I am a match dunce

Trying to dust off my math skills and really understand the math behind the craps odds & payouts.

I'm taking an example from the Craps Appendix,

This is written:

Quote:

Buying Odds

4 and 10: [(3/9)×2 + (6/9)×(-1)]/1 = 0.000%
5 and 9: [(4/10)×3 + (6/10)×(-2)]/2 = 0.000%
6 and 8: [(5/11)×6 + (6/11)×(-5)]/5 = 0.000%

I understand deriving the probabilities down to the fractions and multiplying them by the payouts.

But why the division at the end (1, 2, 5 respectively)? That structure is seen throughout article - what factor is that?

Thanks!

Looks to me like the numerator is the average return, and the denominator is the initial bet. On the 4 & 10 you're wagering 1 to win 2, on the 5 & 9 you're wagering 2 to win 3, and on the 6 & 8 you're wagering 5 to win 6.

Right - it's just normalizing the payouts to units. The actual unit-based payout on the buy 5 bet isn't 3, it's 1.5 (3/2), while the loss is 1. The formula just moves the 2 outside.

Oh, I see that now. And the $1/$1 payouts don't include this, which makes sense. I just didn't see it. Nor can I type "math." Is it Friday yet?

Thanks!