Law of large numbers and roulette
By admin. Filed in Roulet |
The law of large numbers is something that every roulette player should know about. The wikipedia definition is a bit long so I take this from Berkley University’s website.
The Law of Large Numbers says that in repeated, independent trials with the same probability p of success in each trial, the percentage of successes is increasingly likely to be close to the chance of success as the number of trials increases.
Think in terms of coin tossing. If you tossed it 3 times, you may get 3 heads, 3 tails or 1 of another 6 possibilities. You wouldn’t say that the coin is fixed though, if there were 3 heads in a row. However, you might say be able to say that after 100 heads in a row.
The law of large numbers says that you should be getting towards the true probability after a large number of trials. So after 100 tosses of a coin, you would expect between 40 and 60 heads. Any more or less and you might start to consider the coin to be bias.
Note, thats its the percentage that counts, not the absolute number. Its a misconception that after say 100 coin tosses the exact number of heads and tails should be 50/50. It would be more surprising if this was the case. As the number gets larger, say a million, you’d expect around 500 000 heads and tails give or take a few thousand.
So in roulette, some gambler believe that, say, after 10 reds, the sequence has to start running in to blacks to satisfy this law. This is not true. For simplicity, lets say the true probability of red is 50%. The law of large numbers says that after a large number of trials the observed number of reds will be close to 50%. So after 10 spins all red, you get this observed probability. 100% red, 0% black.
Have another 10 spins. Lets say that this time, you get 5 red, 5 blacks. The observed results are 75% red, 25% black (15 vs 5). Say another 10, with 5 red, 5 black, thats 66.7% to 33.3%. You can see it getting closer to 50/50 without any long runs of black. After 500 spins, the run of 10 reds at the start has negligible impact.
Over a year at the casino, you would expect to see these long runs of blacks and reds. Just because 10 reds have come up it doesn’t mean that the wheel is rigged or biased (even though it could be). Thats why doubling up strategies are all doomed to failure. Things could go well for hours, days even but sooner or later a long run will wipe you out. Even playing with level stakes means that the luckiest players will still get wiped out.
The way to profit from this is to play as little as possible. It might not be fun but the way to do it, is to stick all your money on an even money roulette bet and walk away.
