This gambler and the gamblers fallacy

The gamblers fallacy, in short, is the belief that previous events have an impact on future events. More specifically, it says that if a run of results are biased in one direction, the liklihood of the opposite result occuring increases. So a coin toss that gave four results of ‘heads’ in a row, would mean that the next coin toss is more likely to be ‘tails’ than the actual odds.

Looking at the coin toss as an example, the odds of either heads or tails coming up are both evens, that is, one to one, expressed as 1/1 in fractional odds format, and 2.00 in decimal odds format.

If there was a sequence of results that were all heads, believers in the gamblers fallacy would think that the liklihood of tails coming up on the next toss would be far higher than the expects odds of evens.

The root here is that all such random events are in fact random and are not related to each other. Ok, I get that.

But what about the opposite view? If, for example, heads had come up 20 times in a row, are the odss of heads coming up on the very next toss really evens?

I guess that is why I am a gambler then, because I have a hard time getting my head around that. I guess I do believe in the fallacy, at least somewhat.

In games like blackjack, where there is a finite deck, the removal of some cards from the deck as they are dealt will obviously have some impact on the remaining hands that can be dealt. But in games like roulette where there is an infinite number of spins of the wheel, the result of all the previous spins can have no impact on the next spin.

But in my heart I believe that the true odds must come out in the long run. If for example the number one has not come up in 200 spins then, yes, I believe that it is more likely to come up on the next spin.

After all, the reliability of the true odds working themselves out is what all casinos are built on. Casinos don’t mind their gamblers having a lucky streak. So long as they can get the gambler to play for long enough they believe that the house edge will kick in.

And we know that they are right.

Isn’t that then the reverse of the fallacy?

As long as I believe that the previous results can be factored in to the future results, I will always be looking for a gambling system that works.