# Ask the Wizard #231

Larry from Las Vegas, NV

The following table shows the probability of a dealer 21-point hand according to the number of cards and number of decks.

### Probability of Dealer 21-Point Hand

Cards | 1 Deck | 2 Decks | 6 Decks |

2 | 0.0482655 | 0.0477969 | 0.0474895 |

3 | 0.0537557 | 0.0530246 | 0.0525656 |

4 | 0.0184049 | 0.0184945 | 0.0185388 |

5 | 0.00310576 | 0.00326001 | 0.00335881 |

6 | 0.000291717 | 0.000344559 | 0.000380387 |

7 | 0.0000160093 | 0.0000234897 | 0.000029251 |

8 | 0.000000456411 | 0.000000997325 | 0.00000152356 |

9 | 0.00000000466991 | 0.0000000239012 | 0.0000000526866 |

10 | 0.0000000000064214 | 0.000000000262229 | 0.00000000115152 |

11 | 0 | 0.0000000000009179 | 0.0000000000148827 |

12 | 0 | 0 | 0.0000000000001003 |

13 | 0 | 0 | 0.0000000000000003 |

The next table shows the value in cents of the three prizes. The row for the 7-card prize is the value per hand of the $500 bonus for a dealer 7-card 21. The row for the 8-card prize is the value per hand of a $25,000 prize for a dealer 8-card 21. That should be multiplied by the ratio of the current jackpot to $25,000, for the value at any given moment. The row for the envy prize is the value per hand dealt at all other tables in the room of the $500 prizes for the jackpot hitting at another table.

### Value of Prizes per Hand Dealt

Prize | 1 Deck | 2 Decks | 6 Decks |

7-card $500 win | 0.80¢ | 1.17¢ | 1.46¢ |

8-card $25,000 win | 1.14¢ | 2.49¢ | 3.81¢ |

8-card $500 envy bonus | 0.02¢ | 0.05¢ | 0.08¢ |

Assuming a total of 8 active tables in the room, and 60 rounds per hour, and a $25,000 jackpot, the value of this promotion is $1.26 per hour at a single-deck table, $2.41 at double-deck, and $3.48 at six-deck.

Robert from Lawton

For the benefit of other readers, the house edge is the ratio of expected casino profit to the original wager, and the hold is the ratio of actual casino profit to chips purchased. The hold will usually be much higher, because over time the same chips will circulate back and forth. The longer the player plays, the more the house edge will grind down those chips, resulting in a greater hold, but an unchanged house edge.

There is no formula expressing a relationship between house edge and hold. To get from one to the other you would need to know how much the players bet, how well they play, and how long they play. I have said this many times, but I don’t understand why casino management cares so much about the hold *percentage*. What should matter at the end of the day is the hold, or the actual profit measured in dollars.

John from New York

I think you misread Skanskey’s table. He rates 7-6 suited equally with A-9 off-suited with a 5. I rate 7-6 suited with an 11, and A-9 off-suited as a 10. So we both put them about the same.

Eddie from Seattle

The expected number of total rolls is 1671/196 = 8.5255. Interestingly, the expected number of rolls for a point is exactly 6. That leaves 2.5255 come out rolls. So the percentage of come out rolls is 2.5255/8.5255 = 29.6%.

Dorothy from Miami, FL

For the benefit of other readers, a point is a commission charged for the loan. For example, on a $250,000 loan one point would be $2,500. I’m going to assume that the borrower would add the point to the principal balance, and never pay down the principle early.

The following table shows the equivalent interest rate without the point, according to the interest rate with one point and the term.

### Equivalent Interest Rate with No Points

Interest Rate with One Point | 10 years | 15 years | 20 years | 30 years | 40 years |

4.00% | 4.212% | 4.147% | 4.115% | 4.083% | 4.067% |

4.25% | 4.463% | 4.398% | 4.366% | 4.334% | 4.318% |

4.50% | 4.714% | 4.649% | 4.617% | 4.585% | 4.570% |

4.75% | 4.965% | 4.900% | 4.868% | 4.836% | 4.821% |

5.00% | 5.216% | 5.151% | 5.119% | 5.088% | 5.073% |

5.25% | 5.467% | 5.402% | 5.370% | 5.339% | 5.324% |

5.50% | 5.718% | 5.654% | 5.621% | 5.590% | 5.576% |

5.75% | 5.969% | 5.905% | 5.873% | 5.842% | 5.827% |

6.00% | 6.220% | 6.156% | 6.124% | 6.093% | 6.079% |

6.25% | 6.471% | 6.407% | 6.375% | 6.344% | 6.330% |

6.50% | 6.723% | 6.658% | 6.626% | 6.596% | 6.582% |

6.75% | 6.974% | 6.909% | 6.878% | 6.847% | 6.834% |

7.00% | 7.225% | 7.160% | 7.129% | 7.099% | 7.085% |

7.25% | 7.476% | 7.412% | 7.380% | 7.350% | 7.337% |

7.50% | 7.727% | 7.663% | 7.631% | 7.602% | 7.589% |

7.75% | 7.978% | 7.914% | 7.883% | 7.853% | 7.841% |

8.00% | 8.229% | 8.165% | 8.134% | 8.105% | 8.093% |

8.25% | 8.480% | 8.416% | 8.385% | 8.357% | 8.344% |

8.50% | 8.731% | 8.668% | 8.637% | 8.608% | 8.596% |

8.75% | 8.982% | 8.919% | 8.888% | 8.860% | 8.848% |

9.00% | 9.233% | 9.170% | 9.140% | 9.112% | 9.100% |

9.25% | 9.485% | 9.421% | 9.391% | 9.363% | 9.352% |

9.50% | 9.736% | 9.673% | 9.642% | 9.615% | 9.604% |

9.75% | 9.987% | 9.924% | 9.894% | 9.867% | 9.856% |

10.00% | 10.238% | 10.175% | 10.145% | 10.119% | 10.108% |

This shows that a 5.75% interest rate with one point is equivalent to a 5.842% with no points. In other words the payment would be the same both ways, assuming the point charged is added to the principal balance. Your other offer was 5.875% with no points, which is higher than 5.842%, so I would take the 5.75% with the point.

P.S. For those of you wondering how I solved for i, I used the rate function in Excel.