When it comes to gambling at a casino, making informed bets can mean the difference between winning big and losing everything. Understanding the concepts of expected value and variance can help you make smarter bets and increase your chances of coming out ahead.
Expected Value
Expected value (EV) is a mathematical concept that represents the average outcome of a particular bet over a large number of trials. In other words, it is the amount of money you can expect to win or lose on a bet over time. To calculate the expected value of a bet, you need to know the probability of winning and losing, as well as the amount you stand to win or lose.
For example, let’s say you are playing a game of roulette and you place a bet on red. The probability of winning this bet is 18/38 (there are 18 red slots out of a total of 38 slots on the wheel). If you win, you will receive even money (1:1) on your bet. If you lose, you will lose your entire bet. The expected value of this bet can be calculated as follows:
- Probability of winning: 18/38 = 0.4737
- Probability of losing: 20/38 = 0.5263
- Payout for winning: 1:1
- Payout for losing: -1
To calculate the expected value, you simply multiply the probability of winning by the payout for winning, and multiply the probability of losing by the payout for losing, and add the results:
EV = (0.4737 x 1) + (0.5263 x -1) = -0.0526
This means that for every $1 you bet on red in roulette, you can expect to lose 5.26 cents on average over the long run.
Variance
Variance is another important concept to understand when it comes to casino bets. Variance refers to the range of possible outcomes for a particular bet. A high variance bet has a wide range of possible outcomes, while a low variance bet has a narrower range of possible outcomes.
For example, let’s say you are playing a slot machine with a high variance. This means that the machine has the potential to pay out a very large jackpot, but the odds of hitting that jackpot are very low. The range of possible outcomes for this bet is wide, with the potential for a huge win or a total loss.
On the other hand, a low variance bet might be something like betting on red in roulette. The range of possible outcomes for this bet is narrow, with a relatively small win or loss compared to the size of the bet.
Putting It All Together
Understanding both expected value and variance can help you make smarter bets at the casino. By calculating the expected value of a particular bet, you can determine whether it is a good bet or a bad bet over the long run. By considering the variance of a particular bet, you can decide whether you want to take a riskier bet with a higher potential payout, or a safer bet with a lower potential payout.
Of course, there is no guaranteed way to win at the casino. All casino games are designed to give the house an edge over the long run. However, by understanding the concepts of expected value and variance, you can make more informed bets and increase your chances of walking away a winner.