# Rng Primer: Gambler’s Fallacy

Hello everybody, Geek Generation here.

In an earlier post, Coding Luck into a Game, i talked about how a programmer might conceivably, inconceivably rather, include luck into the programming code of gacha boxes so that a player who opens gacha boxes when he/she is “lucky” would have a better chance of getting desirable items.

Some of the factors contributing to bad understanding of rng (randomness) could be that we have a poor understanding of the math behind the problem. Even with proper understanding, the math could sometimes be counter-intuitive, leading to poor estimation or poor interpretation.

This post, i’ll talk about Gambler’s Fallacy, which could be the reason for poor understanding of math. Following that, in another post, i’ll talk about the Monty Hall Problem, which highlights the possibility of having poor estimation or poor interpretation because the math is counter-intuitive.

Worry not though, these posts are not going to full of number crunching, if any at all, in them. I’m classifying them as math simply because them seem mathematical to me.

Gambler’s Fallacy

Let’s say we have a fair coin that lands on heads 50% of the time and tails for the other 50% of the time. Then i flipped the coin 10 times, getting heads every time. What’s the probability of getting a tail on the 11th time?

If you answered 50%, you probably know about the Gambler’s Fallacy. However, if you answered, very very likely such that the probability is more than 50%, that would be incorrect. In school we learn that the probability of flipping the coin heads 10 times in a row is calculated by 1/2 x 1/2 x … (10 times). But what does that mean? First thing to note is that we’re multiplying by 1/2 because the probability of each individual flip has exactly 50% chance of landing on heads. Ergo, the last, 11th flip, also has exactly 50% chance of landing on heads.

Why is that so? For the very simple reason that the coin has no memory of its previous flips. The coin, on it’s 11th flip, does not know that it had landed on heads for 10 times previously, hence will not in any way skew the probability toward landing on tails because of it had a history of flipping heads.

The same thing applies to gacha boxes and randomness in games. Opening a streak of bad luck boxes doesn’t improve your chances with the next boxes. Opening a streak of good luck boxes doesn’t deplete your luck. If you believe otherwise, you’d be committing the Gambler’s Fallacy.

The thing is, lots of people do fall for the Gambler’s Fallacy every now and then, including people who know about the Gambler’s Fallacy, myself included. Sometimes, lapses in judgement do occur, especially if you’re the one popping gacha boxes or booster packs.

Until next time, Geek Generation out.