## Musical Dice -- Expected Rolls To Break Even

#### Written January 21, 2022

* I had come back from a trip to Lake Charles yesterday, and was recalling a number of craps sessions I'd had on the trip, in which I was using a strategy where I was only betting the 6 and the 8 on the Place bets. I thought I'd lower the risk of losing a lot of money, versus when I was doing regression betting. I was expecting more winning sessions than what I had, however. My question was, what went wrong?*

* Then I started thinking about trying some other strategies, like returning to my Two-Hit Blackout strategy, or the Quarter Pounder With Ease strategy (Bryan from Hawaii Craps Shooter's strategy). Then I recalled what Bryan from Hawaii Craps Shooters sais on his Iron Cross video, talking about HBE, or Hits to Break Even. It made me think about the 6/8 strategy I'd been using, and although it only required two hits to break even, the chances of getting those two hits were smaller than Bryan's Quarter Pounder With Ease strategy, because Bryan's strategy covered more numbers.*

* Then it occurred to me that what really needs to be discussed, regarding these strategies, is what I call the expected rolls to break even. For the Iron Cross strategy, six hits are needed to break even, and since every number except for the 7 is covered with the Iron Cross, the expected number of rolls needed to break even is also 6. But for the 6/8 strategy, that is quite a different story, since 6 and 8 together only cover 10 out of 30 possible combinations on the dice that are not 7. So what I did to figure out the expected number of rolls to break even with the 6/8 strategy, I developed what I call a No-Seven Hit Probability, or N7HP, dividing the number of combinations covered by the strategy, by the total of non-seven combinations on the dice. In this case, that probability is 10/30 or 1/3. From there, to calculate the expected number of rolls to break even, I took the number of hits needed to break even and divided it by the probability, or multiplied the number of hits by the reciprocal of that probability. So the 6/8 strategy has an expected number rolls to break even (or ERBE) of 6 rolls. No wonder I would either be making little money, or losing money, if the roll isn't a long one!*

* Below is a chart of some common strategies used at the craps table, and the resulting expected rolls to break even for each strategy. The I-5 column represents the total investment in the strategy at the 5-dollar level, and similarly for I-10, I-15, I-25, and I-50. Of course, if you are playing the Pass Line and odds, the HBE and ERBE numbers will be higher.*

## STRATEGY | ## I-5 | ## I-10 | ## I-15 | ## I-25 | ## I-50 | ## HBE | ## N7HP | ## ERBE |

## Iron Cross | ## $39 | ## $61 | ## $100 | ## $144 | ## $305 | ## 6 | ## 30/30 = 1 | ## 6 |

## 6/8 | ## $12 | ## $24 | ## $36 | ## $60 | ## $120 | ## 2 | ## 10/30 = 1/3 | ## 6 |

## Across | ## $32 | ## $64 | ## $96 | ## $162 | ## $324 | ## 5 | ## 24/30 = 4/5 | ## 7 (6.25) |

## 5/6/8 or 6/8/9 | ## $17 | ## $34 | ## $51 | ## $85 | ## $170 | ## 3 | ## 14/30 = 7/15 | ## 7 (6.43) |

## Inside | ## $22 | ## $44 | ## $66 | ## $110 | ## $220 | ## 4 | ## 18/30 = 3/5 | ## 7 (6.67) |

* Some notes on the above chart: On the Iron Cross strategy, the Field bets are the table minimum, and the Place bets for the 5, 6, and 8 are 1½ times the units. For the $25 table, the 5, 6, and 8 Place bets have 7 units each. For 8 units, alternatively, add another $17. Note that you can use $35 for the Field bet, with 10 units for the 5, 6, and 8 Place bets. Each payout will pay $35, whether it is a field roll or a 5, 6, or an 8 roll. For the Across strategy, the total investment numbers for the $25 and $50 tables include the Buys for the 4 and 10 Place bets.*

* With all the many expected rolls needed to break even on the above strategies, it is no wonder some people turn to regression-style betting, that is, having big bets on the Place bets for a few hits, then regressing the bets down to the level that what was earned on those few rolls will pay for everything, and you will then be in the profit. The below table shows some of these regression strategies.*

* One regression strategy is the Quarter Pounder With Ease strategy, designed by Bryan of Hawaii Craps Shooters, where he does a modified version of the Iron Cross strategy for two hits, placing 6 and 8 for $60 each, $35 on the Field bet, and hopping the 5's for $10. After two hits of making a net of $25 each, or a quarter each, the bets get regressed down to 44 inside, for a profit of at least $6. Most likely, this strategy was designed specifically for a $10 table. If I was to do this strategy for a different minimum bet, for a $5 minimum, I'd only need one hit before I regress to 22 inside. On a $15 table, I'd need three hits before regressing down to 66 inside. For $25 and $50 tables, I'd use larger dollar amounts, doubling it up for a $25 table, and doing four times the normal dollar amount for a $50 table. In the cases of the $15 table and up, the HBE and ERBE would both be 3.*

* There is also my Two-Hit Blackout strategy, which I designed for a $15 table, where you place 440 total on the inside numbers, then after two hits, regress everything down to 4 units on all the Place bets. Profit margin, even factoring in 4 units for the Pass Line, and 2 times that for odds, is at least $100. For a $25 table, what I'd do to maintain that $100+ profit margin, is not place anything for odds upon regression, but rather build that up with additional hits on the numbers. This strategy can be scaled down to 220 inside for $10 tables, and $110 inside for $5 tables. For $50 tables, my strategy would probably be the same as for a $25 table, but risking twice as much.*

* There is also the Pineapple Press strategy, also designed by Bryan of Hawaii Craps Shooters, where he starts with 320 across, that is, 10 units on each of the Place Bets (I'll use $324 here to include the Buys on the 4 and 10). With the money from the first hit, 6 and 8 get pressed, then on the second hit, the 5 and 9 get pressed, then on the third hit, the 4 and 10 get pressed. The bets remain up there for a fourth hit (dubbed the Money Shot by Bryan, a.k.a. Mr. Money Shot), then they are reduced to 160 across, that is, 5 units on each Place bet (I'll use $162 here to include the Buys). This strategy seemed to be designed for a $25 table, but I'm assuming this can be scaled up or down for higher or lower minimum bet tables. For a $5 table, I'd start with two units on each Place bet, or 64 all the way across. For a $10 table, that amount across would be $130 (including 1 each for the Buy on the 4 and the 10). For a $15 table, the across amount would be $194, once again including 1 each for the Buy on the 4 and the 10. And for a $50 table, I'd put $650 across, including the $5 vig for each the 4 and the 10.*

* Still another regression strategy, this one designed by Crappy the Craps Man, from Regression Obsession, involves placing the 6 and 8 for $60 each, then after the first hit, regress those bets down to $30 each, then from there, placing the residual red chips on the 5 or the 9, and with each subsequent roll, take the green chips for profit, and press with the red chips. When the 5's and 9's start hitting, use those red chips to bet and press the 4 and 10, and when the 4's and the 10's hit, use the red chips to press the 6 and the 8. Crappy adds that for early seven-outs, to double the size of the bets until one hits, then regress down to the original $60 level. The main point of this strategy is that the regression occurs after only one hit on either the 6 or the 8. I think this was designed for a $10 table, but you can use the same strategy on a $5 table. On a $15 or a $25 table, you can still use $60 bets on the 6 and the 8, but you may have to hold on to the red chips until you get enough to branch out to the other numbers, covering the minimum bet. For a $50 table, I'd double the size of those bets to $120 each, then on the one hit, regress down to $60 each.*

* The first time I'd ever heard of regression betting, was on one of Beau Parker (a.k.a. the Dice Coach)'s videos, where on a $5 table, he demonstrated a simple regression strategy, where he had two units on each of the Place bets, except for the point, then after two hits, he'd regress them down to one unit across, except for the point. The figures in the table reflect what would be the case if such a strategy was used for the higher minimum bet tables, doubling up the units for the first two rolls, then regressing down to the minimum. With this strategy, I used what the N7HP would be if the point was 5 or 9 (the N7HP would be the average number), and calculated the ERBE from there.*

## STRATEGY | ## I-5 | ## I-10 | ## I-15 | ## I-25 | ## I-50 | ## HBE | ## N7HP | ## ERBE |

## Quarter Pounder With Ease | ## $165 | ## $165 | ## $165 | ## $330 | ## $660 | ## 2 | ## 30/30 = 1 | ## 2 |

## 6/8 Collect The Greens | ## $120 | ## $120 | ## $120 | ## $120 | ## $240 | ## 1 | ## 10/30 = 1/3 | ## 3 |

## Beau Parker's Regression | ## $54 | ## $110 | ## $164 | ## $274 | ## $550 | ## 2 | ## 20/30 = 2/3 | ## 3 |

## Two-Hit Blackout | ## $110 | ## $220 | ## $440 | ## $440 | ## $880 | ## 2 | ## 18/30 = 3/5 | ## 4 (3.33) |

## Pineapple Press | ## $64 | ## $130 | ## $194 | ## $324 | ## $650 | ## 4 | ## 24/30 = 4/5 | ## 5 |

* SPECIAL NOTES: If I had done ANYTHING to misrepresent or mis-characterize ANY of these strategies, PLEASE PLEASE let me know by emailing me at musicaldice323@gmail.com, and I'll correct it. It is NOT my intention to misrepresent or mis-characterize these strategies. I admire and respect all you craps vloggers. You've been a major inspiration to me. The main purpose of my presenting these strategies is to show what the expected number of rolls would be before you break even, using these strategies.*

* CONCLUSION: As you can see, with each of these regression strategies, the expected number of rolls before you break even, is lower than the typical strategies used in the first table. However, the risk is much greater with the regression strategies. Early seven-outs is the enemy of any of these strategies, especially the regression strategies. But if you're willing to take that risk, you have a better chance of breaking even, and making more money with these regression strategies. An expression I first heard by poker pro Phil Helmuth, in regards to playing poker, also applies to playing craps: "Fortune favors the bold." Whatever strategy you decide to use, good luck! ☺ *