$20000 at $0.20 martingale betting

[iDimension]

Hello. I'm watching a twitch streamer and he is currently on one of those CSGO betting websites, if you don't know what that is it's fine, it's not important.

He is using a martingale system of betting and he started with $20,000 and is betting $0.20 each time. If he loses he doubles his bet, he keeps on doing this until he wins and then the bet starts at $0.20 again. Every win he gets he bets another $0.20.

His odds of winning each bet is 47.5% and the house has 52.5% chance of winning. In order for him to go broke, he would need to lose about 17times in a row right? I think it's less than that because it's not 50/50 chance. So odds of him losing around 17 bets in a row is 1/131,072 apparently... Is this correct?

 

[Orodruin]

The number of bets he has to lose in a row is independent of the odds. The odds only decide how quickly he will lose everything on average. It is well known and analysed that you cannot beat the odds with this type of betting scheme. In the end you are betting a fortune just to regain what you already lost and 20 extra cents. However, it is very easy to fool yourself into thinking you are doing well.

 

[Orodruin]

Also, just the small difference from 50/50 makes a big difference in the odds to lose 17 in a row. It is closer to 1 in 57000. Compare this to the number of runs you would have to do to gain 20000 (the amount you are essentially wagering if committing to the betting system) which is 100000.

 

[iDimension]

So just to clarify he would have to lose 17 in a row to go broke which is about 1 in 57,000 chance?

 

[Orodruin]

So just to clarify he would have to lose 17 in a row to go broke which is about 1 in 57,000 chance?

Yes, but to reach the level when he actually makes as much as he is wagering, he would have to repeat 100000 cycles, meaning that in this time he will go broke almost twice on average. If he wants to double the money, it would be a better bet just to bet it all at once. If you have 20000, there are clearly better ways of investing those.

 

[Orodruin]

Putting it in a different perspective, if he commits he is making a 20000 bet with a gain of 0.2 if he wins. The expected value of this bet is roughly 0.2 - 20000/57000, which is clearly negative. I am sure he could find better odds some other way.