AKs vs. A2s

[Ginogino]

When you win with AKs, there are different ways you can win. Often you win without a showdown. When there is a showdown, you could win unimproved, or with a single pair, with two pairs, trips, a straight, a flush, or a monster (boat or better).

A2s makes an equal number of combinations, but loses out when the 2 is used as a kicker or as a part of multiple 2's when someone else has similar multiples of a different (higher) card. (It also loses out when there's a higher straight, but that is relatively infrequent, I should think).

My question is: in comparing AKs to A2s, how often (as a percentage) does the K make a difference? You will hold each an equal number of times (in theory, though you couldn't prove it by my hand history). This doesn't tell much in terms of the value of AKs, but it does speak to what you lose when playing AXs as "X" scales downward from K to 2. It might also be interesting to compare AKs to AKo, to see in practice the extra value added by suitedness. I know it's what HPFAP/21 (and other 2+2 titles) are about, but I'm curious whether it is possible whether approaching the same questions from another angle might offer further enlightenment. I also suspect that AKs has value (over A2s or AKo) in hands that don't go to showdown. For one thing, I bet AKs in situations where I would fold with A2s, which opens the door to different results, for better and worse.

[togilvie]

I have written a computer program that simulates holdem hands, using fairly realistic play, and allows for statistical tracking of the results. I've done some pre-flop analysis by simulating the play of thousands of hand with each possible set of downcards.

Value of suited cards: I compared the expected value of hands AXs vs AXo. On average, the EV difference between the two hands was approx 1/3 of a big bet.

Value of rank: I also looked at the value of rank by comparing AXs vs A(X-1)s (e.g. AKs vs AQs). On average, each step down in rank is worth approx 1/3 big bet.

These are not definitive answers, as it's difficult to tell how well my program simulates live play. But it should provide a reasonable proxy for it.

Comments are appreciated, if others are seeing similar/different results.

[Ginogino]

Thanks much for your reply! If I read your results correctly, what they are saying, in part, is that AXs is roughly equal in EV to A(X+1)o. And naturally I suspect that there is some fudge factor: in loose (lots of players, little raising) games AXs is worth a little more, while in tight games A(X+1)o does better. Generally my opening standards UTG are, in part, AQo or AJs, so I guess that's about right.

This reveals a lot about limping from EP with Ace and a small card suited, perhaps. UTG+1 with A7s -- would you limp with A8o?

I speculate that for suited connectors the correct adjustment is to elevate each card one step -- JT suited is roughly equal in EV to QJ unsuited. I'll have to think out my betting strategies again. Once more, thanks.