nut flush, and my 65s or JTs may hit 2 pair against overpairs, a straight or a flush.

I guess what Im trying to say is that there are different ways to draw at hands, and using 2 suited connectors and AA kind of covers your bases no matter what flops, whereas using 3 pocket pairs gives you no straight or flush possibilities, and if the board comes low or suited, you probably are losing to 2 pair, a straight, a flush, or a set.

Having KK and QQ in addition to AA means that you are drawing to 2 outs each to be able to use the KK/QQ as sets, whereas 65s and JTs are not only worth a little more than 2 outs to beat AA preflop, but also will beat the KK/QQ 2 outter if they hit with a straight or flush

LetYouDown · #8 06-22-2005, 02:16 PM

I certainly see the validity of your point. I just don't know that the numbers will agree. If I have time, I'll try to write something that can simulate this. I'd be willing to bet that the difference between HU and 7 handed is an immense one.

Siegmund · #9 06-22-2005, 03:14 PM

A quick pokerstove simulation, just to settle the two suggestions so far for the heads up game: AA/KK/QQ = 42.8+16.5+12.8%, leaving 27.9% for the 3 random hands. AA/JTs/65s = 41.9+18.3+15.9%, leaving only 23.9% for the 3 random hands.

A little bit of experimentation revealed that AA/JTs/76s was better (23.54% left over) but going up again to QJs or 87s was worse. Not saying that's the best, just that I can't think of an easy way to do better.

LetYouDown · #10 06-22-2005, 03:24 PM

The 7-6 suited being better makes sense. You're obviously not going to get that much higher than this. I would be curious what the exact answer is, however.