Dealer Giving +EV Bet In Craps?
March 21st, 2011 at 3:57:43 PM
permalink
I recently visited a casino that had $3 craps tables and allowed 20X odds. Playing full odds is supposed to be a house edge of 0.1%.
I noticed on a couple of occasions, more than one dealer would give an extra dollar on certain odds bets placed behind points of 5 and 9.
Here is how it went: one of us would place the $3 pass line bet, and when a point was 5 or 9, we backed it up with $16 (which would pay true odds of $24). Instead, some of these dealers would simply drop a $25 green chip for the win after the point hit. This makes the odds bet on a 5 or 9 a +EV bet by my calculation.
I guess my question is if a casino has lazy dealers that drop the extra dollar, is it enough to overcome the house edge? I assume not. Can anyone run a simulation to determine how much it lowers the house edge? Would it be optimal to start playing $16 behind these points, while playing full odds on all other points? And any ideas on just how lazy the dealers would have to get to completely overcome the house edge (i.e. would paying $50-$32, $75-$48 on odds further mitigate that edge?)
I'm not sure I have the mathematical chops to figure the expected return in these situations.
I noticed on a couple of occasions, more than one dealer would give an extra dollar on certain odds bets placed behind points of 5 and 9.
Here is how it went: one of us would place the $3 pass line bet, and when a point was 5 or 9, we backed it up with $16 (which would pay true odds of $24). Instead, some of these dealers would simply drop a $25 green chip for the win after the point hit. This makes the odds bet on a 5 or 9 a +EV bet by my calculation.
I guess my question is if a casino has lazy dealers that drop the extra dollar, is it enough to overcome the house edge? I assume not. Can anyone run a simulation to determine how much it lowers the house edge? Would it be optimal to start playing $16 behind these points, while playing full odds on all other points? And any ideas on just how lazy the dealers would have to get to completely overcome the house edge (i.e. would paying $50-$32, $75-$48 on odds further mitigate that edge?)
I'm not sure I have the mathematical chops to figure the expected return in these situations.
March 21st, 2011 at 4:15:05 PM
permalink
Sure you do.
I'm confused though. If you are backing up $16 odds, do you get paid a total of $27 or $28. If were the dealer, I would drop $3 on the pass and a quarter on the back and take away the penny. Are you sure the dealer didn't take the penny on top of your odds? When I play craps and am using $16 odds, the dealer will drop a quarter and take away the penny.
But on the 5, the HA by paying 25 instead of 24 with a $3 pass is (($28 x 4/10 - $19 x 6/10) / 19) lowers the HA on the 5 and 9 from 3.16 to 1.05 percent, not enough to reduce the HA overall below zero.
I'm confused though. If you are backing up $16 odds, do you get paid a total of $27 or $28. If were the dealer, I would drop $3 on the pass and a quarter on the back and take away the penny. Are you sure the dealer didn't take the penny on top of your odds? When I play craps and am using $16 odds, the dealer will drop a quarter and take away the penny.
But on the 5, the HA by paying 25 instead of 24 with a $3 pass is (($28 x 4/10 - $19 x 6/10) / 19) lowers the HA on the 5 and 9 from 3.16 to 1.05 percent, not enough to reduce the HA overall below zero.
-----
You want the truth! You can't handle the truth!
March 21st, 2011 at 4:16:46 PM
permalink
I doubt the dealer was overpaying you. In my experience, dealers handle in-game color ups by paying odds + flat together, so you were probably getting 1 green and 2 white ($1) chips for a total of $27, rather than $24 odds + $3 flat.
If you *were* getting paid more than you should have been paid -- that is, you were receiving $3 on the line bet and $25 on the odds -- then your "odds" bet is worth 40c every time you make it. That's more than enough to overcome the -4c EV of each $3 line bet and put you ahead. Optimal play in that scenario, assuming the dealers didn't incorrectly overpay other odds amounts, would be to make $3 line bets (pass/come) continuously, only make $16 odds bets behind points of 5 and 9, always work odds, and then you'd expect to make about 4.6c/roll or roughly $4-5/hour. Of course, $5/hour isn't worth it as an advantage play...
If you *were* getting paid more than you should have been paid -- that is, you were receiving $3 on the line bet and $25 on the odds -- then your "odds" bet is worth 40c every time you make it. That's more than enough to overcome the -4c EV of each $3 line bet and put you ahead. Optimal play in that scenario, assuming the dealers didn't incorrectly overpay other odds amounts, would be to make $3 line bets (pass/come) continuously, only make $16 odds bets behind points of 5 and 9, always work odds, and then you'd expect to make about 4.6c/roll or roughly $4-5/hour. Of course, $5/hour isn't worth it as an advantage play...
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice."
-- Girolamo Cardano, 1563
March 21st, 2011 at 5:07:10 PM
permalink
Are you absolutely sure he wasn't giving you a green and pocketing a white? That's what I would have done. *As the above mentioned*
Its - Possessive; It's - "It is" / "It has"; There - Location; Their - Possessive; They're - "They are"
March 21st, 2011 at 6:00:05 PM
permalink
It was dealer-specific. A couple of the dealers definitely did not take the $1 back (more likely out of confusion than out of habit). I didn't play the $16 odds enough to get a feel for whether every dealer at this casino would do it (most of the time I was placing $30-$50 odds bets).
It probably isn't practical to find these conditions often or for very long, but when I saw the overpay a couple of times, I immediately thought about how it would change the EV and optimal strategy.
So, are you saying in these conditions play Pass Line and Come bets for ($3) until you have the 5 and 9 both covered, place $16 odds bets behind those points, and no odds behind any other points you may have? I suppose playing odds on those changes house edge, but not EV.
It probably isn't practical to find these conditions often or for very long, but when I saw the overpay a couple of times, I immediately thought about how it would change the EV and optimal strategy.
So, are you saying in these conditions play Pass Line and Come bets for ($3) until you have the 5 and 9 both covered, place $16 odds bets behind those points, and no odds behind any other points you may have? I suppose playing odds on those changes house edge, but not EV.
March 21st, 2011 at 6:33:25 PM
permalink
Somewhere down the road my analysis went wrong.
For normal 5x odds, you can calculate the EV and the HA:
EV = 3*4/36+6/36*(33*3/9-18*6/9)+8/36*(25.5*4/10-18*6/10)+10/36*(21*5/11-18*6/11) = -.04242 per pass line bet (this coincides with -0.01414 based on a $1 bet).
HA = EV / average bet = EV / (3*12/36 + 18*24/36) = 0.326 percent (which matches the wizard).
On a 5x table where you now put down $16 odds on the 5 and 9 and get paid 25/16 on the 5 and 9:
EV = 3*4/36+6/36*(33*3/9-18*6/9)+8/36*(28*4/10-19*6/10)+10/36*(21*5/11-18*6/11) = 0.04646 per pass line bet (Player advantage)
HA = EV / average bet = EV / (3*12/36 + 18*16/36 + 19*8/36) = 0.351 percent PLAYER ADVANTAGE.
In the long run, it represents a swing of 8.89 cents per pass line bet. Over 100 come out rolls, an $8.89 swing to a player and a $4.65 player advantage.
For normal 5x odds, you can calculate the EV and the HA:
EV = 3*4/36+6/36*(33*3/9-18*6/9)+8/36*(25.5*4/10-18*6/10)+10/36*(21*5/11-18*6/11) = -.04242 per pass line bet (this coincides with -0.01414 based on a $1 bet).
HA = EV / average bet = EV / (3*12/36 + 18*24/36) = 0.326 percent (which matches the wizard).
On a 5x table where you now put down $16 odds on the 5 and 9 and get paid 25/16 on the 5 and 9:
EV = 3*4/36+6/36*(33*3/9-18*6/9)+8/36*(28*4/10-19*6/10)+10/36*(21*5/11-18*6/11) = 0.04646 per pass line bet (Player advantage)
HA = EV / average bet = EV / (3*12/36 + 18*16/36 + 19*8/36) = 0.351 percent PLAYER ADVANTAGE.
In the long run, it represents a swing of 8.89 cents per pass line bet. Over 100 come out rolls, an $8.89 swing to a player and a $4.65 player advantage.
-----
You want the truth! You can't handle the truth!
March 22nd, 2011 at 2:14:46 AM
permalink
Quote: hardchuck1I recently visited a casino that had $3 craps tables and allowed 20X odds. Playing full odds is supposed to be a house edge of 0.1%.
Somewhat related...
I seem to recall casinos in Illinois are prohibited from rounding down. Therefore, if a dealer wasn't paying attention and a player bet $15 on a 5; it would pay them $23 instead of $22.50. Obviously, 50c isn't worth the time, but thought it was an interesting side note. Illinois has other rules that I haven't seen in other jurisdictions, among them--no coins in the tray and aggregate maximums are prohibited.
March 30th, 2011 at 12:49:06 PM
permalink
Sometimes I'll get overpayed for a winner by $1 or $2...I'll usually just put the extra on the next point's odds, for the boys.
Gambling calls to me...like this ~> http://www.youtube.com/watch?v=4Nap37mNSmQ
March 30th, 2011 at 4:31:08 PM
permalink
I've noticed a similar phenomenon on the Don't side.
Sometimes on no 6 or no 8, I'll lay $42. The correct payoff is $35, but sometimes dealers will pay me $36. I believe they do this because $42 is the correct payoff on $36 place bets. And a $36 place bet is quite common, as people sometimes start with $30 place bets and bump them up one unit ($6) each time they win. Usually a dealer will do this once or twice, then eventually the boxman will correct him. I've tried telling the dealers they're wrong but they either don't listen or insist they're right. So I don't bother anymore.
This has happened to me in many different casinos in multiple states. If you're looking to pocket an extra buck or two on the Don't side it's worth trying. But I mostly play for bigger stakes now.
Sometimes on no 6 or no 8, I'll lay $42. The correct payoff is $35, but sometimes dealers will pay me $36. I believe they do this because $42 is the correct payoff on $36 place bets. And a $36 place bet is quite common, as people sometimes start with $30 place bets and bump them up one unit ($6) each time they win. Usually a dealer will do this once or twice, then eventually the boxman will correct him. I've tried telling the dealers they're wrong but they either don't listen or insist they're right. So I don't bother anymore.
This has happened to me in many different casinos in multiple states. If you're looking to pocket an extra buck or two on the Don't side it's worth trying. But I mostly play for bigger stakes now.
March 30th, 2011 at 6:34:06 PM
permalink
Quote: hardchuck1I guess my question is if a casino has lazy dealers that drop the extra dollar, is it enough to overcome the house edge? I assume not.
The house edge on a $3 bet is 1.4% or 4.2 cents per bet.
If every time you land on a 6 or an 8 and then win & $16 free odds (which is 2*25/396 or about one eighth of the time) you get a free dollar, then that is roughly 12.5 cents per bet, which is more than enough to over 4.2 cents. Specifically you are coming out 8.38 cents per come out roll. Since you can only get roughly 30 come out rolls per hour, it won't make you rich.
Hopefully, this table will show you how the odds for the pass line bet in craps are calculated. The equations are pretty simple. If you start on a "come bet" there are 12 ways to get back to the "come bet", 8 of them involve a win, and 4 involve a loss.
For points, the ways of landing on the point, are the same as the way you win (since you are just hitting your point again).
| states | come out | land 4 | land 5 | land 6 | land 8 | land 9 | land 10 | Sum |
| happening | 12 | 3 | 4 | 5 | 5 | 4 | 3 | 36 |
| win | 8 | 3 | 4 | 5 | 5 | 4 | 3 | |
| lose | 4 | 6 | 6 | 6 | 6 | 6 | 6 | |
| win+lose | 12 | 9 | 10 | 11 | 11 | 10 | 9 | |
| prob happen | 1/3 | 1/12 | 1/9 | 5/36 | 5/36 | 1/9 | 1/12 | divide by 36 |
| prob win if happens | 2/3 | 1/3 | 2/5 | 5/11 | 5/11 | 2/5 | 1/3 | divide win/(win+lose) |
| prob win | 2/9 | 1/36 | 2/45 | 25/396 | 25/396 | 2/45 | 1/36 | 244/495 |
| 251/495 | ||||||||
| - 7/495 |
