I spent several hours on a new hack, in the end I think it fails my own criteria because I was unable to reduce the variance (chance of loss) despite getting the house edge down as low as 1/216 or 0.4%. I thought to share it here regardless, so you can see my logic, and where it broke down.
The Goal – Get free comps with minimal to zero risk.
Comps are fantastic things, back in January 2013 I wrote a post summarizing my 2012 comps, and the total was about $12,000 for that year, including 3 pretty major vacations. The trouble is that comps are kickbacks based upon what the house plans to win from you, so its a losers game.
The Comp Calculation is simple: Comp Amount = Avergage Bet x Time x House Edge
Another way of looking at this is that it is your Theoretical Loss x comp multiplier (a kickback)
The Gig – colluding to reduce risk of loss
Casino games come in two varieties, those that play against the house, and those that the house delivers on behalf of the players. The former cannot work for this gig, but the latter do, and it comes down to exploiting games with minimal edge to succeed. The candidates were: Roulette, Craps and Baccarat. All three of these games allow you to bet against another person, and all have a different ‘Vig’ (short for Vigorish, aka the Juice, or the house take) roulette is an easy one to explain:
In roulette there are 36 numbers, 18 red, 18 black, and either 1 or 2 zeros (EU wheel has only 1 zero, whereas the American version has 2) If we take the EU version:
- Bob bets $100 on Black
- Dave bets $100 on Red
For 36/37 spins of the wheel, we will have no event for the house, it will take Bobs money to pay Dave, and vice versa. But over time, 1/37 spins should be Zero, and the house wins.
The exploit that exists here from the method of comp calculation. While all casinos run on the same basic premise (along with some discretionary ability) not all kick back at the same ratio. For example, if your theoretical loss (theo) is $100 you may find a top class Casino like the Wynn kicking back $27 whereas a lower end off strip casino kicks you $40.
For Roulette, the 1 in 37 loss rate was too high for me, though the chances are, at 1 spin every 3 minutes that you wouldn’t see a zero until around 45 minutes into the game.
Craps may be the solution -Craps 101
Craps is a game of two halves, and two personalities. The two halves are ‘The Come Out Roll’ and the game proper.
Come out roll: The game starts like this. We are seeking to establish a point number, which can be either 4,5,6,8,9,10. Every number you roll on the come out has an impact. 4,5,6,8,9,10 will result in a point being established (the game proper is now afoot) rolling a 7 or 11 will win on the Pass Line (PL), lose on the Don’t Pass Line (DPL); 2,3 will lose on the PL, and win on the DPL… 12 will lose on the PL and push on the DPL.
2,3 and 12 are called Craps numbers, and 12 is special because it is the house edge.
Once we have a point established (a 4,5,6,8,9.10), the Pass Line wins when you roll that number again before a 7 rolls, and loses if the 7 rolls first. The DPL is the exact opposite, losing if the point number repeats before the 7 comes in, and winning if the 7 rolls first.
So that’s the game, two halves (Come Out Roll, and Point Established) and two personalities (PL, and DPL)
It is worth noting that bets behind the PL and DPL are called Odds and are the only bet in the casino with zero edge for the house, however, most casinos will not rate this bet when assigning comps (though they may on discretionary comps from the game supervisor). What this means is that if you were to bet behind the line you could put down any amount, and as long as you had a collaborator to offset this bet, you would have no exposure in the event of a win or loss.
Checking the Math
This is the first time the gig failed. It was late at night and I was lazy, so instead of figuring out the math behind the game outlined above, I just googled ‘pass and don’t pass house edge’ and came across this thread from Wizard of Vegas (the forum attached to Wizard of Odds, a very well respected gaming site) unfortunately thread was started by a guy who didn’t understand the basic premise of probability, but the problem was the answers given were actually incorrect too. At first blush I took them as gospel, but then I did a double take and realized they made no mathematical sense. The comments were, if you play both the PL and DPL simultaneously the house edge becomes the sum of the individual house edges:
- Regular Game PL House Edge = 1.41%
- Regular Game DPL House Edge = 1.36%
That thread stated the house edge of playing both would be 2.77%, which is 1/36 (the same odds as rolling a 12)
However, I thought that this couldn’t be the case, because you don’t lose on a 12 all the time, and you only lose half your money on a 12. Logically speaking, if you had two craps tables side by side, on a regular one and one where you lost all your money (both PL and DPL) on a 12 at any time (regardless of phase of game) they would be different beasts, and the 2.77% is in fact a fallacious number due to this.
I went on to join that forum and start asking questions, I am not a statistician (I did elect Stats in high school, but I also dropped out of high school…) but I have a good eyeball for such things, and now I have the actual number reduced to 0.4% by normalizing the game rules above.
My logic was that in order for you to lose using the PL/DPL gig you need a 12 to roll on the Come Out only, which could be then expressed mathematically as the chances of rolling a 7, then a 12 (not just the chances of rolling a 12) That would be:
1/6 * 1/36 for 1/216 or 0.4%
We have a winner!
The spread here is that if you find a casino that will kick back about 1/3 or more of their Theo, and the Theo for craps is 1.385% (2.77%/2) you could capture comps of 0.46% for a house edge of 0.4%.
While that might sound like a minor spread of 0.06% what you need to consider is that when the house wins it will only take half of your average team bet, but you are being comped on your total average team bet.
- Bob bets $100 PL Theo (loss) for Bob would be 1.41 Comp at 1/3 would be $0.47
- Dave bets $100 DPL Theo (loss)for Dave would be $1.36 Comp at 1/3 would be $0.45
Total comp would be $0.92 for $200, but the expected loss of 0.4 would only impact Bobs play, because Dave can never lose (12 crap is a push, not a loss) so you would actually expect to lose 0.4% of the time, but the impact would be halved. The spread now is a more healthy 0.52.
Why it’s still a failure
I deemed this a failure because of variance. Over infinity, playing a regular game of craps with a 1/216 loss rate you could roll 215 times before the event of a 7 then 12 rolling. However, each “come out roll” has a 1/36 chance of the event occurring. What’s more, statistics are taken over infinity, and there is nothing stopping this theory blowing up by a team entering a dice game and having 10 x 12s roll back to back. The chances of this happening are (1/36 * 1/36) to the power of 10, which is very unlikely, but that isn’t going to make you feel any better if it should happen!
This actually ties into the same fault with stock market returns when people cite an average of X%, as the duration of the investment (or the craps roll) is such as small relative segment and variance is massive.
I hope you enjoyed my failure here. I learned a lot from it, and interestingly enough, by writing up the failure rather than discarding it I actually found a couple of different ‘tricks’ as to how the tables can turn further in your favor, and actually make this a viable strategy. Due to the length I’ll post it as a Part 2, Success! Hacking Comps.
PS – for the statisticians among you, do you see a difference in calculating 7, 12 roll probability with 7 [non point number eg 2,3,7,11] then the 12? I’m wrapping my head around that now.