When Good Gambles Are Really Bad Gambles

Are there ever situations where a good bet should not be made? First we’ll define a good bet: any wager with positive expected value (EV). Expected value is the average return on a bet. Let’s take a bet on the flip of a coin as an example. You and I bet $1, I call heads and you call tails. My expected value is calculated by taking my probability of winning and multiplying that by the amount I win when I win – then subtracting from that my probability of losing multiplied by the amount I lose. The equation looks like this:

EV = (probability of winning) X (amount won) – (probability of losing) X (amount lost).

For our example, EV = 0.5 X $1 – 0.5 X $1 = 0.

If EV = 0, it’s a neutral bet. But what if our opponent offered to pay us $2 when we win, but we only have to pay $1 when we lose?

EV = 0.5 X $2 – 0.5 X $1 = $0.5

In other words, every time we make the bet, we can expect to win 50 cents. A good bet is any one with positive EV. But should every good bet be made?

In short, the answer is ‘No.’ There are positive EV bets that should not be made. This article is applicable to any form of gambling, from sports betting to poker, but the only examples we’ll use from now on are poker ones. You should try extending the concept to other ‘bets’; you might come up with some interesting applications. In poker, the most important examples have to do with tournaments.

Here’s a hypothetical situation: it’s the first hand of a tournament and your opponent goes all-in and shows you his hand. You know that your hand will win against his 51% of the time, so should you call? There are two reasons that you shouldn’t. The first reason is only valid if you’re an above average player. If you decide to call there’s a 49% chance you will be eliminated from the tournament; if you are, it doesn’t matter any more that you’re an above average player. And because you are above average, if you choose to fold to this bet, it is very likely that you will find yourself in much more profitable situations, ones where you have a greater than 1 or 2% advantage. Think about it like this: The small edge you gain by calling is less than your edge in the game overall, thus you should sacrifice small positive EV now in order to increase your chance for positive EV situations later. The second reason that you should fold is that one chip won is worth less than one chip lost. I have written an article about this concept, which I call the law of diminishing returns.

This concept of a bad “good bet” has applications outside of tournaments as well. Many players believe in “taking shots,” playing in a game which is bigger than the size of your bankroll would dictate. Let’s say you have a $1000 bankroll and see a really good $500 buy-in No Limit game with three big fish at the table. You know that you have positive EV in the game, but you also have a good chance of losing half or more of your bankroll. If you do lose a big chunk, you’ll have to play significantly smaller stakes than you currently play, which means less profit long-term. The high likelihood of losing long-term profit outweighs the positive EV of playing in the game. Playing in the big game would limit your overall EV as a poker player because of the high risk to your bankroll (assuming you can’t just replenish it).