Craps STDev

My question concerns the standard deviation of continous pass/come bets with 10x odds vs. the standard deviation of the same strategy don't pass/don't come laying odds. It seems to me that the don't pass strategy has a lower standard deviation.

Thanks,

That's a good question. Without any numbers, I think your intuition is correct - that the don't has a smaller standard deviation. But I also think that one should consider skewness, which I don't frequently see in discussions of gambling. I'd be interested to hear from others, especially if anyone has numbers to contribute.

I would say the SD would be higher for the don't side since your average bet would be higher.

Your average bet between the pass and the don't side would be different. One can Lay more odds to win less on the don'ts.
Pass $5 with $50 odds would cover all point numbers but the Lay Odds are different for the don'ts.
Don't Bets:
Point 4 and 10. $5 flat with $100 Lay Odds (to win $50)
Point 5 and 9. $5 flat with $75 Lay Odds (to win $50)
Point 6 and 8. $5 flat with $60 Lay Odds (to win $50)

https://wizardofvegas.com/forum/gambling/betting-systems/2794-craps-strategy-investment-opportunity/55/
The last post by member "goatcabin" shows how to do the math to calculate standard deviation of pass w/odds.
I know in another post by Alan that he also shows how to calculate continual come with odds, but have not been able to relocate it.
I would, but am on vacation so I leave it until I return home next week.

Alan should show up after his birthday I would imagine. It is a good Craps question.

I read at another forum today is Alan's birthday.
Happy Birthday Alan (goatcabin)

Quote: prmdos

My question concerns the standard deviation of continous pass/come bets with 10x odds vs. the standard deviation of the same strategy don't pass/don't come laying odds. It seems to me that the don't pass strategy has a lower standard deviation.

Thanks,

I wouldn't know how to go about calculating the standard deviation (SD) of continous pass/come bets or continuous don't pass/don't come bets, but I did calculate the SD of a single pass bet and a single don't pass bet each with 10x odds. I get an SD of 10.809 for the pass bet and 10.808 for the don't pass bet. So you're right, the don't pass has the lower standard deviation, but not by much. The difference must be due to the don't pass push on 12.

waltomeal,

I think your point about skewness is very important in this question since my point really revolves around risk of ruin vs pass/come bet. These outcomes are not normal distributions I believe.

Quote: prmdos

My question concerns the standard deviation of continous [sic] pass/come bets with 10x odds vs. the standard deviation of the same strategy don't pass/don't come laying odds.
It seems to me that the don't pass strategy has a lower standard deviation.
Thanks,

Simulation results (400 dice roll sessions)
continuous pass-come: 1unit/10x = $308.88 SD Skew0.26
continuous Dpass-Dcome: 1unit/10x = $303.88 SD Skew -0.3

Quote: ChesterDog

I wouldn't know how to go about calculating the standard deviation (SD) of continous pass/come bets or continuous don't pass/don't come bets,

The best and fastest way to calculate this is with a simulation because the bets do not all resolve at the same time.
Alan Shank has a few threads around showing the variance of a different number of come bets made but no formulas.

The sim results seem to be 20% to 50% higher, depending on the number of odds taken, than just one line bet with the same number of odds.

More on this coming in another thread
Sally