6-23-05A lot of people know things now like "K7 is favored against random hands". The problem is that a little knowledge is a dangerous thing; (I've made this mistake in the past myself). The situation where this usually comes up goes like this - you're on the button, no one has come in the pot, and the big blind is on a pretty short stack. Now, you want to put him all-in here with quite a lot of hands; the question is what hands exactly? A similar question arises when you are the guy in the big blind and the button has just put you all-in. What hands exactly do you call with? Now, the details depend exactly on your opponents are playing, but let's talk in general. First of all, let's toss out this idea of "random hands". The only time these random-hand statistics actually come in is if the big blind guy is forced to be all-in with any two cards, eg. if his stack is less than or only slightly more (eg. <= double the big blind). If his stack is more reasonble where he could fold, (eg. >= triple the big blind), then he's not playing random cards. He'll fold his very weakest hands, and call with better hands. So, now your EV is not based on how your cards do against random hands, rather if he folds some fraction F, your EV is F* his big blind , plus (1-F) * his chip if he calls * P , where P is your chance of winning against hands with which he calls. Note that F and P are linked, if he folds all but very good hands, P will be very low, but F will be very high, so your EV is good. He can compute his optimal F to fold, but we don't really need to get into that. Basically we know he's going to keep high cards and fold low cards. What does that mean? Well, for one thing, hands like K2 don't look so good any more. K2 is a 50/50 hand against random cards, but against someone who will fold some hands, that greatly increases your chance of being dominated by Kx. Basically in all-in scenarios, all you care about is domination. If you go in with AK and he has 56, you're only a 60/40 favorite - not a very good overlay at all. If you go in with K2 and he calls with 56, you're only a 55/45 favorite!! On the other hand, if you go in with K2 and he calls with K7, you're a 35/65 dog. So, roughly, you want hands that dominate, not hands that are dominated. In fact, it's better to have hands like 56s where both cards are likely live.
Let's consider one other case - say you're in the big blind, very nearly all in (perhaps you have two big blinds left to call with; if you only had 1 big blind left, you have to call with any two cards), at a full table. Someone in early position makes a solid raise, and all else fold. It was a full table, so he probably has a pretty good hand, even though you are nearly all-in. What should you call with? Well, we see the answer above. Hands like K2 are bad calls, because it's likely you're dominated. Obviously you can call with any pair or very high cards; depending on his exact tightness, very high cards might by A9,KT,QJ or better - eg. hands that have a good chance of dominating, not too much fear of domination. The other hands you can call with are hands that are likely to have two live cards - especially low suited connectors, like 56s,67s,etc. (though suited is not a big factor, it's just a nice little bonus). Oddly this is a situation where you might lay down K9, but call with 89 or 79.
One more case - let's say you're playing No Limit against someone who's just way too tight preflop. If they come into a hand, you fold, because they're only playing super-premium hands. Now, they're making a mistake, so you can make money on that; their mistake is they fold their blind too often, so you need to be stealing it. So, in any good steal position, you want to bet at them. They will only call with very premium hands (pairs, A9 or better, etc), and raise with super-premium hands (JJ or AK or better). So, what hands should you raise with? Well, you can almost raise with any two cards, they're just folding way too much. You should fold some hands, and this is a very extreme case where *if they call* they're likely to have dominating hands, so you should fold hands like A2, K2. Hands like 56s are better. If they raise, you throw almost any hand away, so the only question is what do you want to have on the flop if they call. With weak high card hands you're too likely to be dominated, your best cards to steal with are low suited connectors. Note that this is a bit different because we're not talking about all-ins, but actually seeing the flop with chips to spare.