Saturday, August 19, 2006


Maths Can Only Take You So Far

I already mentioned that I'm not too keen on Harrington Vol. 3. Most of the book, as I said before, is talking about very high-level thinking and I found a lot of it quite frustrating, in that for example he'll say you should bet the river because "a good player [meaning your opponent] won't bluff", without explaining why he won't bluff.

Towards the tail end though, there are a few online Sit and Go examples which delve into the world of equity calculations. As some of you know, I wrote a program to make these calculations quite a while back, and I'm very familiar with how these work. While the idea is basically sound, like most poker calculations, the results are only as valid as your initial assumptions.

Take this example from HoH 3, problem 39. Standard 50/30/20 sit and go. 4-handed, blinds 100-200, Player A (5000 chips) moves in UTG. B (1500 chips) and C (5000 chips) pass. You're in the big blind with 2000 chips. What's your minimum calling hand ? The book assigns a hand range to A and calculates the equity of all possible outcomes, concluding that the minimum calling hand here is JJ/AKs. That is, you should pass TT or AK off.

The first (and lesser) problem is that this is a completely irrational move for Player A to make. How often do you see someone actually do that ? However, the calculation would be much the same if he had made it, say, 1600, so we'll let that one slide. The much bigger problem is that the standard equity calculation takes no account of how people actually play. It starts at the top assuming that each player's chance of winning is directly proportional to his stack, and works out 2nd and 3rd probabilities in the same way. No account is taken of the fact that, in practice, Players A and C are extremely unlikely to move all their chips in together. People will play cautiously, check down hands that they might have bet in a winner-take-all sat, and so on.

Let's look at another scenario. 3 players have 3000 chips each and you have 1000. By the standard calculation, your chance of making the money is 42%. My gut feel is that, in practice, it won't be as high as that. It might be significantly lower, depending on how well your opponents play. We all know by now that if two players clash, they lose some equity between them to the two players sitting the hand out. When considering one hand "in a vacuum", this implies that tight play is required. In practice though, if you're passing and passing and passing because you don't want to give up this equity to folders, I feel (notice I'm very carefully using the word feel rather than think) that this isn't the best way to play.

I could go on, but the bottom line is that a strict equity calculation does not take into account how play changes in a proportional pay-out sit and go. It doesn't take into account the big advantage you have when you have your opponents covered, particularly those opponents on your left. If the book mentioned this, that would make a big difference. But it doesn't. It presents these equity calculations as mathematical fact, and that's wrong in my book. For sure you have to play cautiously in many bubble situations but passing TT or AK in the scenario described is too much. I stress again that the results of any calculation are only as trustworthy as your initial assumptions (remember Paul Samuel ?), and I really think that the author(s) here haven't played a lot of sit and goes. If they had, their experience might lead them to question the maths here.

Thursday, August 10, 2006


A Moderately Amusing Razz Hand

I was playing a $100 HORSE single table on Full Tilt this morning when I observed the following razz hand. Hero, with (??)KQKK has called a bet on every street (god bless him). Villain with something like (??)2523 bets the river, and hero reluctantly gives it up. Villain promptly shows (23)2523(5), which I thought until about 5 seconds ago was a full house.

But it isn't, it's, erm, 2s and 3s with a 5. All the same, if the hero had two separate non-K-or-Q cards in the hole, he passed the best hand. I will draw the line at calling this amusing, and not heap too much scorn on the hero given how I misread it myself at the time !

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