Calculating house edge in Craps for uncommon payouts?

Hi,

I recently found this new online casino where you can gamble using Bitcoin Cash. They claim that their games are provably fair, and that they have among the lowest house edge in the business (with a 99% expected return). I would appreciate if someone could help me calculate the house edge for their place and buy bets on their craps game, in order to figure out when to choose which bet, and to see how they compare to Vegas. In Vegas I normally place the 6 & 8 for a 1.52% house edge, and the 4 & 10 for a 1.67% house edge (paying $1 commission on a $25 bet AFTER a win only). Especially I don't know how to calculate and compare the house edge on buy bets depending on if you pay commission on every bet vs only when when you win. Any help would be greatly appreciated.

Here are their payouts:
All Buy bets: Pay 1% commission up front and receive true odds on win.
Place 4 & 10: Pays 39 to 20.
Place 5 & 9: Pays 29 to 20.
Place 6 & 8: Pays 29 to 25.

Interestingly, I can easily see that their payouts on 4/10 and 5/9 place bets are higher than in Vegas. However, because they chose to pay 29 to 25 on the 6 & 8, I guess to be consistent with their "xx to 20 payout" on the other numbers, that's actually lower than 7 to 6. So that's not good. I guess it's because if they went up to the next value higher, 30 to 25, then the house edge would be 0%. So I'm especially wondering how the house edge on a 29 to 25 place bet payout would compare to a buy bet with a 1% commission upfront.

Also, if someone has an excel formula or ready-to-go spreadsheet where you can punch in your variables to calculate the house edge, that would be awesome.

Here's the general formula to calculate player EV:

EV = ( 1 + O ) * p - 1, where O is the odds paid, and p is the probability of winning.

For 4 or 10, p = 1/3. For 5 or 9, p = 2/5. And for 6 or 8, p = 5/11.

Place 4 & 10: Pays 39 to 20. EV = (1+39/20)*(1/3)-1 = -1.667%.
Place 5 & 9: Pays 29 to 20. EV = (1+29/20)*(2/5)-1 = -2%
Place 6 & 8: Pays 29 to 25. EV = (1+29/25)*(5/11)-1=-1.818%

With 1% commission paid up front:
Buy the 4 or 10: EV = [ 1 + (2-.01)/(1+.01) ]*(1/3)-1 = -0.990%
Buy the 5 or 9: EV = [ 1 + (3-.02)/(2+.02) ]*(2/5)-1 = -0.990%
Buy the 6 or 8: EV = [ 1 + (6-.05)/(5+.05) ]*(5/11)-1 = -0.990%

Quote: Don911

Hi,Also, if someone has an excel formula or ready-to-go spreadsheet where you can punch in your variables to calculate the house edge, that would be awesome.

ok, I have what you want. had to clean it up first

here is Excel in Google
https://goo.gl/6uLxbf

the yellow cells should be changed only
I did not protect the sheet so be careful!



the buy bets are actually really easy as long as you know the values
(I included the easy part too)
for the edge

up front Buy bets
formula
$vig/(wager+$vig)

on win Buy bets
formula
$vig/(wager+$pays)

try it out, really sweet too!

hope this helps out
have fun!
Sally

Thanks to both of you for those quick answers and the spreadsheet! So according to your numbers, it seems as if I shouldn't use any place bets at all at this casino, but instead use only buy bets, regardless of which number I wish to bet on. It will be interesting to compare the win/loss rate at this casino, compared to Vegas where the house edge is around 0.5% higher on the place/buy bets that I normally use. Thanks again!

P.S. Has anyone found an online casino that has an even lower house edge than this one on place/buy bets?

I’ve never played online but those are great odds.

Besides being the best play, the math is much easier for the buy bets...1% commission and true odds instead of 39/20, 29/20, 29/25.

Though I’m surprised they didn’t set the 6&8 place payouts at 47/40 or 59/50...since they have lowered the edge on everything else.

Quote: Don911

and the 4 & 10 for a 1.67% house edge (paying $1 commission on a $25 bet AFTER a win only).

that 1.67% edge is for $20 unit bets (like $20, $40, $60 etc)
1/60, 2/120, 3/180 and so on

your $25 Buy with just $1 on a win edge is 1/75 or about 1.33%
so you do just fine there
sweet!

Quote: Don911

Especially
I don't know how to calculate and compare the house edge on buy bets depending on if you pay commission on every bet vs only when when you win.
Any help would be greatly appreciated.

hope we helped out

I never played craps online
hope you do well
Sally

Quote: Ace2

Though I’m surprised they didn’t set the 6&8 place payouts at 47/40 or 59/50...since they have lowered the edge on everything else.

but most all place bettors place the 6&8 so they made it higher so the casino makes more. That has to make the shareholders happier (if there are any)

now, imo, most do not know how to figure out the house edge of non-standard craps payouts and even when they know it could be a higher edge, I still think most would still place the 6&8 as it is 'in their style of play'

Sally

Quote: mustangsally

that 1.67% edge is for $20 unit bets (like $20, $40, $60 etc)
1/60, 2/120, 3/180 and so on. Your $25 Buy with just $1 on a win edge is 1/75 or about 1.33%
so you do just fine there

That's great! I didn't think of that. I always bet in increments of $25, and the commission I pay in Vegas is always $1 on $25, $2 on $50, $4 on 75 and then the full 5% ($5) on $100. So with $25 and $50 bets buying the 4 and 10 in Vegas, the vig is even lower than placing the 6 or 8. Nice! :-)