The Gambler’s fallacy
The Gambler’s fallacy is a psychological error, also referred to as the fallacy of the maturity of chances. It is the belief that deviations from expected behaviour revert to mean. This is often referred to as ‘the law of averages’, I prefer to call it ‘The flaw of averages’
It layman’s terms it’s the feeling your mind gets when 15 reds pop up on the roulette table. There can’t be a sixteenth can there? So you bet black. In reality, in a fair game, bet one through 15 contains, in probabilistic terms, exactly the same chance of occurring and therefore your mindset shouldn’t change. If fact there is a possibility that the market will never actually revert to mean in individual unit terms.
If you look at the following graph, this is based on a strategy that I am examining at the moment. I am attempting to break even. Why? Because if I work out where that bar is I can estimate what I need to do to vault over it. The way I have set up the record keeping is to examine the market gross of commission. Because commission is a distortion on the underlying strategy.
You can see at the start we are up significantly, but as the strategy progresses the overall percentage starts to revert to mean. This is what fools a lot of people. Yes the percentage is reverting to mean, but not necessarily the underlying numbers, the reds or blacks. You can see as we approached the right hand side of the graph the overall strategy is more or less at break even, but this is nearly 900 iterations into the sample. So even a small -ve here turns out to be a big number of individual events.
This is where the ‘law of averages’ breaks down. Overall the percentage variation on a break even strategy will shrink, but the actually number of events could theoretically never catch up. Even a tiny, tiny, percentage -ve will still add up to a lot when multiplied by a large number.
The core of the fallacy though is that somehow red or black have some memory of what just happened, they don’t. The interesting thing in sports markets is that some events are definitely independent, while some are definitely or partially related. That’s a fun thing to explore.
Category: Trading strategies
