Best Full House?

[Boris]

Interesting question I found on

Paul Kedroskey's Blog.

"You may assume you are playing straight five-card stud poker (everyone gets five cards, all closed, no exchange) with (say) five companions, using a single normal deck. As a result of God owing you a favor, you are entitled to a full house, and you get to choose the full house you will get. Which should you choose?"

According to the blog, this question is the subject of a paper published in the most recent edition of Chance.

I think we are to assume the game has a no limit betting structure.

[RustyBrooks]

Interesting. I'm guessing that the answer is not aces full, or even kings or queens full, because you'd like your opponents to pay you off with big two pairs and trips. Any full house will be good an overwhelming percentage of the time. You'd also want to avoid full houses that had Ts or 5s, because you'd cut down on the straights considerably. Maybe like 2s full of jacks or something.

[RustyBrooks]

I read the solution and I don't agree with it.
* Maximum blocking of straight flushes would be tens full of fives.
* you really need to be able to get paid off. You will be up against quads or a straight flush so infrequently that I don't think I'd even worry about it.
The solutions given make more sense if there is no betting.

Given that you will stack off every time someone has quads or a straight flush, how much on average do you need to make on hands where no one has a better hand, is the important question.

[Gonso]

The best full house IMO is the one you flop with holding pairs in the TT-77 range, when there is also an overpair on the board. For example, holding 99 on an AA9 board. It's so hard for a lot of people to fold an ace here, especially a good one. Better players might be able to escape with AJ, but not before losing at least a little money.

[RustyBrooks]

There's no flop, there's no pocket pairs, etc. Read the question. This is like 5 card draw, with no draw, that is, you are dealt 5 card and there is no further dealing or drawing.

[Gonso]

In that case I'd leave the best possible cards available to the other players to give them the best chance to make a hand.

Deuces full of treys would be my choice here, using all four suits.

Someone might point out that this increases their chances to make better hands than you, and I'd agree, but I think the difference is negligible.

[RustyBrooks]

Right. The answer in the article seems to be focused most on winning the most # of times, but it doesn't really matter if you win 9999/10000 or 9998/10000, as much as it does, how much do you win, when you win.

[sh58]

any full house w/o an A, K, Q, J, T or 5 is good so that you will get paid off the most. i'd go for 99922.

[Gonso]

[ QUOTE ]
any full house w/o an A, K, Q, J, T or 5 is good so that you will get paid off the most. i'd go for 99922.

[/ QUOTE ]

taking 3 nines out kills a tons of possible straights