Craps Promotion at
February 24th, 2012 at 11:41:41 PM
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Normally I don't post questions asked to me by Email, but this one is "Ask the Wizard" worthy so I am making an exception. Here is the question.
Hi Wizard, I wanted to ask you a question that is intriguing and if you want, you can post to your site. A river boat casino in Chicago is running a promo that if you hit all 6 unique points, they will give the shooter $4000. In this scenario, does a player have an edge playing $5 on the pass only on his rolls? Thanks! Matt
I worked out the answer, but I won't deprive you of the fun of working it out on your own. The hardest part is what is the average number of come out rolls (pass line bets made) per shooter?
From my craps appendix 5 we know from the Fire Bet that the probability of a shooter making all six points is 0.000162.
Enjoy.
Hi Wizard, I wanted to ask you a question that is intriguing and if you want, you can post to your site. A river boat casino in Chicago is running a promo that if you hit all 6 unique points, they will give the shooter $4000. In this scenario, does a player have an edge playing $5 on the pass only on his rolls? Thanks! Matt
I worked out the answer, but I won't deprive you of the fun of working it out on your own. The hardest part is what is the average number of come out rolls (pass line bets made) per shooter?
From my craps appendix 5 we know from the Fire Bet that the probability of a shooter making all six points is 0.000162.
Enjoy.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 25th, 2012 at 12:07:38 AM
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Was not this question already in an Ask The Wizard column?
The Grand Victoria Casino in Elgin, Illinois offers a promotion called "Craps for Cash."
about 2/3 way down.
Same promo?
https://wizardofodds.com/ask-the-wizard/187/
The Grand Victoria Casino in Elgin, Illinois offers a promotion called "Craps for Cash."
about 2/3 way down.
Same promo?
https://wizardofodds.com/ask-the-wizard/187/
winsome johnny (not Win some johnny)
February 25th, 2012 at 3:18:06 AM
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I figure this gives the $5 player an 11% advantage.
Method 1:
((0.492738 * 5) * (0.000162 * 4005) * (0.5071 * -5)) / 5 = 0.577 / 5 = 0.1154 = 11.54%
Method 2:
Sim'd it out for 1,000,000 shooters. Code is here. Output was $0.529653 expected win per shooter at $5 for an advantage of 10.5%. I'm guessing my sim was wrong.
Method 1:
((0.492738 * 5) * (0.000162 * 4005) * (0.5071 * -5)) / 5 = 0.577 / 5 = 0.1154 = 11.54%
Method 2:
Sim'd it out for 1,000,000 shooters. Code is here. Output was $0.529653 expected win per shooter at $5 for an advantage of 10.5%. I'm guessing my sim was wrong.
February 25th, 2012 at 4:07:48 AM
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I get the free 4k is worth about 13 cents per come out roll. Since the come out roll is negative EV about 7 cents per roll, the overall bet is around plus 6 cents positive EV, or around 1.2%.
February 25th, 2012 at 5:34:42 AM
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Quote: WizardHi Wizard, I wanted to ask you a question that is intriguing and if you want, you can post to your site. A river boat casino in Chicago is running a promo that if you hit all 6 unique points, they will give the shooter $4000. In this scenario, does a player have an edge playing $5 on the pass only on his rolls? Thanks! Matt
Not to derail what I believe is to be a math thread, but unless the poster is on the Indiana side of Chicago and at Majestic Star it seems more likely the minimum bet is going to be $10, and quite possibly $15 for pass line bets.
To make it more math friendly (and realistic), what is the maximum, minimum bet for this to be at least a break-even scenario. I should also note that if you're factoring in odds, most casinos in the Chicago area offer EITHER 100x odds, or 10x odds.
"One out of every four people are [morons]"- Kyle, South Park
February 25th, 2012 at 8:10:51 AM
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I didn't know I addressed this promotion before. However, I think my answer was slightly off. The shooter will have to make multiple pass line bets to achieve the six points, depressing the value a little. The answers I've seen so far, including my own, didn't take this into account. So, what is the expected number of come out roll bets per shooter?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 25th, 2012 at 8:36:33 AM
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Yes, slightly off.Quote: WizardI didn't know I addressed this promotion before. However, I think my answer was slightly off. The shooter will have to make multiple pass line bets to achieve the six points, depressing the value a little. The answers I've seen so far, including my own, didn't take this into account.
So, what is the expected number of come out roll bets per shooter?
from:
Ask the Wizard #123
Looks like the answer there also has another answer totally unrelated appended to it.
a) expected number of rolls per shooter: 8.525510204 (=1671/196)
b) length of each decision: 3.375757576 (=557/165)
So, I get
c) expected number of come out roll bets per shooter: 2.525510204 (=495/196) (a/b)
winsome johnny (not Win some johnny)
February 25th, 2012 at 9:04:52 AM
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Also,Quote: WizardSo, what is the expected number of come out roll bets per shooter?
If the probability of a seven-out on any given hand is =(784/1980)-from the perfect 1980 table- the expected number of come out roll bets per shooter is just the inverse or 1980/784
added:
Alan, "goatcabin" also shows this
Craps Forum | Posted: 16 February 2010
February 25th, 2012 at 10:40:23 AM
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Yes, the expected number of come out rolls per shooter is 1980/784 = 2.5255.
The house edge on the pass line is 7/495 = 1.41%.
At $5 each, the expected cost would be $5*(7/495)*(1980/784) = $0.1786.
From the Fire Bet we know the probability of the shooter hitting all six points is 0.00016243475. The value of the $4000 bonus for doing is is 0.00016243475*$4000 = 0.649739.
The typical shooter can expected to bet $5*2.522 = $12.61.
I submit for the consideration of the forum that for the $5 shooter the advantage on the pass line bet is (0.649739 - 0.1786)/12.61 = 3.74%.
The house edge on the pass line is 7/495 = 1.41%.
At $5 each, the expected cost would be $5*(7/495)*(1980/784) = $0.1786.
From the Fire Bet we know the probability of the shooter hitting all six points is 0.00016243475. The value of the $4000 bonus for doing is is 0.00016243475*$4000 = 0.649739.
The typical shooter can expected to bet $5*2.522 = $12.61.
I submit for the consideration of the forum that for the $5 shooter the advantage on the pass line bet is (0.649739 - 0.1786)/12.61 = 3.74%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 25th, 2012 at 11:42:04 AM
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I agree.Quote: WizardI submit for the consideration of the forum that for the $5 shooter the advantage on the pass line bet is (0.7440 - 0.1786)/12.61 = 4.48%.
fire.bet is an auto bet file for WinCraps for this exact promotion.
' This system tracks the points that a shooter makes in a hand.
' The shooter wins $4000 if all 6 points (4,5,6,8,9,10) are made in any order
' Repeat points are allowed. All that matters is that all 6 numbers are made.
Interesting. This sparked interest back on 2007.
Of course I had to run it, after a few small adjustments and the 4.48% looks to be the correct value.
So betting $20 or less on the pass would be a players advantage and no players advantage above $20.
Very different from the Wizard's original $45 wager answer
winsome johnny (not Win some johnny)
February 25th, 2012 at 4:03:35 PM
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I disagree.
The probability to the shooter hitting all 6 points in a fire bet is .0001621 from your table, not .0000184, so the $4000 bet has an EV of .6463
The average bet is 1980/784 x 5 = 12.6276
The advantage then is (.6463 -.1786)/12.6276 = 3.70%
By the way, the odds that the player wins the bonus after n points is:
n=6 0.0000296
n=7 0.0000421
n=8 0.0000362
n=9 0.0000246
n=10 0.0000145
n=11 0.0000078
n=12 0.0000040
n=13 0.0000019
n=14 0.0000009
....
The probability to the shooter hitting all 6 points in a fire bet is .0001621 from your table, not .0000184, so the $4000 bet has an EV of .6463
The average bet is 1980/784 x 5 = 12.6276
The advantage then is (.6463 -.1786)/12.6276 = 3.70%
By the way, the odds that the player wins the bonus after n points is:
n=6 0.0000296
n=7 0.0000421
n=8 0.0000362
n=9 0.0000246
n=10 0.0000145
n=11 0.0000078
n=12 0.0000040
n=13 0.0000019
n=14 0.0000009
....
-----
You want the truth! You can't handle the truth!
February 25th, 2012 at 4:14:45 PM
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I am no math major, but I think the odds are 10 to 1 against. Or maybe slightly higher.
February 25th, 2012 at 5:02:07 PM
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Are we all in a hurry today?Quote: boymimboThe probability to the shooter hitting all 6 points in a fire bet is .0001621 from your table, not .0000184, so the $4000 bet has an EV of .6463
All are not correct, boymimbo is close.
I see the probability of hitting all 6 points is 0.000162434749269826 from the Wizard's table and his Excel worksheet.
.000162434749 is from my calculation.
ev = 0.649738997
The average bet is (1980/784)*$5 = 12.62755102
The advantage then is (0.649738997-0.178571429)/12.62755102 = 3.7312664% for a $5 pass line wager
and my sim in WinCraps returned 3.75812% from 100 million shooters.(small sample size for the firebet)
(the original version of the fire.bet in my WC stopped after the 6 points were hit.
So that had to be changed and the $4000 had to be added to the bankroll)
$10 wagers 1.1585625%
$15 wagers 0.003009945
$18 wagers 0.000151385
$19 wagers -0.000600867
$20 wagers -0.001277895
February 25th, 2012 at 6:08:23 PM
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care to recheck?Quote: boymimbo
By the way, the odds that the player wins the bonus after n points is:
n=6 0.0000296
n=7 0.0000421
n=8 0.0000362
n=9 0.0000246
n=10 0.0000145
n=11 0.0000078
n=12 0.0000040
n=13 0.0000019
n=14 0.0000009
....
I will also recheck mine.
we do not match
I will see if the Wizard has this broken down.
Lets compare next week!
Go UK Wildcats!
February 25th, 2012 at 7:05:26 PM
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Sorry, clerical error. Using the probability of making all six points of 0.000162434749269826 I get an advantage of 3.74%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
