What is the standard deviation of potential winnings in a casino session where a player makes 5957 bets on the number 17 for a total of 2,116,780$ and turned a net profit of $67,520?
I am trying to figure out what the standard deviation with regards to winnings in $$$ is, for the following Roulette session:
The house edge in roulette is 5.26%, meaning we expect a player to lose $5.26 for every $100 wagered. If the player wagered a total of $2,116,780 we expect him to lose an estimated $111,342.6.
In this case the session ended with the player being up $67,520. Can we determine the standard deviation of total gains/losses for a session of this sample size? And additionally, would anyone be able to compute the probability that the player ends up +$67,520 for a session of the specified number of spins?
Probability of winning a number bet: 1/38
Probability of losing: 37/38
N (sample size) = 5957
Any help on this would be soooo appreciated!