Eli5: Why can’t you just double your losses every time you gamble on a thing with roughly 50% chance to make a profit

Question

This is probably really stupid but why cant I bet 100 on a close sports game game for example and if I lose bet 200 on the next one, it’s 50/50 so eventually I’ll win and make a profit

In: 4566

Answer 1

This is referred to as a Martingale system in gambling and it will always fail you in one way or another. Not because the math doesn’t work, in theory, but because of reasons a couple others have mentioned —

1. You will encounter a losing streak that requires you to wager more than you have.
2. Even if you have an arbitrarily large sum to wager after a long losing streak, all casinos and bookies have limits on wager sizes they’ll accept so your infinite stack of cash becomes more of a risk to them than they’re willing to accept.

On the topic of losing streaks, I heard a statistics professor talking about a coin flipping exercise she does with her students each semester. She has one group “randomly” choose a string of 100 coin flips, e.g. where they just make up results and write them down — pretending to replicate a coin flip situation.

The second group is instructed to actually flip a fair coin and record the real results.

Both groups record their results on a whiteboard. The professor leaves the room during this process and doesn’t know which set of results is the real one until looking at them closely, and pretty much always identifies which is real and which is fake — with far greater than 50% accuracy.

How does she do it? The fake group tried to make it look real by having very few, if any long strings of the same result (e.g. there are very few HHHH type sequences — they tried too hard to make the coin look … too fair, for lack of a better term).

But the professor knows, mathematically speaking, the chances of having a string of, say 6+ of the same result in a row with a fair coin over the course of a hundred flips actually quite high. Much higher than our intuition suggests. So she looks for which set has the largest run of the same value, or the set which has the most runs of 4-5 matching values in it.

All that to say, the probability of a crushing losing streak with your Martingale strategy is a lot higher than you think.