Quote:JumboshrimpsI was playing 6:5 at a strip casino a while back and had consumed just enough free booze that I doubled-down every time I got a blackjack against a deal 2-6. fortunately, I won evey time. But, I wonder how bad my decision was. Anybody done the math? How about if blackjack paid even money? Would it make sense then?

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks, and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136, and against a 6 is 0.667063. Both are much less than 1.2. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where you should triple on a blackjack against a dealer 6.

You can verify this by looking at the chart for doubling an 11 versus a six versus hitting. The expected value of doubling is exactly double that of hitting.

The expected value on blackjack is 1.2 on a 6-5 game.

The expected value of doubling and hitting A-10 is as follows:

Dealer | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | A |
---|---|---|---|---|---|---|---|---|---|---|

Double | .4706 | .5178 | .566 | .6147 | .6674 | .4629 | .3507 | .2278 | .1797 | .109 |

Hit | .2384 | .2603 | .283 | .3073 | .3337 | .2921 | .23 | .1583 | .1195 | .143 |

Quote:WizardQuote:JumboshrimpsI was playing 6:5 at a strip casino a while back and had consumed just enough free booze that I doubled-down every time I got a blackjack against a deal 2-6. fortunately, I won evey time. But, I wonder how bad my decision was. Anybody done the math? How about if blackjack paid even money? Would it make sense then?

My blackjack appendix 9 is useful to answer questions like this. For example, assuming six decks, and the dealer hits a soft 17, the expected value of doubling on a blackjack against a dealer 5 is 0.622136, and against a 6 is 0.667063. Both are much less than 1.2. Even if a blackjack only pays even money, as is unfortunately sometimes the case now, you should stand on the blackjack. The only game where you should not stand on a blackjack is in Triple Up 21, where you should triple on a blackjack against a dealer 6.

I can't believe I'm going to belabor this, now that the Wizard has spoken, but I simply must. What's wrong with the following analysis?

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 10 * 0.667063 = $6.67063

Quote:Jumboshrimps

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 5 * 0.667063 = $3.33

Corrected.

The table shows the expected return for one unit , not two.

Quote:teddysQuote:Jumboshrimps

Expected return on $5 bet resulting in a natural = 5 * 1.2 = $6

Expected return on $5 bet doubled on 11 = 5 * 0.667063 = $3.33

Corrected.

The table shows the expected return for one unit , not two.

Okay. So I can expect to win $3.33 on my initial $5 unit. And another $3.33 on the other $5 unit. Right?

I understand that the chart reflects the expected return on a single unit. So, when I am dealt any eleven against a dealer 6, and opt to double down, the expected return on that initial unit is .667063.

OR, are you all trying to tell me that the expected return on that initial unit is half that?

Taking the blackjack wins $12.

Whether you decide to hit or double 21 you would always take one card on a six.

Hitting blackjack wins, on average, $3.337.

Doubling blackjack wins, on average, double: $6.674

You don't win $13.34 (.6674 x 20).

Here is the table that makes up the result of hitting blackjack. It is off a little bit because I am using the Wizard's appendix 2 which takes the dealer probability for 8 decks S17.

Your hand | Dealer | 17 | 18 | 19 | 20 | 21 | Bust | Total |
---|---|---|---|---|---|---|---|---|

Hand | Probability | .16564 | .10621 | .10639 | .10159 | .09725 | .42292 | 1 |

12-16 | 5/13 | Lose | Lose | Lose | Lose | Lose | Win | -.05929 |

17 | 1/13 | Push | Lose | Lose | Lose | Lose | Win | .00088 |

18 | 1/13 | Win | Push | Lose | Lose | Lose | Win | .02180 |

19 | 1/13 | Win | Win | Push | Lose | Lose | Win | .03815 |

20 | 1/13 | Win | Win | Win | Push | Lose | Win | .05415 |

21 | 4/13 | Win | Win | Win | Win | Push | Win | .27778 |

Total | 1 | .02548 | .00000 | -.01637 | -.03126 | -.06732 | .42292 | .3335 |

The expected value for hitting is 1/2 as much as doubling.

When you hit or double 11 you have a better chance of getting 12-16 than you do 21. The dealer only busts 42% of the time. On the other 58% of the time, the dealer has a chance of beating or pushing you.