Analysis in Practice

You open for $5 in early position. Everyone folds except the player under the gun who originally checked to you and who now raises another $5. We'll assume you know this player will never make such a play without three-of-a-kind or better. We'll also assume that with the antes and your implied odds it would be incorrect to fold even if you knew your opponent had a pat hand. So the question is whether you should simply call the $5 raise or reraise another $5.

Your opponent's raise tells you he has either trips, which must necessarily be smaller than your three aces, or a pat hand. If he has trips, you have the best hand and are the favorite to win the pot; if he has a pat hand, you have the second-best hand and are an underdog to win the pot. According to draw poker distribution, your opponent will have three-of-a-kind about 65 percent of the time and a pat hand about 35 percent of the time. When he has a pat hand, you should obviously not reraise. However, it's nearly 2-to-1 he has trips. Should you therefore reraise ?

The answer is no because when you only call and your opponent draws cards, you can draw one card, as though you had two pair, and check-raise after the draw. Assuming he calls your raise, which he will almost always do, and neglecting the slight chance of your opponent improving to a full house when you don't, you win $30 (plus the antes) by playing this way - $10 before the draw and $20 afterward when you check, your opponent bets $10, and you raise to $20. In contrast, by reraising $5 before the draw and coming out betting $ 10 afterward, you win a total of $25 - $15 before the draw and $10 afterward. Thus, the 65 percent of the time your opponent has three-of-a-kind, you win $5 more by calling instead of reraising. At the same time, the 35 percent of the time he has a pat hand (and you don't improve to a full house), you lose only $10 instead of $15, a savings of $5. Therefore, in this situation a call is the correct play since it is right all the time whether your opponent has three-of-a-kind or a pat hand.

Your opponent, who is a good player, checked and called your bet on the flop. When the deuce falls, your opponent checks again. Should you check or bet your pair of kings?

In hold 'em, any time an opponent bets, calls, or raises, good players ask, "What could my opponent have done that with?" Then they think of the various hands the opponent might have to do what he did. So when your opponent called your bet on the flop and then checked on fourth street, you try to determine what hands he might have that prompted him to play the way he did.

Your opponent could be slow playing a better hand than yours - say, K,9 or 6;6. You estimate there's a 25 percent chance he has such a hand. He might have a fairly good hand such as K,J or K,10. You figure those hands at 25 percent, too. Your opponent might have a mediocre hand like K,4 or A,9 or 10,10. The chances of those hands you put at 35 percent. And you figure there's a 15 percent chance your opponent has 8,7 and is drawing to a straight.

You know that if you bet on fourth street after his check, your opponent will probably call with his fair hands, with a straight draw and at least call with his big hands. However this player will probably fold his mediocre hands because the pot is not big enough to justify calling with them. Therefore, after your opponent checks on fourth street, it turns out the correct play may be to check it right back." Your intentions are to bet on the end if your opponent checks and call if he bets.

The rationale for this play is that, like many players, this opponent will fold his mediocre hands if you bet on fourth street to avoid having to call twice to see what you have. Your checking on fourth street makes it easier for him to call on the end, not only because you have made it cheaper but also because you have shown weakness. Obviously checking is also the better play that 25 percent of the time you have the worse hand. Finally, checking on fourth street induces a bluff on the end.

The drawbacks to checking on fourth street are:

1.	It gives your opponent a free card to outdraw you.
2.	There's a 25 percent chance -your opponent has a hand like K,J or K,10, with Which he would probably call twice.

It is important that the pot be small - say, under $60 in a $10-$20 games - to make checking right because you gain only one bet by checking and betting on the end into your opponent's mediocre hands, but you lose the whole pot if the free card gives your opponent the best hand.

Notice that the percentages support checking as the correct play on fourth street.

Opponent's	Approximate	Best Play
Possible Hands	Chances
Better than Yours	25 percent	Check
Mediocre hand	35 percent	Check
Fair hand (K,J or K,10)	25 percent	Bet
Straight Draw	15 percent	Bet

Because you expect your opponent to fold his mediocre hands if you bet on fourth street, and you want to win at least one more bet from those hands, the correct play 60 percent of the time is to check. It is correct to bet only 40 percent of the time. You usually pick the play that is likely to be right most of the time: Therefore, you check.