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Beyond Advantage Play

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.  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 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. 

It depends on what bet is being made.  The answer depends on the bet 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.  Here are the results:


Payoff # of Sevens in 36 Tosses Corresponding SRR
Pass/Come 1 – 1 5.574 6.46
Place 6/8 7 – 6 5.860 6.14
Place 5/9 7 – 5 5.663 6.36
Place 4/10 9 – 5 5.492 6.55

These numbers clearly reflect the advantage of place betting the six and eight as the best strategy for precision shooters, right?  Well, maybe not.  It does not take into consideration the one bet the casino does not have an advantage of in a random game – the Free Odds bet.  These bets have the effect of reducing the amount of influence necessary to gain and edge – and can become positive expectation wagers.   It also doesn’t take into consideration the total amount of cash you are risking at any given time. 

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 the number 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 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 you have to 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 without betting the farm.

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