1. ## Prob distribution

The roulette wheel has 38 “pockets”.
The “pockets” are numbered 1, 2, …, 36; 0 and 00.
Half of the “pockets” 1, 2, …, 36 are coloured red, the other half are black. 0 and 00 are green.
If a player outlays $b in a bet on red, and the result of the wheel’s spin is * red, then the casino (“house”) pays the player$2b (ie, the $b outlaid in the bet, plus$b).
* not red, then the casino keeps the $b that the player bet. Felipe’s strategy was: Bet #1:$1 on red.
Bet #2: $2 on red. Bet #3:$4 on red. etc

Assume that the wheel is “fair”, that is, a ball thrown into the spinning wheel is equally likely to fall into any one of the 38 “pockets”. Assume that the casino does not impose betting limits.

4. ## Re: Prob distribution

Yes you got a sequence of i.i.d. Bernoulli random variables , but you are not simply summing them to got a Binomial distribution; instead you have

5. ## Re: Prob distribution

Originally Posted by BGM
Yes you got a sequence of i.i.d. Bernoulli random variables , but you are not simply summing them to got a Binomial distribution; instead you have

I dont get the part. Why do u multiple the random variable by 2 and then minus 1?

6. ## Re: Prob distribution

It is because those are Bernoulli random variables which take values only; and I use to represent the event that winning on that bet (obtaining red color)

7. ## Re: Prob distribution

Originally Posted by BGM
It is because those are Bernoulli random variables which take values only; and I use to represent the event that winning on that bet (obtaining red color)
Ok, i get it now. But it is not the probability distribution, it is just the probability equation. I'm guessing if the probability distribution is an uniform distribution as each bet has the same probability.

8. ## Re: Prob distribution

Yes, you have correctly figure out the support of distribution.

The outcome after bets can be written as

The summation here actually can be regarded as a binary number with digits:

So each realization of will have a unique sum - and the sum will be the even integers ranging from .

And you just need to state these support points after subtracting the constant. The problem here is that is not necessarily one-half so you may not have a discrete uniform distribution at the end.

9. ## Re: Prob distribution

umm.. but how could i tabulate the probability distribution? I will need to create a table for the probability of each bet..

so.. does it begin with something like below?

Bet Prob Financial outcome
1 0.4737 2(0.4737)-1
2 0.4737 2[2(0.4737)-1] etc?

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