The coin only has 2 outcomes - much less than the roulette wheel! You could assign +1 and -1 to heads and tails, respectively, and it would have the same variance of 1/2 on a fair coin. In other words, 1/36 is not much different from 1/37. The number of outcomes on the wheel is “less” relevant to the calculation. In the even money case, all outcomes are 1 unit away from zero (+ or - makes no difference) whereas, in European roulette, you have one outcome that is closer to the mean than the others, the -1/2 when hitting zero on the wheel. Think of variance as a (more complicated) measure of distance of all outcomes from the average value. The variance of getting either +1 or -1 with equal probability is higher than the variance of getting +1, -1, or -1/2, as in single zero, because of the -1/2 outcome.
I think I see the confusion… This is the variance of the BET outcome, not the WHEEL/BALL outcome. How can having 1 less # give more variance? So without a 0, var is higher? (.5 vs 0.4736)
