## 30 April 2012

### This is NOT the best full house to have in poker

I was surprised, because it seems counterintuitive, but the math (below the link) is irrefutable.

Think about it first before peeking.  Why would aces over 8s be better to have than aces over kings?

Aces over kings would beat any other full house, but isn't the best for beating straight flushes. From the explanation at Futility Closet:
Specifically, each of the hands AAA99, AAA88, AAA77, and AAA66 will prevent 13 straight flushes — each ace prevents one, and each spot card prevents five.

These are thus the best to choose; of the 40 possible straight flushes, each leaves only 40 – 13 = 27 straight flushes that can beat us. By contrast, the impressive-looking AAAKK leaves 40 – 6 = 34, or even more if we haven’t covered all four suits.

1. but in trying to protect against some very rare hands, doesn't this make you vulnerable to other full houses?

1. The strength of a full house is dependent only on the rank of your high cards. Since the hand in question contains 3 aces, there's no way for anyone else to have a full house that would be stronger.

2. How about having AQ with AA778 on board, with your opponent having A8?

2. The article's theory only holds true if you are not playing a version of poker with community cards (e.g. Texas Hold'em). In such variants, there could be multiple AAA full houses to worry about.

However, in straight, draw or stud poker all of the cards in your hand belong solely to you, so there can never be more than one AAA full house in a round. Therefore you'd only have to watch out for 4s of a kind and straight flushes, so the theory would work.

3. Doesn't the full house hand prevent 16 (rather than 13) straight flushes?
Each midcard prevents five straight flushes, so the two of them prevent 10.
Each ace prevents two straight flushes (A-10; Ace-5), so the three of them prevent 6.

4. "By contrast, the impressive-looking AAAKK leaves 40 – 6 = 34, or even more if we haven’t covered all four suits."

Kind of like the picture that does not include a diamond?

5. Dateline: Deadwood, SD (August 2, 1876)
"You playing for a full house, Aces and Eights, Bill?"

6. Okay, I agree with what you have. But in terms of possible payoffs, I'd go with
KKKAA as the best possible full house (not worrying about the possibility of straight flushes.) Any other AAXXX would give the holder a false sense of security and having him/her betting the farm.

7. Having the handle Anonymous is either very common or Anonymous talks to themself. (Please excuse the use of the word 'themself', all the Anonymouses [Anonymice ?] or just Anonymous, may be of either gender, the moniker itself gives no indication).

1. Yeah. I keep telling people if they want to log in as an anonymous, that's fine, but just sign a name at the end. But they don't. Perhaps these anonymouses don't expect/want replies directed toward themselves - they just want to say something and go away.