Years ago some friends of mine where having a discussion about Las Vegas in which I learned that each of these individuals, who I would consider generally above the grain in terms of intelligence, had fallen for the gambler’s fallacy.
In a nutshell, the gambler’s fallacy is the mistaken belief that if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future. For example, it would be the belief that if Black has come up 5 times in a row during a game of roulette, then betting Red on the next spin would increase your odds of winning because Red is “due” for a hit.
If this is the basis for your betting strategy, stop now!
A brief description of bets and probability:
A bet is a wager that one or more events will occur given the possibility of varying outcomes. The probability of the wager is based on the number of winning outcomes divided by the number of possible outcomes.
Every wager in a pure bet takes place in a closed universe where there are a finite number of winning results and a finite number of total possible results.
Let’s take a wager that you will flip a coin and get heads three times in a row. There is one possible winning outcome: HHH. There are eight possible outcomes: HHH, THH, THT, TTH, HTH, HTT, HHT, and TTT. Therefore, the probability of winning is 1/8. In other words, there is 1 possible winning outcome out of 8 possible outcomes. If the bet was that you will get all heads OR all tails, then the probability changes to 2/8, or 1/4.
The bet takes place in a closed universe where the outcomes are limited by what reality dictates and the winning outcomes are dependent on whatever the gamblers choose in advance.
When the bet is that you will flip a heads in a single coin flip, a new universe is created to satisfy the conditions of that individual bet. You are no longer including the results of the previous flips or future flips, because what happened previously is not at play with the new conditions that are being set forth with the new bet…nor are the results of future flips important as to whether you win or not. If you get your heads, the wager taker is not going to come back and say, “OK, now let’s flip again to see if you win”. The wager didn’t include future events, nor does it include past events.
In this case, there is one possible winning outcome: H. There are two possible outcomes: H and T. The probability of victory is 1/2, one out of two.
This doesn’t change based on what previous results were because the previous results are not part of the bet. They are irrelevant.
If you were betting in the 3 heads universe, there are more outcomes and therefore more opportunities for loss. In the one head universe, there are only two outcomes that are physically possible and that is what you are betting on, nothing less, nothing more.
Indeed, if the previous results were 10 heads in a row, that is amazing! The probability of that is very highly against. However, in the one heads bet, the total number of possibilities that made the 10 heads in a row such a feat are not in play for you. You weren’t betting the last 10 flips would be heads. Your universe is smaller. Your bet is limited to the outcome of one flip, not the combined possible outcomes of a larger universe you aren’t participating in.
One doesn’t affect the other. That’s the important part. For the person who started at the beginning trying to flip 10 in a row, the probability is against him because the possible outcomes are enormous. The one coin flipper has a smaller universe because they didn’t start when the 10 flipper did. What happened previously isn’t relevant to them.
Now, substitute a coin flip for the 38 possible results in a roulette spin (American) and the same holds true. The probability of the next spin being black is 18/38. (47.36%) There are 38 possible outcomes, 18 of which are black. This is true for each and every spin. The results of previous spins don’t matter. You aren’t betting on the past results! If we could place wagers on previous outcomes, we’d all be rich! LOL!
Find a betting combination that maximizes your potential profit and stick with it. Placing a larger bet because you think the next outcome can be predicted will make the casino love you!