Gambler’s Fallacy: Roulette Strategy
Three 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, have fallen for the gambler’s fallacy. I have tried to talk them out of it, but only one is receptive to the discussion. This is my most recent attempt to bring him back to common sense….
A bet is a wager that one or more events will occur given the possibility of varying outcomes.
The odds of the wager are based on the number of winning outcomes divided by the number of possible outcomes. (A house edge is generally added on top of this.)
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 outcomes.
Lets 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,TTT
Therefore, the odds of winning are 1/8. If the bet was that you will get all heads OR all tails, then the odds change 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. The odds are adjusted appropriately.
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 lets 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,T
The odds of victory are 1/2.
This doesn’t change based on what previous results were because the previous results are no longer a part of the bet. They are irrelevent.
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 odds of that are 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 at 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 that started at the begining trying to flip 10 in a row, the odds are enormous 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) the same holds true. Don’t confuse yourself based on past results. Find a betting combination that maximizes your potential profit and stick with it. Changing your bet willy nilly based on previous outcomes will make the casino love you!
I’m writing a script for a television pilot, and was curious if the numbers used on a Roulette Wheel have any basis in the field of “numerology”, astrology, or supernatural ? Thanks !
Hi shawn, my name is rey from California, I lived in Berlin Germany for almost 9 years and got heavily involved
Wiq in the computerized roulette. Did you know these games are programmed, even the ones here in California, and even the real live person roulette where I play. The program is identical. I tell the players and dealers and some suspects something and others don’t believe me. If you have time I want to show you what I know and learned. Thanx