You can be playing nickel and dime limit Hold’em with your friends in the garage, or $25/$50 high stakes No Limit Hold’em at the Bicycle Casino in Los Angeles. It doesn’t matter. The object remains the same: to win money. That’s how the game is scored. The “winner” is the person who won the most money.To anyone serious about wagering money, whether it be a single bet on a single betting round from one hold’em hand, or if it’s a huge parlay bet on a set of sports games for the week, one thing always must be considered–expected value.
The mathematical expected value is the amount a bet will average, winning or losing, or the course of a long period of time. If you make this bet once, you may either win or lose, and casual wagerers (and losing players) only consider the short-term result. Credit (or blame) is always given to luck. Serious wagerers know better than luck. What will happen if I make this bet a thousand times? I’m going to win some, and I’m going to lose some, but financially, where will I be after wagering my money on this bet numerous times over the course of a long period of time?
Most of the time, you know everything you need to know to determine the value of a wager before you actually place the wager. In roulette, you are given 35-to-1 odds on a 37-to-1 chance to hit. If you make a $1 bet one thousand times, you will have wagered $1,000. You will win the bet approximately once every 38 times (approximately 26 out of 1,000). For every time you win, you will be paid thirty-five times your bet, which in this case, your pay would be $35. If you’ve made this bet one thousand times and won it twenty-six times, you’ve won a total of $910. You’ve lost $90 over the course of one-thousand $1 bets, due to what’s called the “house edge.” In this case, a $1 bet in roulette has an expected value (EV) of -$0.09.
The casual gambler probably isn’t even reading this far, but to a serious bettor, he understands “Every time I bet on roulette, I’m losing 9%.” It’s true, you will win some and you will lose some, and if you’re just looking to have some fun, there’s nothing wrong with throwing some money on the roulette table. But if like your money and you’re serious about your wagering, you’re looking with something you can get a better expect value out of.
Let’s say you have a gambling friend who wants to bet a $1 on the flip of a coin. If he wins, you pay him $1, and if you win, he pays you $1. After one flip, you’re going to either be up $1 or down $1. But suppose you and your friend flipped the coin a thousand times. Since the odds of a flipped coin landing on heads are exactly the same as the odds of it landing tails, the more time you flip the coin, the closer the win-to-loss ratio approaches exactly 50%. After a thousand flips, you may have won some money, and you may have lost some money, but you’re probably neither up or down any more than $10 (1% of the $1,000 wagered). And if you are up or down any amount at all, it’s because of “statistical anomaly,” or what bad gamblers call “luck.” Because you win exactly the same amount as you lose, and the odds of winning and losing are exactly the same, this wager has an EV of $0. This is what’s called an “Even Money,” bet.
Now, suppose you refused your friends offer to flip the coin for a $1 each. You know it’s even money and only a waste of time, because you’re a serious gambler and you don’t want to wait around for statistically anomalies to come around and pay you off. You’d be better off working at McDonalds, at least there you can probably get some free food. But your friend really, really wants to gamble with you, so he ups his stake. If he wins, you still pay him just $1, but now, if you win, he pays you $2. Your friend isn’t very smart.
The odds of the results of the flip haven’t changed at all. The coin will still land on one side exactly half of the time, and on the other side the other half of the time. But now, you’re getting paid $2 when you win, but only losing $1 when you lose. So once again, if the coin is flipped one thousand times, you’re going to win just about as often as you lose. Any variance from 500 wins, 500 losses, again, is statistical anomaly. You lost five hundred $1 bets to your friend, but your friend lost five hundred $2 bets to you, and now he owes you $500. This wager has an EV of +$0.50. You’re going to profit $1 for every two bets made, for an average of fifty cents per bet.
Any time you know the odds of winning, as well as how much you’re wagering, and the amount you will win, you can easily figure whether you have a positive or negative expected value. First, know the pay-outs. For comparison’s sake, it’s best to express them in X-to-1 odds. So, if you have to wager $1 to win $5, you’ve been given 5-to-1 odds. If you have to wager $5 to win $1, you’ve given 1-to-5 odds, or 0.20-to-1. Now, figure your chances of winning the bet. If you will win the bet once in five times, you will win once and lose 4 times, so you have 4-to-1 odds against. If you win the bet four in five times, you will have 1-to-4 in favor, or 0.25-to-1.
Now, compare the pay out to the odds. If you have a 5-to-1 pay on 4-to-1 odds, you have a positive expected value (in this case, 20%). If you have given 0.20-to-1pay out on 0.25-to-1odds, you have a negative expected value (-20%).
If you’re playing poker, no one person is going to be giving you payout odds. Your odds are the “pot odds.” Any time you going to call the bet, your pot odds are the total amount of money in the pot versus the amount is costs you to call. Once you’ve determined your chances of winning the hand, you can now determine the expected value, not only of continuing on with a call, but also of folding. If you do not make a bet (or fold in a hand of poker), your expected value is always going to be $0. You’re wagering $0, and have no chance at winning any money. In order to be a serious, successful bettor, you must always make the play with the most positive expected value.
So, you determine the expected value of continuing on with the hand. If you have a negative expected value, you must fold and save money. Money saved is money earned. If you have a positive expected value, you must continue on with the hand. You may only win the hand once in ten times, but if there is enough money in the pot to give you a positive expected value, you’re actually losing money by folding and accepting a $0 value move.
If you’re playing poker, a good call or good fold is based purely on the expected value of the play (versus other options) and has nothing to do with the actual outcome of the hand. If you fold your flush draw because the pot odds were giving you a negative expected value, you should not be upset when the next card dealt would have made your flush. Instead, simply realize that by taking the bet, you would have accepted a negative expect value, and to make that mistake, you’ll eventually go broke.
The importance of knowing how to get the most value out of your bets can not possibly be seen after just one bet, or just one session of wagering. It takes a long period of time to begin to see the difference making these value choices will make. Because of this casual gamblers pay no attention to it. A serious gambler absolutely must. If you’re taking a bet with even a slightly negative expected value, you’re losing money. And if you take this bet, even with a negative EV of one one-thousandth of one percent, over a long enough period of time and with enough bets, even the richest man in the world will go broke. Likewise, if you’re continuously taking bets with even a slightly positive expected value, over a long enough period of time and with enough bets, you’ll be very profitable.
And this is how casinos make their money. They offer bets which give casual wagerers a minutely negative expected value. Enough of these casual gamblers come through the casinos, and the casinos take enough bets that it rakes in a very large amount of money. It’s not luck. It’s statistics.