Am I Making a Good Bet? Part 1

This is a question that arises over and over, not only just in poker, but also in every form of gambling. If the answer is yes, then there is also the related question of ‘Am I making the best bet?’ In fact, in a slightly different form, these questions arise in all games, even those without gambling. In games like chess, the questions become: ‘Am I making a good move?’ ‘Is there a better move?’

First things first, how do you know if you’re making a good bet? Let us begin with the idea of expected value (also known as EV or expectation.) EV is the average you will win or lose from taking a particular action. If you flip a coin for $100, on average you will break even. Your EV is zero. If you get 200 when you win, but only lose 100, the your EV is plus 50. The actual outcome can never be +50. It might be +200 or -100, but the average outcome is +50. If you are at all unclear or confused by what expected value is, you should drop everything else until you understand it. Here is a short quiz on expected value. There are some poker questions, and some questions that are about other areas.

1. There is 500 in the pot. Your opponent is all-in and has a big pair. You have a flush draw. (He has A A, you have A K board is Q 9 7 4) What is your EV?

2. You buy a computer for $1,000, and can also buy a three-year theft insurance for $100. There is a 2 percent chance your computer will be stolen in any year. What is the EV of the insurance?

3. You are head-up with 200 in the pot on the river. Your opponent checks, and you have the worst possible hand, but you think a 200 bluff will work 55 percent of the time. What is the expected value of the bluff?

4. You know nothing about football, but you always bet on teams with animal names (Bears, Lions, Broncos) when they play teams with human names (Patriots, Redskins, 49ers.) When you bet in the sports book, you lay 110 to 100 on each game (you win 100 or lose 110.) What is the expected value of betting five games?

5. You are head-up and have the nuts on the river. If you bet 150, your opponent will call one-third of the time. If you bet 90, he will call half the time. If you bet 40, he will always call. You want to make the bet with the highest expectation. How much should you bet?

Answers:

1. Your EV is a little more than 102. Your will make your flush with nine of the remaining 44 cards. So 9/44 of the time you will win 500, which equals 102.27. If you approximated the answer in your head, give yourself full credit for saying around 100.

2. The expectation for purchasing the insurance is -$40. 2 percent of 1,000 is $20 per year. For three years, this is $60, but you have to pay $100. On average you will lose $40 purchasing insurance.

3. The bluff gains you $20. You can figure this out two easy ways. First, you win .55 × 200 when our bluff works for +110, but you lose .45 × 200 for -90 when it doesn’t. Your net is +$20. The second method is a little easier, .55 wins minus .45 losses = .10. 10 percent (.10) of 200 is $20.

4. Your expectation is to lose $25. On average you lose $5 per game, and you are betting five games.

5. If you bet 150, and he calls one-third of the time, your average gain will be 50. If you bet 90, he will call half of the time, and your average gain will be 45. If you bet 40, he always calls and you win 40. Betting 150 has the highest expectation even though it is the bet that is called least. This is a case in which all three bets are good, but 150 is the best.

In the next few columns, I will look at a variety of situations in which you have to determine if you are making a good bet or which of several bets is the best bet. In the meantime, try and think about your decisions in terms of expected value, even decisions that have nothing to do with gambling or with money. Which route should I take to work? What restaurant should I eat at? Should I study poker or just go play? ♠

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.