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It's More Fun When You Win!

Volume VII : Issue #6

Date June 2007

In This Edition:

A Word From Soft Touch

Fair Market Value in Craps...

Today's Wisdom...

A Labor of Love...

Newsletter Archive Links

Soft Touch

PS If you have any suggestions for the new dicesetter.com website or newsletter please send them to me at Ed@dicesetter.com and I'll have a look and see how we can incorporate them into our future plans.

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Fair Market Value in Craps

Mike in Hawaii

When you place a cheque (OK, a chip) on a craps layout, you can ask an interesting question. How the answer to this question changes based on what point is set, whether or not the next roll is a come out roll, and exactly where on the felt you place it, is quite interesting and instructive.

The basic question is this: Once a $5 red chip is on the felt, what is it really worth? How much should you pay, or be paid, to pick that chip up and call off the bet right now?

Let's have an example. Your friend bets $5 don't pass. The shooter throws a four. Your friend says "Fooyee I never win on fours" and reaches to pick up his chip. What should you do?

The answer might surprise you. The second that $5 chip hit the don't pass line, it was no longer worth $5. When the shooter missed hitting a 7 or 11 on the come out roll and set a point of four, the value of that chip changed again, dramatically.

From moment to moment each chip has a future. There is a finite list of things that can happen to it, both positive and negative. When you take all these things together, with their proper weights and values, both plus and minus, you end up with what that chip is really worth now that it has been bet. This is its Fair Market Value. The table below illustrates all the future paths a chip on the pass line faces and the long term, average probability of each outcome.

When you toss a nickel on the pass line, it instantly changes value. (It is a bit like driving a new car off the lot for the first time.) It is now a $4.93 chip, not a $5 chip. Why? The chart above shows all the things that lie in its future. When they are all added up, they come out about seven cents short of $5.00. Or about 1.4% less than they should total. Where have we seen that percentage before? It is the well known "House Advantage" on a pass line bet.

Now this is the value of the chip awaiting the come out roll, all filled with hope for a natural win. Once the come out roll is over, If the chip still survives to face the "Chasing a Point" phase of the game, its average value (considering all possible points that might be set and the probability of each one) drops to just $4.37. That is a grizzly 12.5% house advantage. Think about that for a minute...

Time's up. The house advantage on a Hard 4 or a Hard 10 bet is just a bit over 11%. The house advantage on a Hard 6 or a Hard 8 is closer to 9%. In short, the future for a poor red pass line chip, which was a once proud $5 American Cash Money Bill, has turned rather sour after missing the natural win on the come out roll.

It gets worse. This $4.37 is the average value after the come out roll. Since we will know by then what point was set, we can re-compute the Fair Market Value of that chip again based on which pair of points, 6 & 8, 5 & 9, or 4 & 10, is actually being chased. Remember the points arrange themselves in pairs with similar math properties.

Check out the bad news. If the point is 6 or 8, then your pass line bet is still worth $4.55. If the point is 5 or 9, its value drops to just $4.00. But if the point is 4 or 10, the damage is massive. The Fair Market Value of that chip would be just $3.33! The house advantage on that poor thing is 33 percent!

No wonder the Casino considers this a "Contract Bet". You would be at a HUGE advantage if you could drop a nickel on the pass line, wait to see if you get craps or a natural win and then if you set a point, just pick up your red chip and put it back in your rail to await the next come out roll. On average if a point is 4 or 10, the Casino has already won about 33% of all money trapped on the pass line.

So What Just Happened?

When Craps entered the second phase, Chasing Points, the rules changed, but the odds did not. The odds stayed at even money. Even money was not that bad a deal before the come out roll because of all the wonderful things that could happen on that first roll. So when everything was considered, including all the great stuff that happens 22% of the time on the come out roll, the deal was only sour by 1.41%.

But after the come out roll the only thing that matters is the odds of making your point vs. sevening out. Even in the best case, a point of 6 or 8, the 1 to 1 odds is a bad deal. In the case of a point of 4 or 10, it really stinks! Stuck with one to one odds as the hand goes south with the setting of a point, the pass line chips are no longer being properly compensated for the new increased risk that lies in their future. Thus their Fair Market Value is degraded.

Let's say that again. Stuck with one to one odds as the hand goes south with the setting of a point, the pass line chips are not being compensated for the new increased risk that lies in their future.

We can take a side trip to faerie land to show another aspect of this. What if we lived in a wonderful world where the pass line was not a contract bet? What if you could plunk down your nickel and then if the game advanced to Chasing a Point, just pick it up and opt out of the bet at that point?

The Casino would be crazy to allow that! If you essentially convert all the points to a "Push", like the 12 on a don't pass line wager, and make the pass line a one roll, come out roll only bet. The house takes a terrible beating. This phase of the game favors the shooter a whopping 33% when isolated by itself. The Casino is counting on the two thirds of the time that the game will advance to Chasing a Point to get its turn at the lopsided vig.

What about the DARK SIDE?

(insert funky breathing)
 

Everything changes when your world goes dark. Interestingly enough, even though there is a slight change in the house advantage on a don't pass bet, the value of a $5 chip dropped on the don't pass line is still basically $4.93. One can simplify by saying the house advantage on both the pass line and the don't pass bets are essential the same 1.4% without committing too big a crime against Math.

Over on the Dark Side, we are quietly crossing our fingers and hoping for anything BUT a 7 or 11. What happens to the value of our chip if the shooter misses a natural win? It shoots up in value! If it survives a come out roll, the average value of the $5 chip is now $5.63. It has a positive house advantage, which is a bit awkward to think about. Let's say it has a Better's Advantage of 12.5% on average. But again, which point is set makes a big difference.

Things are basically reversed. Now the worst paying points for the Dark Side are 6 and 8. But even there, the value of the chip goes up dramatically. If the point being chased is 6 or 8, the chip is worth $5.45 or has a Better's Advantage of about 9%.