sillybuffalo
New member
- Joined
- Sep 18, 2013
- Messages
- 9
One popular strategy for gambling on roulette, the "martingale," gives a very high probability of a positive outcome. Here's how it works, for a gambler who starts with a stake of $15. In the US roulette wheels have 38 equally-likely outcomes, 18 each Redand Black and two Green (European wheels have 37 outcomes, with only one Green). Themartingale strategy is to double the bet after each loss:
For #2, is the P[X>0] just the same as P(X=1)?
I need help getting started with 3 and 4.
Thanks!
- Bet $1 on Red. If Red appears (US probability 18/38), quit with winnings $1. Otherwise,
- Bet $2 on Red. If Red appears (US probability 18/38 again), quit with winnings -$1+$2=$1. Otherwise,
- Bet $4 on Red. If Red appears, quit with winnings -$1-$2+$4=$1. Otherwise,
- Bet $8 on Red. If Red appears, quit with winnings -$1-$2-$4+$8=$1. Otherwise,
- You're broke, so you have to quit anyway with total winnings -$1-$2-$4-$8= -$15. Hitchhike home.
- Find the probability distribution of X, i.e., find p(x)=P[X=x] for every real number x.
- Find P[X>0].
- Are you convinced that the strategy is indeed a "winning" strategy? Explain your answer.
- The queen of England is said to have a net worth of about 400 million dollars. If she commits to play the martingale strategy until she either wins $1, betting on Red every time and doubling her bet each time Red does not appear (as in steps 1-4 above, continuing indefinitely), or loses everything, what is the probability that she wins $1? What is the probability she loses $400,000,000? What is the expectation of her gain?
For #2, is the P[X>0] just the same as P(X=1)?
I need help getting started with 3 and 4.
Thanks!