Don’t Bet the River in Limit Hold’em Just Because You Have a Good Hand
By Tony Guerrera
Every decision in hold’em requires careful thought. If you have the stone-cold nuts, you need to figure out how to play the hand such that you make the most money possible. If you have a marginal holding, you need to figure out how to get to showdown while preserving your stack. Today, we’ll be examining playing in position on the river in hold’em.
Many players, when they have what appears to be a good hand, bet as a reflex. In a game in which careful thought is the key to success, reflex actions usually can’t be a good thing, and guess what? Betting as a reflex on the river when you have a decent hand in position is not a good thing. To put it another way, you shouldn’t bet in position on the river in hold’em just because you think you have the best hand.
Let’s first consider limit hold’em. Suppose the board is A
T
9
6
2. On the flop and the turn, your opponent checks to you, you bet, and he calls. On the river, your opponent checks. You have AK, and you think that your opponent is on a distribution looking like the following: [AK,A2]||[KT,QT]. Against this hand distribution, the probability that you have the best hand is 
, the probability that you are tied is 
, and the probability that you lose is 
. Does this mean that your EV for a bet on the river is:
The answer, which is surprising to some is “no.” The reason why this isn’t your EV for a bet on the river is because your opponent isn’t going to call you with every hand in his distribution. He’s going to fold some hands that you have beaten, but he’s definitely going to call (or raise) with hands that have you beaten.
With that in mind, let’s reevaluate the EV of a bet on the river. Suppose that your opponent will call you on the river with the following distribution: [AK,A9]||[A6]||[A2]. When you are called or raised, the probability that you win is 
, the probability that you tie is 
, and the probability that you lose is 
. Assuming that you fold when your opponent raises, the following expression gives your EV for a bet on the river:
Therefore, it’s not enough to simply know that you are ahead of an opponent’s distribution when you bet in position on the river. Instead, for a bet in position on the river to be proper when you have a hand that has a good chance of holding up in a showdown, you need to make sure that your hand is ahead of an opponent’s calling distribution. You can beat 99% of your opponent’s hands, but if your opponent is only going to call you with the one hand that has you beaten, then it’s improper to bet on the river.
With television’s hype of no-limit hold’em, some players these days barely regard limit poker as real poker. The real fact of the matter is that limit poker takes a lot of skill to play really well, and one of the most important skills needed in limit poker is knowing when to value bet on the last round of betting versus checking on the last round of betting (notice that I’ve moved away from the specific world of limit hold’em now, and that I’m talking about the more generalized world of limit poker). You and your opponents have no flexibility in the amounts you can bet, so at times, reading your opponents and putting them on hands can actually be more difficult. In no-limit hold’em, you can make lots of small mistakes, but you can make up for them by making correct decisions in one or two huge pots. In limit hold’em, you don’t have that luxury. Every small mistake you make hurts a lot, so it’s really important to be on top of things. And while every betting round of every hand is important, one of the most important parts of a hand in limit poker is the last betting round because the betting limits are higher in later betting rounds than they are in earlier betting rounds. So with that in mind, think very carefully about every value bet you make in limit poker, and may all your moves be +EV!
Tony Guerrera is the author of Killer Poker by the Numbers.
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