Am I Making a Good Bet? Part Two

This is the essential question that a poker player or for that matter any gambler must continually keep asking. Every good bet has a positive expected value (also know as EV or expectation.) A positive EV means that a bet will be profitable, on average or in the long run. I devoted a lot of the first column in this series to determining what expected value signifies and how you can calculate it. Let’s look a practical case. You are in the cut-off (the last player to act before the button.) Everyone has folded up to you. Stack sizes range from 50 to 100 big blinds (BBs). You have J 7.

The table has been fairly tight. You feel that if you raise to 3.5 big blinds, you will win an uncontested pot about half the time. About 30 percent of the time someone will call, and you will be an underdog. However, you will have better position than either of the blinds. You may make the best hand or you may be able to steal later. Based on that you think you will break even on subsequent action when they call, but since you already have put 3.5 BBs in the pot as an underdog, you rate to lose an average of .5 BB when called. The other 20 percent of the time, someone will three-bet, and you will fold. I have given you a lot of information. Do you have enough to make a decision? If so, what is your decision? If not, what more do you need to know?

I hope you said you need more information. You need to know how much is in to pot. In a cash game, the pot will consist only of the blinds. For example, in a $5-$10 game there is $15 in the pot when it gets to you. In a tournament, there might also be antes. For example, you could be playing with 100-200 blinds and a 25 ante. In this case there is 525 in the pot when it gets to you. There are other factors that you might want to consider, but for now let’s try to analyze these two cases.

The cash game:

Frequency Result in $ EV in $
.5 or 50% +15 +7.50
.3 or 30% -5 -1.50
.2 or 20% -35 -7.0
TOTAL 1.0 or 100% -25 -1.00

We can tell we have considered all the cases since the frequencies add up to 100 percent. We took the result for each case and multiplied it times the frequency to find the expected value. Then we added up the expected value of all the cases, and found we would have a small loss (about one tenth of a big blind) on this play.

The tournament:

Frequency Result in $ EV in $
.5 or 50% +525 +263
.3 or 30% -100 - 30
.2 or 20% -700 -140
TOTAL 1.0 or 100% -275 +93

When we follow the same procedure for the tournament, we find we will show a slight profit, about the size of the small blind. I hope the degree of detail and the math haven’t scared you. This is the kind of situation that will frequently occur, and that can be analyzed away from the table. I provided very exact percentages for everything. In real life, nothing is ever that clear. Your opponents, your table image, distance to the bubble in a tournament, and many other factors go into estimating the percentages. Based just on the above analysis, we decided that raising to 3.5 BBs was a small winner in a tournament. You are making a good bet. You also have to ask, could I make a better bet?

The obvious question to examine is what would change if your raise was smaller. If you could achieve the same results by raising only 3 BBs, your results would be better. Many top tournament players make their raises even smaller. The min-raise to somewhere between 2 and 2.5 BBs has proved very effective in recent years. The smaller raise has a higher EV. It seems to produce almost as much return with a lot less risk, although that trend may be changing.

There is another important factor that comes into play, especially in cash games. You must consider the fact that you will be playing more than this one hand with the same opponents. If taking a little the worst of it on this hand, convinces them that you are raising with a wide variety of hands, then you will lose a little EV here, but gain a lot of EV when you really have a big hand. There is a lot more to discuss on the topic of EV and making good bets, and I will continue to do so in following columns. In the meantime, keep thinking about situations in terms of EV. Ask yourself if you are making a good bet. ♠

Steve ‘Zee’ Zolotow aka Zebra is a very successful gamesplayer. He has been a full-time gambler for over 40 years. With two WSOP bracelets, over 50 cashes, and a few million in tournament cashes, he is easing into retirement. He currently devotes most of his Vegas gaming time to poker, and can be found in cash games at Bellagio and at tournaments during the WSOP. When escaping from poker, he spends the spring and the fall in New York City where he hangs out at his bars: Doc Holliday’s, The Library and DBA.