Variance and Odds in Gambling

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Variance and Odds in Gambling

Every casino has placed advantages (also called the house edge) over all its games, allowing them to make huge profits. Although the casino may lose money to a few lucky gamblers every once in a while, the casino can still make up for their losses.

So why are there still many people flocking to the casinos, knowing that the house edge makes a game virtually impossible to win? Most of these players may not have an idea that they're bound to lose ultimately, or they think that they can turn the odds in their favor.

Knowing that the odds are stacked against you the moment you enter a casino, why would you still bother to gamble at all? The answer to this is that you can still "shift" the odds in your favor, if you know how to, and when. This theory can be explained by the mathematical theory called variance.

Variance, to quote the dictionary, is the square of a standard deviation. The what? You don't have to be a math wizard to understand variance. The following example will give you an idea of what variance is and how it applies to casino gambling.

Let's say that you flip a coin 1,000 times, expecting heads to appear 500 times, and tails also 500 times. For example, you place a $1 bet for each flip, winning if the head appears. Now, because of the existence of the house edge the casino will not pay you exactly $1 if you win. Instead, the casino pays out the amount subtracted by the house edge percentage. So if the house edge is 0.4%, the casino will pay you $0.96 (1 x 0.4).

To compute the negative expectation, just subtract the expected amount of winnings from the expected amount of losses. The negative expectation after 1,000 coin flips is $20 (500 x $1 = $500; 500 x $0.96 = $480; $500 x 480 = $20).

Here is where variance comes into the equation. You take 100 flips out of the 1,000, and suppose that out of these 100 flips, 65 are heads and 35 are tails. In this situation, you earn $62.40 (65 x $0.96) and lose $35 (35 x $1), making a profit of $27.40.

You can see that the short-term, high variance of 100 flips has negated the long-term negative expectancy of 1,000 flips. This shows that it is still possible to win during the periods of high variance. In the long run, the odds will even out and the casino will make the profit as expected.

The key to winning in gambling is to be in the right place at the right time, when the high variance comes your way. Nobody knows for sure when the variance will favor you. Occasional gamblers who gamble for the short term are more likely to hit positive variance than the frequent gamblers. The more you gamble, the more the odds will even out, and the house edge will then work in the casino's favor.



Las Vegas Croupier AC Casinos Close for the First Time in 28-Year History Monitored lists	Variance and Odds in Gambling Every casino has placed advantages (also called the house edge) over all its games, allowing them to make huge profits. Although the casino may lose money to a few lucky gamblers every once in a while, the casino can still make up for their losses. So why are there still many people flocking to the casinos, knowing that the house edge makes a game virtually impossible to win? Most of these players may not have an idea that they're bound to lose ultimately, or they think that they can turn the odds in their favor. Knowing that the odds are stacked against you the moment you enter a casino, why would you still bother to gamble at all? The answer to this is that you can still "shift" the odds in your favor, if you know how to, and when. This theory can be explained by the mathematical theory called variance. Variance, to quote the dictionary, is the square of a standard deviation. The what? You don't have to be a math wizard to understand variance. The following example will give you an idea of what variance is and how it applies to casino gambling. Let's say that you flip a coin 1,000 times, expecting heads to appear 500 times, and tails also 500 times. For example, you place a $1 bet for each flip, winning if the head appears. Now, because of the existence of the house edge the casino will not pay you exactly $1 if you win. Instead, the casino pays out the amount subtracted by the house edge percentage. So if the house edge is 0.4%, the casino will pay you $0.96 (1 x 0.4). To compute the negative expectation, just subtract the expected amount of winnings from the expected amount of losses. The negative expectation after 1,000 coin flips is $20 (500 x $1 = $500; 500 x $0.96 = $480; $500 x 480 = $20). Here is where variance comes into the equation. You take 100 flips out of the 1,000, and suppose that out of these 100 flips, 65 are heads and 35 are tails. In this situation, you earn $62.40 (65 x $0.96) and lose $35 (35 x $1), making a profit of $27.40. You can see that the short-term, high variance of 100 flips has negated the long-term negative expectancy of 1,000 flips. This shows that it is still possible to win during the periods of high variance. In the long run, the odds will even out and the casino will make the profit as expected. The key to winning in gambling is to be in the right place at the right time, when the high variance comes your way. Nobody knows for sure when the variance will favor you. Occasional gamblers who gamble for the short term are more likely to hit positive variance than the frequent gamblers. The more you gamble, the more the odds will even out, and the house edge will then work in the casino's favor.