How to minimize mistakes and use expected value to your advantage
By Jim Feist
Mistakes happen. All the time. They happen in sporting events, at card tables, on our way out the door, when we lock our keys in the car, bump our heads, and on and on. Even oddsmakers make mistakes. Oddsmakers goofed on the Giants/Patriots Super Bowl, opening New England at minus -4. Most of the money for two weeks poured in on the Giants, closing at minus -2½.
Pats wide receiver Wes Welker made a critical drop late in the game. The Giants made three potentially huge mistakes (three fumbles) but were able to get all three back. And that’s one of the keys to winning in sports, poker and life: minimizing mistakes.
Successful gamblers understand that the only thing that matters is expected value. The expected value is the long-run average of the results of independent repetitions, such as rolling dice, kicking extra points in football, or going all-in when quality cards are in your favor. You will lose at times, but over the long haul the expected value will help you grind out an anticipated profit. It’s all math: Actuaries do this for insurance companies, and successful gamblers do it by weighing the odds and consistently putting the cards in their favor.
The opposite of this is luck. Sometimes you win with luck and sometimes you lose, but over the long haul luck will even out. And breaking even is no way to stay alive financially, be it cards, horses or sports. Expected value is mathematical probability that you can rely on.
If you watched the Super Bowl, think about the Giants’ winning touchdown. The Giants were in a position to wind the clock down and kick the field goal with no time left. Instead, the Patriots defense opened like the Red Sea and Moses—err, NY RB Ahmad Bradshaw—spun into the end zone, not sure whether he should score or not, in one of the strangest TDs in history.
Patriots Coach Bill Belichick took some heat for allowing the Giants to score that touchdown, but he explained afterwards that kicking a field goal from that distance gave the Giants a roughly 99% chance to win the game. Allowing that TD with a minute left, and giving his team a chance to drive down the field and score a TD, had a greater expected value for the Patriots to win the game than if they’d sat back and hoped New York missed the field goal.
At the poker tables, the only thing that matters in the long run is the expected value of any wager you make. So a small mistake is a decision with a small negative expected value and bigger mistakes mean larger negative returns, biting your bottom line. For instance, if you’re playing a $1 no-limit game and make a decision that has an expected value of five cents, a nickel is very little. If it was a bad decision, it would be a small mistake.
However, a big error is a decision with a large negative expected value, such as a mistake that costs you ten or twenty percent in a hand. That’s significant. How do you identify these big mistakes? You have to understand two factors:
1. The Quality of Your Hand Against Your Opponent’s Hand. In poker, you never know what your opponent holds, but your reads can enable you to make a reasonable guess of what your opponent’s hole cards may be. This takes skill and experience. It’s okay to make small mistakes because poker is a game of minimal information. You can never know for certain what your opponent’s cards are, but it’s essential to limit or eliminate the big mistakes. The key is that when evaluating any mistake in retrospect, you need to factor in the chance that the opponent may have had a different hand, too.
2. The Size of the Pot. The size of the pot affects the expected value of decisions you make at the table. For instance, suppose your opponent bets $40 and you assess you have a 25% chance to win. Is it time to call? It depends on the size: If the pot is zero dollars, then no. That would be a mistake of roughly $20 ($80 X 25% – $40). However, if the pot is $200 before your opponent makes the wager, you would only be putting in $40 into a final pot of $280 ($200 plus the two bets of $40). Factor in you perceived 25% chance to win and your expected value from the pot is $65. Since $65 is much more than $40, then go ahead and call. Conversely, if you had folded, you would have made a $30 mistake.
Like an actuary or a competent football coach, it’s all about putting the odds in your favor – and minimizing your mistakes via skill and experience.