How Much of an Edge is an Edge?

A while back a good friend of mine complained that – after years of practice the best he could achieve was an SRR of 7.12. To his way of thinking he was not playing with enough of an edge, and his results at the table seemed to support this. He just wasn’t making a lot of money. Since a long term SRR of 7.12 is pretty strong in my book, I took a couple of hours to crunch some numbers and try to determine exactly what he was doing wrong. In the end – it wasn’t his toss that was killing him – it was his betting.

Let’s look at what it takes to get an edge at banker’s craps – then consider where my pal might be going wrong. Over the long haul, in a fair craps game the seven will show up an average of once in every six tosses. This fundamental fact is the basis for all odds calculations in casino craps. The six or eight, for example, will show up an average of once in every five tosses. So the true odds of a six or eight showing up before the seven is 6-5. Hence the “free odds” payoff of 6-5 behind the line.

Everyone who has ever read a basic craps book has seen the graphic that depicts this, showing six ways to make the seven, five ways to make the six and eight, four ways to make the five and nine, and three ways to make the four and ten. But these are “average” expectations. In no way does it mean that a seven will magically appear exactly once in every six rolls. Instead, small deviations from “average” occur all the time. Sometimes the universe gives you an abundance sevens. Sometimes the universe gives you an abundance of box numbers. And these random “streaks” may last an hour, a day, a week, or even years for individual players, depending largely on being in the right place at the right time.

Precision craps shooters seek to influence the randomness of the game by setting the dice to specific arrangements and executing a careful, controlled toss. How good does a precision shooter have to be to gain an edge over casino craps? The answer is – depends. To a great degree it depends on what bet is being made.

For this example, we’re not going to concern ourselves with what number is being rolled instead of the seven. We’ll simply look at the impact of a reduction in the number of sevens thrown, and search for a break-even point for each of the major bets on the table. For those of you with WinCraps, it’s easy enough to do these calculations yourself. Just go to the Probability tab, click on Configure and enter the desired number of rolls out of thirty-six. Then click on the Advantage tab to view the expected value of the various wagers. Since out newsletter software doesn’t support table graphics, I’ll just tell you what the best bets are – in order of value to the player.

First off – place the Six and Eight. You can toss 5.86 sevens over the course of 36 decisions and still have an advantage on the six and eight. The corresponding SRR at that level is just 6.14.

Next is the Place the Five and Nine. Yeah, I know some folks who drank the famous gaming author’s Kool-Aid and swore off betting the five and nine because of their high (4%) vig. But if you can whittle the number of sevens you toss down to 5.663 out of 36 throws then you’ll have an advantage there as well. That corresponds to an SRR of just 6.36.

What’s next in our betting scheme? Pass and/or Come Betting. Now here’s the rub. You can’t toss the dice without having a Pass Line bet, so you’re stuck with this one. But I have better news for you after we look at the numbers. Pare your sevens down to 5.574 in 36 and you’ll have an edge on these even money bets. That corresponds to an SRR of 6.46. However, that’s just for the even money bet. It does not take into consideration the one bet where the casino does not have an advantage on – even in a random game – the Free Odds bet. These bets have the effect of reducing the amount of influence necessary to gain an edge and can become very positive expectation wagers. However, it also doesn’t take into consideration the total amount of cash you are risking at any given time.

Last on the list is the Place Bet on the Four and Ten. We’re discussing the Place bet instead of the Buy bet because the vast majority of the players I see betting the Four or Ten start out Placing them for $10, then Buying them on the first hit. To gain an edge on the four or ten you’ll need to get your sevens count down to 5.492 out of 36 for an SRR of 6.55. No step for a stepper, right?

These calculations clearly reflect the advantage of playing the Pass Line with Odds plus Place betting the Six and Eight as the best strategy for precision shooters, right? Well, maybe not. Now let’s return to my friend’s game for a moment and consider this. This particular player favors the Mini-V hard-four set. His typical action is to play a table minimum Pass Line bet with no odds, then to Place the four and ten for $10 each, and buy them out of the first “hit.” After a hit on one of his buy bets he takes single odds on his line bet and presses it up a unit on each successive hit on a buy bet. He is playing to what he believes to be his signature numbers – the four and ten – and his “best bet” – the line bet with odds.

Now let’s head to Heavy’s Perfect World Casino and toss a hand. Five on the line and the shooter establishes the six as his point. No odds taken. Placing the four and ten for ten each. Second toss – nine. Third toss – eight. Fourth toss – eleven. Fifth toss – four. Buy it and get $2 change. Sixth toss – eight repeats. Seventh toss – ten. Buy it and get $2 change. Now we’re prepared to rake it in. Eighth toss – seven out, line away. Net loss – $21. So where the heck did the advantage go?

Now, to be fair, I’ve seen this gent step up to the table and throw half a dozen fours in a single hand, locking up a quick hundred or more. And some occasions he catches a streak and really cleans up. But by far, the Perfect World Casino results I just ran through come closer to what happens to him on a daily basis.

So how do you fix it? In my opinion you simply have to bet it correctly. If you know for a fact that you have a long-term SRR of 7.12, then it seems logical that you should lock up a profit within seven rolls. And that gets us back to our old friend – regression betting. Using the same series of numbers we used at the Perfect World Casino – let’s risk just six additional dollars and play a simple regression. We’ll play a table minimum pass line bet for $5. No odds taken. The point is six. Place $26 across. Second toss is a nine. Collect $7 and come down off the four and ten. We’re removing the highest vig bets – the wagers we have the least advantage on – first. The third toss is an eight. Collect $7 and come down on the five and nine. You now have just the $5 flat bet and the $6 eight working, and you have a guaranteed $3 win locked up. Fourth toss is an eleven. Fifth toss is a four. Sixth toss is a repeater on the eight. Collect $7 and bring down the eight. You now have a $10 guaranteed win locked up. But the six is a good number and taking free odds makes it even better, so you take single odds – retaining a guaranteed $5 win. On toss seven the ten shows. Then, on toss eight you seven out.

How did we fare that time? Instead of losing $21 our player made $5 – a positive swing of $26. Of course, this is a Perfect World Casino example and it plays directly to the point I am trying to make. If your SRR is 7.12 – why would you have your bets working on toss seven – eight – or nine? You have to play YOUR percentages.

What does it take to get the edge at banker’s craps? Frankly, not a lot. But it doesn’t take a lot to swing the edge the other way either. And even WITH an edge – you have to play it to your advantage. Play smart – use regression moves to lock up a win early. Then, if you catch a streak you are positioned to take advantage of it without betting the farm.