Exact value of bets on a roulette wheel

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This is the location of the highest bar. To simplify, the highest bar means the ball is bouncing this distance most. So it makes sense to place our bets in this area of the wheel. In this case, our Amgen profit would have been substantial.

But if we had bet and a plus value of 10, we would not have had any wins at all. How could this be possible, if we have a very strong edge? This may be the horizontal distance numbers of 7,8,9,10,11,12,13,14, Now does it matter that the bull never landed at distances 9 and 10?

Not really, because we are still betting on the correct region. And there you have it. Simply by covering more numbers, we reduce variance. An inexperienced gambler will consider variance their enemy. This system may expect a certain event to happen, and it usually does. But they find that the rare occasion eventually happens, and wipes out there bankroll.

This is how they see variance. They think this rare event is the problem that they must overcome. Another example is the law of a third. This states that after 37 spins, approximately one third of the numbers will be repeats. Often systems are designed around this principle, in the hopes that 37 unique numbers will never appear in 37 spins.

This is tremendously harmful oversight on their part. The reality is any sequence of numbers over 37 spins, is just as likely as any other sequence of 37 spins. Consider a smaller example will you ever see the sequence of 1,2,3,4,5? Probably not. And will you ever see the sequence 32,9,18,14,2? But given enough spins, you will see each of these sequences the same amount of times. This is because you increase bet size to cover losses, and most of the time you achieve this. The problem then seems like the rare loss puts you back at square one — you lose your winnings plus more.

Variance is unpredictable. You never know if or when something unpredictable will happen. You test the concepts on any fair casino. Consider this useful training on new casino sites This is a very backwards understanding. For example, say there was 45 black numbers, and 50 red numbers.

The net winnings on a roulette wager can be thought of as a discrete random variable. This results in net winnings of 1. This results in net winnings of We use the above information with the formula for expected value. It helps to remember the meaning of expected value to interpret the results of this calculation.

The expected value is very much a measurement of the center or average. While we might win several times in a row in the short term, in the long run we will lose over 5 cents on average each time that we play. The presence of the 0 and 00 spaces are just enough to give the house a slight advantage.

This advantage is so small that it can be difficult to detect, but in the end, the house always wins. Share Flipboard Email. Courtney Taylor. Professor of Mathematics. Courtney K. Taylor, Ph. Updated April 27,

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