Gambling

[Teddy6451]

Hello, i wanted to make sure how do i count the probability of 18 consecutive losses/wins occuring in a 50% chance game in a million bets? That is, if i make a million bets in total, what is the probability that 18 consecutive losses or wins will occur?
Thanks in advance!

 

[BigBeachBanana]

Do you stop once you get 18 consecutive wins?

 

[blamocur]

Do you stop once you get 18 consecutive wins?

Does it matter?

 

[blamocur]

Hello, i wanted to make sure how do i count the probability of 18 consecutive losses/wins occuring in a 50% chance game in a million bets? That is, if i make a million bets in total, what is the probability that 18 consecutive losses or wins will occur?
Thanks in advance!

My quick and dirty script using Markov chain gives me around 85.15% chance.

 

[BigBeachBanana]

Does it matter?

You can get multiple 18 consecutive wins with 1M trials.
18wins, 1 loss, 18 wins, etc...
The difference is the probability of getting exactly one 18 consecutive win vs multiple 18 consecutive wins.

 

[blamocur]

You can get multiple 18 consecutive wins with 1M trials.
18wins, 1 loss, 18 wins, etc...
The difference is the probability of getting exactly one 18 consecutive win vs multiple 18 consecutive wins.

I interpreted this as the probability of getting at least one run of at least 18 wins. I.e. if you get several runs of more than 18 wins they are still counted in the probability. But it is up to the original poster to clarify.

 

[Steven G]

You can get multiple 18 consecutive wins with 1M trials.
18wins, 1 loss, 18 wins, etc...
The difference is the probability of getting exactly one 18 consecutive win vs multiple 18 consecutive wins.

What about 24 consecutive wins? How many times did you have 18 consecutive wins?

 

[BigBeachBanana]

What about 24 consecutive wins? How many times did you have 18 consecutive wins?

I should've been clearer. You can have multiple 18+ consecutive wins.

 

[Teddy6451]

I interpreted this as the probability of getting at least one run of at least 18 wins. I.e. if you get several runs of more than 18 wins they are still counted in the probability. But it is up to the original poster to clarify

Yes, i did, indeed mean At least 18 consecutive wins Or losses. So the probability is about 80% if i decide to bet a million times?
The events are fully independent.
But what's weird is that i have already made a few million bets and the very highest total amount of either wins or losses was 16... Not 17 or 18 a single time ...

 

[blamocur]

Yes, i did, indeed mean At least 18 consecutive wins Or losses. So the probability is about 80% if i decide to bet a million times?
The events are fully independent.
But what's weird is that i have already made a few million bets and the very highest total amount of either wins or losses was 16... Not 17 or 18 a single time ...

I'll try to simulate this later.
I've only estimated the probability of consecutive wins. For wins or losses the probability should, of course, be higher (97.8% if we believe they are independent).