Gambler’s Fallacy? Data, RNGs and Software-Based Casino Games

One of the most simple and, at times, effective ways of winning at roulette is called the Martingale System. Its success depends on, among other things, a mathematical 'flaw' in the payout rates of the basic roulette game.

Here's how it works:

On the roulette table, you can place a certain number of even money bets – red or black, odd or even, etc. The payout for guessing correctly is 1:1, i.e., if you bet $10, you would win $20 ($10 + your stake).

So, let's say you bet $10 on red and lost. The Martingale System advises doubling the bet to $20. If that bet wins, you would win $40. This would mean your total outlay would be $30 ($10 from the first losing bet, $20 from the second bet), making a profit of $10. If the first two bets lost, and you doubled the next to $40, you would make $10 profit from the third bet.

If you follow this system, you will eventually make a profit no matter how many times you have to double the bet. There are significant dangers though: What happens if you run out of money? What happens if you reach the table betting limits? The Martingale System is, therefore, not infallible, but it is mathematically sound.

The reason we talked about the Martingale System is that it perfectly demonstrates something called the gambler's fallacy, and it highlights how casino players can often misinterpret data. We know that the ball will eventually land on red because probability dictates it should happen eventually, but we have trouble comprehending that the chances are the same with each spin of the roulette wheel.

Gambler's Fallacy

The gambler's fallacy is the erroneous belief that if an independent event happens frequently (or infrequently), it impacts the chances of it happening again. So, if the roulette ball landed on red three times in a row, it's more likely to land on black in the next spin, right? Wrong. The chances are exactly the same (about 48.65% for a European roulette wheel).

You can look at it in another way, with lottery numbers: If the winning lottery numbers were 3, 7, 13, 19, 25 and 41, you would imagine that this combination is less likely to be the winning set the next week. But we know that it would have exactly the same chance as any other combination of six numbers. Yet, still, the human brain doesn't believe the probabilities.

RNGs Ensure Outcomes Are Random

Roulette and lotteries are real games, but what about virtual ones? If you look at how to play Top Trumps, a simple celebrity-inspired casino game, you will see that the RTP is 95.00%. RTP (return to player) is the amount that the game pays back to players over time. You can look at it as the game having a house edge of 5%.

To run this game, or other virtual games, the casino will use RNG (random number generator) software. They will use algorithms that have been set with some preconditions, but the only one that we are sure of is this 95% RTP. Moreover, we don't know the timeframe for the payout rates. Normally, these things are worked out over millions of plays. As such, it is impossible for the player to work out what comes next in the sequence.

Again, though, with these types of software-based game, the gambler's fallacy is at work. If we win, we believe it is less likely we will win with the same number or spin the next time. If we lose, we believe the RNG will make it more likely to win with the next spin. The truth is, however, that we cannot anticipate the likelihood of the subsequent outcome – just like the non-virtual casino games.

If you look at online virtual roulette, many versions of the game will provide a history option. It will show numbers that have appeared frequently, prompting the player to think of it as a data set. But, considering everything we have talked about above, this data is useless. So, why do they put it up there? Because regardless of how much we tell ourselves it doesn't matter, we still think, perhaps subconsciously, that it counts for something. That's the gambler's fallacy.