The "Golden Dice Challenge" is a prop bet at the MGM Grand in Detroit. It's one of several new bets being offered to craps players at casinos across the country. The Wizard of Odds calculates the "Vig" on this bet to be a whopping 27% But as our guest writer, Chuck D. Bohnes points out, despite the high vig, this bet may be easier to beat than a placed 5. Here's how he sees it:
By "Chuck D. Bohnes"
Can you beat the Golden Dice Challenge?
Skill thresholds for parlay-type prop bets:
The Golden Dice Challenge proposition bet has a whopping 27% vigorish ... and, yet, the skill threshold to beat it is less than the skill threshold needed to have an advantage on placing the 5. One actually only need overcome a -3.29% house advantage per decision.
A player who throws random come-out rolls and attains an SRR of 1 in 6.55 on the point cycle will break-even. Is that skill level a lot lower than you guessed when you saw the vigorish of 27%?
The Golden Dice Challenge can be deconstructed into eight parallel parlay bets. This wager, therefore, is subject to the same cumulative vigorish effect inherent to any parlay-type bet.
Let’s examine a simple parlay of the Big Red as an example of the cumulative vigorish effect. The Big Red is a prop bet that typically pays five FOR one (four TO one) if the next roll is any seven. The true odds are five to one against rolling a seven. The house advantage on Big Red is 16.7%.
Note that even though the cumulative vigorish is higher for the parlay bets, the SRR needed to overcome the house advantage does not change.
A Skilled Shooter’s Break-Even:
If a shooter can de-randomize the dice enough to overcome the house advantage on a single Big Red bet, then that same skill level will allow that player to overcome the parlay bets, despite their higher cumulative vigorish.
Suppose a skilled shooter rolls one seven every five rolls. That skilled player’s expected value (EV) on the Big Red bet is zero. Similarly, that same skill level (one seven every five rolls) will provide an EV of zero for each of the parlay bets.
Cumulative Vigorish Disguises Required Skill:
Parlay wagers have very high vigorishes because of the cumulative effect. The vigorish for a parlay bet, thus, muddles our ability to easily recognize the skill threshold necessary to beat it. One way to calculate the skill threshold required to beat a parlay bet is to calculate an "Internal Rate of Return." Yes, the same IRR you calculate for your traditional investments and businesses.
Using IRR Calculations to Measure Required Skill:
We can use the Golden Dice Challenge as an example of how to calculate the IRR/Skill Threshold needed to beat a parlay-type proposition bet. The Golden Dice Challenge has a pay-off schedule dependent upon the number of passes a shooter makes before the first seven-out. For this prop bet, come-out craps are a blank, a no decision. A single successful decision, therefore, is rolling either a natural or a point winner before rolling a seven-out.
First, create a table calculating the expected value (EV) for every number of consecutive successful decisions. Note that the sum of the EV column is the house advantage. The following table assumes a random roller.
The probability column is calculated as: probability(success)^(# of successes) * probability(seven-out).
The EV column is simply probability * profit (loss).
Note that for the Golden Dice Challenge the probability(seven-out) is 1 minus probability(success). The probability(success) for a random roller is approximately 55.4545%. The probability(seven-out) for a random roller is approximately 44.5454%. Remember these percentages apply specifically to this prop bet and are not the percentages for pass-line decisions.
Second, calculate the internal rate of return on the EV column. One fast way is to insert in a spreadsheet the formula "=IRR(EV column)," where EV column is the array of numbers under your EV heading.
Results. If you inserted probabilities for a random roller, then the resulting “IRR” represents the Skill Threshold per Decision for the Golden Dice Challenge that you must overcome, which is a house advantage per decision of 3.29%. If you used a skilled shooter’s probabilities in column B, then the “IRR” will indicate the implied advantage per decision in the Golden Dice Challenge. Keep in mind that the advantage per decision is a weighted average over eight parallel parlay-type bets.
If you are a random roller, then the high cumulative vigorish on parlay-type prop bets is very real and very expensive. However, if you can consistently de-randomize the dice then you should calculate the Skill Threshold required to beat a new parlay-type prop bet before you let the high cumulative vigorish scare you away.
I have no conviction that I, or anyone else, can de-randomize dice in a casino. If you believe that you can, well, then that's your business, not mine.
Chuck D. Bohnes
For a thorough explanation of this bet and other Craps "Side" "Prop" and other Craps bets, visit Michael Shackelford's Wizard of Odds site.
"Chuck" is member of our private forum, where this APC topic and many others were originally discussed.