What is "justifying your opponents’ optimistic calls in Texas Holdem?" Well, say you bet one-fifteenth of your stack with a good poker hand. Your opponent calls with a gutshot, because she figures that she’ll hit it one-eleventh of the time, and that she’ll stack you if she does and make fourteen times her investment.

If she’s right, and she does stack you when she hits her straight, then, in addition to offering her high implied odds, you have made the error of "justifying her optimistic call." If, on the other poker hand, you thwart her by folding before she gets your whole stack in, then you have done well.

Many no limit Texas Holdem players’ eyes are bigger than their heads. They often call decently-sized flop bets with longshot draws because they assume that if they get there, they’ll stack you a large percentage of the time. If they are wrong, though, and they get your stack only a small percentage of the time, then they will lose money in the long run on these calls.

You can use this loose-calling tendency against your opponents if you refuse either to offer too high implied odds or to justify optimistic calls. That is, before you bet with good poker hands, you should mentally decide whether you are willing to pay off a big bet with the poker hand or not. (Obviously in Texas Holdem, sometimes you will decide one way, but change your mind later in the hand. Nevertheless, you should always be asking yourself, "Am I willing to lose a lot?")

Whenever you bet or raise in Holdem, always have an answer in your head to the question: "Am I planning to pay off a big bet on this poker hand, or will I fold if it comes to that?"

If you are willing to risk losing a lot, then you should usually avoid offering too high implied odds to players with the most likely draws. Bet enough so that if they call, they will lose money over the long term even if they do get you to pay off a big bet when they get there.

If you aren’t planning to pay off a big bet (because you don’t think this player will often bluff), though, then consider whether your opponent will call too often with weak draws, hoping to bust you. If she will, then use the fact that you aren’t justifying her optimistic call to your advantage. Bet an amount that will look small enough to her, but that you know actually is too much for her to call because you know that you won’t go broke.

For instance, say you have

on the button with a single opponent and a flop of

There is $100 in the pot, and you have only $800 left in your stack. With such a strong poker hand and so little left to bet, you likely will be betting your entire stack before the end of the hand. So if your Texas Holdem opponent assumes he can call a flop bet, hoping to bust you on a happy turn card, he’s right. He can bust you that way.

In that case, you should bet enough on the flop to avoid offering your opponent too high implied odds for the likely draws. In this case, the strongest likely draw is middle or bottom pair, a hand like 9♠ 8♠. With five outs (ignoring the backdoor draws for simplicity), he will get there about 5/45 times, or he’s 8-to-l against. With $100 in the pot and $800 left in your stack, he’s got $900 total he can win.

If he gets there with a nine, which will happen 3/5 of the time he improves, you have eight outs (three aces, two queens, and three treys). If he gets there with an eight, then you have only the two queens. So even if he gets there on the turn, you’ll draw out on the river 12.7 percent of the time.

0,127 = (3/5)(8/44) + (2/5)(2/44)

So, on average, when he gets there on the turn and all the money goes in, he’ll win $900 87.3 percent of the time, and he’ll lose $800 12.7 percent. His expected win in that circumstance is $684.10.

$684.10 = (0.873)($900) – (0.127)($800)

He’s 8-to-l to make his poker hand, and he stands to win $684.10 if he does. You should bet at least $684.10/8 = $85.51 to avoid offering too high implied odds. If you bet any more than $85.51, then you will profit from his call. A pot-sized $ 100 bet would be fine. Slightly more than the size of the pot, perhaps $120, would be even better if you think your opponent is likely to call such a bet with middle pair.

You don’t have to figure this precisely while you play Texas Holdem. Just realize that you should offer him less than about 10-to-1.

But what if you have $5,000 left rather than only $800? Now a willingness to go to the felt indiscriminately can be costly. To avoid offering too high implied odds to someone with middle pair or a gutshot, you’d have to bet many times the pot. And if you do that, you’re likely to get action mainly from flopped two pair and sets.

While A♥ Q♥ is likely to be tops on a Q♠ 8♦ 3♥ flop, it is no certainty. And when you commit to $5,000 in betting to protect the $100 in the pot, those rare times you are beaten will destroy you. Instead, you should estimate how much you’re likely to lose while finding out that your ace-queen is no good in Holdem. Let’s say for simplicity that you’ll lose an average of $684.10 (as you did in the previous example) figuring out your ace-queen has been outdrawn. (The better your opponent plays, the higher this number will be, almost by the definition of "good" versus "bad" player.)

In Texas Holdem practice, it’s very difficult to make such an estimate with any real precision. For the purpose of this text, we will often make "estimates" with the foresight of Nostradamus. We are primarily teaching the mathematical processes for coming to conclusions, not telling you whether to raise or fold in specific situations. Thus, the actual numbers we choose are largely irrelevant. It’s the process we use to come to a conclusion from those numbers that is important.

You should now bet an amount large enough to make sure your opponents won’t profit by trying to outdraw you, but small enough so that they might think that you have mistakenly offered them too high implied odds.

Since $85.51 was a large enough bet to avoid pricing your opponent in for an average loss of $684.10 before, it still is now. So you should bet more than that. But you shouldn’t bet so much that your opponent will never call. Once you have bet enough to offer too low implied odds, you want your opponent to call. So don’t blow them out of the water. Bet an amount that they might call.

Keep in mind that your better opponents will look at your remaining stack and try to estimate how much they can get out of you if they hit their draw. Then they will compare that amount to your bet and try to decide whether they can draw profitably or not. Ideally, you want to bet an amount that you know is too much for the likely draws to call, but that is small enough that it might tempt your opponents.

When betting good poker hands with deep stacks, bet enough to make your opponents’ draws unprofitable, but not so much that they won’t often call.

Good luck.

Also recommended:

1. When Your Opponent Could Have One of Several Draws
2. Expectation and Multiple Possible Hands
3. The Importance of Implied Odds in Texas Holdem
4. Imperfect Information and Implied Odds in Holdem
5. Implied and Effective Odds Explained