Roulette Odds
The arithmetical formula for anticipation reads as follows:
Expectancy = [probability of a winning outcome X the amount you would
win] + [probability of a losing outcome X the amount you would lose]
Which kind of makes sense. What you would be expecting to win on the
bet, combined with what you would expect to lose, should tell you what
you're expected outcome is.
For the single dollar bet in roulette mentioned above:
E = [1/38 x 35] + [37/38 x (-1)]
= 0.921 + (-0.97368)
= -0.0526
= -5.26%
The negative simply shows you that you are expected to walk away down,
as expectation is calculated as 'player expectation'. Turn this around
into a positive gives you the 'casino expectation' or house edge. So
now you can see where the house edge in American roulette comes from,
and how it weighs in at 5.26%. You'll find that the roulette odds behind
every single bet on the table work out to the same unquestionable house
edge, with the omission of the five number bet, which doesn't pay it's
odds back as well as the other bets on the table, and works out to an
even worse house edge of 7.89%.
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