Is This a Good Promotion?

Stickman,

I have found a local promotion that is as follows. Shooter makes no extra bet and is paid 10X their line bet when they throw 13 rolls between sevens. If you throw a seven on the comeout roll, the count simply resets. You can win multiple times during the same hand. The promo pays a maximum of $500 per win. I won it twice last night at $10.

Could you try to run some numbers that could show what the EV is on this? The promo lasts all month. It seems that it might give an edge off the top. I'm considering playing only a $50 line bet with $50 odds and no other bets and trying to get a heads-up game so that I can throw as many hands per hour as possible.

Wanna fly to Seattle and help?

William

William,

Anytime a casino gives you something for nothing it is a good thing. Let's look at this first from a high level. The pass line bet has a house edge of 1.4%. That means a random shooter will lose 14 cents for every $10 bet on the pass line or $14 in 100 hands. If a shooter was able to go 13 rolls without a 7 only once in every 100 hands, he would win an extra $100 and be ahead $86! I suspect someone may have gotten fired over this promotion.

Let's look at it in a little more detail. A random roller average hand length is about 8.5 rolls. A random roller has one 7 for each 6 rolls on average. This gives him a Sevens-to-Rolls Ratio (SRR) of 1 in 6. The average hand of about 8.5 includes hands of all different lengths. How many of these hands are 14 rolls or more?

While there may be a way to calculate the edge using pure math, I do not know what it is. I do have a software tool that can do the job, however. Smart Craps software can be used to simulate all types of shooters and table payoffs. One can also program virtually any betting system in the software. It gives a plethora of detail about the results obtained from these simulations. So what does it say about how many hands are longer than 14 rolls? According to Smart Craps the percentage of hands of 14 rolls or more is 17.7 percent. Getting paid an extra 10 times your line bet 17% of the time is more than enough to offset the house edge.

There is one problem with this percentage, however, there could be come out 7s in the hands that are 14+ rolls. Fortunately, Smart Craps can be programmed to mimic the promotion by counting the number of rolls without a 7 - so I programmed it. Here is what I did and the results. You mentioned that you could win multiple times on the same hand. I am not sure if you meant that the no-7s counter restarted each time you got paid for 13 non-7 rolls in a row, so I simply allowed only one win of the promotional incentive per hand. This is the most conservative way to calculate the edge.

Out of one million hands, a random shooter will collect the bonus 132,501 times. With a $10 line bet, the bonus will be $100 each time it is collected. By adding the bonus money to the calculated loss of 1.42% of the total amount bet (which Smart Craps accumulated as $25,241,960*) we go from a net loss of $358,420 to a net win of $12,891,680. Dividing this bet the total amount bet yields a player advantage of 51%. RUN don't walk to take advantage of this promotion before the casino goes belly-up - and, by the way, I will see you in eight hours, which is as soon as I can fly to Seattle! There is no way this one will last long and I want to get in on it before someone is fired or the casino goes under.

* The total amount bet is the sum of all pass line bets placed and decided. Each hand can have several line bets placed. For example: a 2, 3, 7, 11, or 12 thrown on come-out will each count as $10 toward the total amount bet. After a point is established, each time it is made (or the shooter sevens out) counts as $10 toward the total bet amount.

As stated in the beginning, anytime the casino gives you something for nothing it is a good thing. Let's look at similar possible promotions to demonstrate how powerful "free" bets are.

• Shooter is paid one times the line bet if they go 13 rolls without a 7. In this case the shooter will win $1,325,010 in a million hands and go from a loss of $358,420 to a net win of $966,590. Dividing the net win by the total amount bet gives a player edge of 3.8%. So even simply paying the pass line bet as a bonus gives the player a hefty edge.
• Shooter has to bet an additional amount up to the pass line amount and is paid 10-to-1 if the shooter goes 13 rolls without a 7. Assuming the shooter bets $10 on the additional bet, the total amount bet will be twice the $25,241,960 or $50,483,920. He will lose $358,420 on the pass line bet. He will win $1,325,010 on the 132,501 he throw 13 time or more and he will lose $13,916,950 on the 1,391,695 time he doesn't throw 13+ rolls without a 7 for a net loss of $12,950,360 and a house edge of better than 25%.

The difference is placing an additional bet rather than getting a bonus without betting anything more. Free bets make a world of difference. Take advantage of them whenever possible.

Follow-up Note: I received this email shortly after the original email:

Stickman,

Well, the night that I found the promo I won it two out of five hands. I drove up there (60 miles) to play it the following week but they had canceled it. Lost too much I guess.

William

May all your wins be swift and large and all your losses be slow and tiny.