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A gambler bets $1 on the number "19" 1600 times in roulette. This bet pays 35 to 1. What is the give-or-take on the estimate of his winnings?

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1 Answer

Assuming that it is American roulette, The number 19 appears once out of 38 other numbers.  that means you have a 1/38 probability of winning. 
 
that 1/38 chance will pay you $35 and the 37 other ties will pay you $-1.  So let's say you play only 38 times.  Probability says you will lose 37 times and win once, meaning you will lose $37 and win $35.  All in all you lose $2 every 38 tries.  How many groups of 38 tries is there in 1600?  42.105.  Multiply that by -2 and you get 84.21, which is close enough to 84.36 with the error being a difference of rounding.

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