Craps Question for the Math People

What's standard deviation if I'm playing craps; I'm a wrong bettor, and I only lay odds, most of the time single odds(sometimes double if I'm feeling lucky), when the point is 4 or 10. I'm making $5 don't pass bets. What can I say, I like low variance and am easily entertained. Any help with the number crunching would be great. Thanks.

Quote: Joegambler

What's standard deviation if I'm playing craps; I'm a wrong bettor, and I only lay odds, most of the time single odds(sometimes double if I'm feeling lucky), when the point is 4 or 10. I'm making $5 don't pass bets. What can I say, I like low variance and am easily entertained. Any help with the number crunching would be great. Thanks.

Here are some numbers:

$5 DP, standard deviation $4.99951
for 60 bets, ev is -$4.21, SD $38.73

$5 DP, lay single odds on 4/10 only, avg. bet $6.71, SD $6.71
for 60 bets, ev is -$4.21, SD $52.

$5 DP lay double odds on 4/10 only, avg. bet $8.43, SD $9.07
for 60 bets, ev is -$4.21, SD is $70.25

$5 DP lay single odds on all numbers, avg. bet is $10.49, SD is $9.90
for 60 bets, ev is -$4.21, SD is $76.69

OTOH, suppose you made a don't come bet instead of a don't pass, and didn't make a second DC until the first was resolved? That would result in only about 80% as many bets, so 48 in the same time frame. Then, if you laid double odds on all points, the numbers would be:

$5 DC, lay double odds - avg. bet $15.29, SD $14.47
for 48 bets, ev would be -$3.37, SD $100.26

You would be getting more variance for less expected loss.

I understand that you are laying odds only on 4/10 because those bets have the best chance of winning, but they also have the shortest payoff and the biggest loss if you lose.
Cheers,
Alan Shank