Check-Raising in First Position
With very strong hands your options are to try a check-raise or to come out betting. The key factors in deciding whether to check-raise are:

1. The chances your opponent will bet if you check.
2. The chances your opponent will call your raise.

The second factor is just as important as the first, because if there were no chance your opponent would call your raise, it would usually be wrong to check since you'd risk not winning even a single bet when your opponent checks behind you. However, all but very tough players will generally call your raise after you have checked and they have put in an initial bet. They might grumble as they do it, but they'll do it.

In limit games the decision to check-raise or come out betting can be determined by a precise formula. To simplify, we'll assume you know for sure you have the best hand. First, determine what percentage of times your opponent will call if you bet. That's one side of the equation. Next determine what percentage of times your opponent will bet if you check but then fold when you raise. Finally, determine what percentage of times your opponent will bet if you check and then call your raise. Now double this last percentage. If the sum of the last two percentages is greater than the first, it is correct to try a check-raise.

This formula may sound overly complicated, but it really is not. Let's say you think there is a 70 percent chance your opponent will call if you bet. But you also think there is a 40 percent chance he will bet if you check and call your raise, thus rewarding you with a double bet; and perhaps there's another 10 percent chance he'll bet if you check but fold when you raise. Because you'll win two bets 40 percent of the times that you check, you double that figure to 80 and add the remaining 10 percent chance your opponent will bet and fold when you raise. That adds up to 90, and since 90 is greater than the 70 percent chance that your opponent will call your bet, it is right to check raise.

Another way of looking at the problem is in terms of expectation. Let's say you bet 100 times, and you check with the intention of raising 100 times. In the former case, you'll win 70 bets; in the latter you'll win 80 bets when your opponent bets and calls your raise and 10 more when he bets and folds, for a total of 90 bets. You win 20 bets more by check-raising, and so check raising has greater expectation than betting out.

Most players do not check-raise enough on the end. They'd rather go for the single bet in the hopes of getting called. However, it is worth taking a little chance of losing one bet if there is a good chance of gaining two bets. Since most players will automatically call a raise when you check-raise, you can simplify the above formula. In general, you should check with the intention of raising if you believe the chances of your opponent's betting when you check are at least half as good as the chances of his calling when you bet. Nor should you get discouraged if you occasionally check and your opponent checks behind you. Check raising is a long-run gamble like everything else in poker. If you know you should win two bets in a particular situation more than half as often as you would win one bet, then you made the right play by checking even if it didn't happen to work. Sometimes you also gain an added benefit when a check-raise doesn't work. Since your opponents noticed you checked a good hand once, they may become a little timid about betting behind you on future hands, thus saving you some bets on second-best hands with which you were planning to call if they bet.

Check-raising on the end works best against average-to-good players. You should try it less often against weak players and tough players. Weak players tend to call so much on the end when you bet that you have to be pretty certain they will bet for a check-raise to be profitable. If, for example, you are sure your opponent will call if you come out betting, you have to be over 50 percent sure he will bet if you check before you consider check raising. Even 50 percent isn't good enough unless you are also sure your opponent will call when you raise (which, of course, a weak player will most likely do).

Against tough players you would check-raise less often because tough players tend not to bet as many hands on the end as they call you with, and they frequently throw away their hands when you raise. Thus, the chances of winning a double bet with a check-raise decrease.

There is one major time to deviate from the general check-raise formula, and that is when you think you can win three bets by betting, getting raised, and then reraising. A classic example of such a situation against an average player in seven-card stud occurs when you look like a straight on board but have a hidden full house, and your opponent may have a flush. You bet your apparent straight, your opponent raises with his flush, and you lift him out of his seat by reraising.

Small Pairs
The Jack was raising while looking at three overcards to his Jack. There was a real good chance he had me beat. Making trip 8s was unlikely with the 8 gone. And even if I made Queens up, it was likely that I would be beat by either Kings up or Aces up. There was just too much competition and I had too little of a chance, even though I was getting good money odds on a call.

But in a different situation a small pair can be a strong hand. Another recent hand involved me starting with a pair of 7s. This one I played, even though some of the characteristics of the hand weren't as strong. The hand itself wasn't as strong, but the situation was more advantageous, making the relative strength better.

I was dealt (7? 3?) 7?. Note that not only is a pair of 7s smaller than a pair of 8s, this time I had a split pair, a very small kicker, and no two-card flush draw. This wasn't really very strong.

But the upcards I was looking at were three 2s, a 4, an 8, and two Aces. My cards were completely live, and most of the other players' cards weren't. Only one player had a higher live upcard than me. Looking at two opponents with an Ace up is a much better situation than looking at only one opponent with an Ace. When that 8 folded to the bring-in, I had an easy raise. Even if all I won was the $1 bring-in, a raise in this situation didn't carry much risk with it. It was unlikely anyone had a better hand, and if they did, it was okay because my cards were live.
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