The costliest roulette bet on the table

On an American roulette wheel (38 pockets), a straight-up bet on one number pays 35:1, while the notorious five-number bet (covering 0, 00, 1, 2, 3) pays only 6:1. Over $100 staked, how many more dollars do you expect to lose on the five-number bet than on the straight-up bet? Give a decimal to two places.

Show hints (2)+
  1. Compute each bet's EV per $1 separately: single is 138(35)+3738(1)\tfrac1{38}(35)+\tfrac{37}{38}(-1), five-number is 538(6)+3338(1)\tfrac5{38}(6)+\tfrac{33}{38}(-1).
  2. The two edges differ by 138\tfrac1{38}; scale by $100. Do not assume they are equal.

Answer

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2.63 (± 0.01)

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Asked at: SIG, DRW

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