July 3rd, 2017 at 9:05:33 AM
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Hi,

I was wondering the chances of ever winning 4 times your bet on some sort of typical video BJ machine - say 6 deck continuous shuffle - with only 1 split allowed (e.g. 4x bet win could be from: split then 2 doubles). So like the chance you split * the chance you nail a 9 or 10 or whatever you need against the dealer up card for both hands * the chance you actually win both hands. I estimate its about 1/4000 hands. This analysis could have applications for players trying to limit their jackpot exposure and also for players trying to calculate the EV loss of having a short BR.

I was wondering the chances of ever winning 4 times your bet on some sort of typical video BJ machine - say 6 deck continuous shuffle - with only 1 split allowed (e.g. 4x bet win could be from: split then 2 doubles). So like the chance you split * the chance you nail a 9 or 10 or whatever you need against the dealer up card for both hands * the chance you actually win both hands. I estimate its about 1/4000 hands. This analysis could have applications for players trying to limit their jackpot exposure and also for players trying to calculate the EV loss of having a short BR.

July 10th, 2017 at 7:36:37 AM
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Hi scotty, and welcome to the forums.

I think you're a bit off on your thinking of individual events in a hand. First, to calculate a proper house edge you did not list all of the necessary rules we'd need to know. I'll refer you to the Wizards House Edge Calculator where you can see all of the different options: https://wizardofodds.com/games/blackjack/calculator/

Next, let's assume typical rules and a house edge of "around" .5% (this is somewhat trivial to the win rate of the hands assuming 'average' rules). The hand rates for blackjack are approx. as follows:

1) Win = 42%

2) Loss = 49%

3) Push = 9%

Thus on any given hand before its dealt you generically have approximately a 42% chance to win the hand. This doesn't take any counting/etc in to mind (though even counting doesn't drastically change the win rate). So the odds of winning 4 generic hands in a row is .42^4 = .03, 3%, or about 3/100... a bit better than 1/4000 hands =P.

When you get in to splits and doubles I believe your win rate should actually go up, as splits and doubles by basic strategy are player advantageous situations (for the most part... there are defensive splits such as 8-8 vs dealer 10 for example).

I think you're a bit off on your thinking of individual events in a hand. First, to calculate a proper house edge you did not list all of the necessary rules we'd need to know. I'll refer you to the Wizards House Edge Calculator where you can see all of the different options: https://wizardofodds.com/games/blackjack/calculator/

Next, let's assume typical rules and a house edge of "around" .5% (this is somewhat trivial to the win rate of the hands assuming 'average' rules). The hand rates for blackjack are approx. as follows:

1) Win = 42%

2) Loss = 49%

3) Push = 9%

Thus on any given hand before its dealt you generically have approximately a 42% chance to win the hand. This doesn't take any counting/etc in to mind (though even counting doesn't drastically change the win rate). So the odds of winning 4 generic hands in a row is .42^4 = .03, 3%, or about 3/100... a bit better than 1/4000 hands =P.

When you get in to splits and doubles I believe your win rate should actually go up, as splits and doubles by basic strategy are player advantageous situations (for the most part... there are defensive splits such as 8-8 vs dealer 10 for example).

Playing it correctly means you've already won.

July 10th, 2017 at 7:46:21 AM
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I don't think he was looking for the odds of winning 4 separate hands in a row

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything

July 10th, 2017 at 7:46:21 AM
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I don't think he was looking for the odds of winning 4 separate hands in a row

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything

It sounded to me like he's trying to find out how often you'll end up winning 4x your original bet on one individual hand , such as getting dealt two 3's against a drealer 6, splitting , getting doubles on both hands and winning everything

July 10th, 2017 at 10:34:29 AM
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So a single split with a double after a split allowed on any card. Assuming that the dealer is single decking you and reshuffling after each deal? And hit soft 17.

That is easy enough to calculate. According to the Wizard's guide on single deck, you split on:

-pair of 2s against a 2 - 7

-pair of 3s against a 2 - 7

-pair of 4s against a 4 - 6

-pair of 6s against a 2 - 7

-pair of 7s against a 2 - 8

-pair of 8s always

-pair of 9s always except a 7 or 10

-pair of Aces always (but you can't double after a split so forget about that) s those are removed.

I then determined the cards you needed to get to double on both hands and then calculated the number of combinations where that was available. For example, if you have a pair of 2s against a 6 you have to draw a A, 3, 4, or 5 to double. There are 16 * 15 = 240 combinations of cards that will get you those two combinations out of 49 * 48 remaining cards (2,352) or a 10.204% probability that you can double both splits.

The total odds of you splitting a hand with the opportunity to double is 1.780773%.

The total odds of you doubling both hands after splitting is 0.08111%

Chart is below, using Wizard's combination blackjack analysis table 9.

The odds of you winning?. I have to go back to work.

That is easy enough to calculate. According to the Wizard's guide on single deck, you split on:

-pair of 2s against a 2 - 7

-pair of 3s against a 2 - 7

-pair of 4s against a 4 - 6

-pair of 6s against a 2 - 7

-pair of 7s against a 2 - 8

-pair of 8s always

-pair of 9s always except a 7 or 10

-pair of Aces always (but you can't double after a split so forget about that) s those are removed.

I then determined the cards you needed to get to double on both hands and then calculated the number of combinations where that was available. For example, if you have a pair of 2s against a 6 you have to draw a A, 3, 4, or 5 to double. There are 16 * 15 = 240 combinations of cards that will get you those two combinations out of 49 * 48 remaining cards (2,352) or a 10.204% probability that you can double both splits.

The total odds of you splitting a hand with the opportunity to double is 1.780773%.

The total odds of you doubling both hands after splitting is 0.08111%

Chart is below, using Wizard's combination blackjack analysis table 9.

Dealer | Player | Probability | Cards to DAS | # of Combs | Odds of getting Combs | Total Probability |
---|---|---|---|---|---|---|

A | 8,8 | 0.00024379 | 3 | 12 | 0.005102041 | 0.0000012438 |

A | 9,9 | 0.00024379 | 2 | 12 | 0.005102041 | 0.0000012438 |

2 | 2,2 | 0.000181 | 7 8 9 | 132 | 0.056122449 | 0.0000101582 |

2 | 3,3 | 0.00036199 | 6 7 8 | 132 | 0.056122449 | 0.0000203158 |

2 | 6,6 | 0.00036199 | 3 4 5 A | 240 | 0.102040816 | 0.0000369378 |

2 | 7,7 | 0.00036199 | 2 3 4 | 110 | 0.046768707 | 0.0000169298 |

2 | 8,8 | 0.00036199 | 2 3 | 42 | 0.017857143 | 0.0000064641 |

2 | 9,9 | 0.00036199 | 2 | 6 | 0.00255102 | 0.0000009234 |

3 | 2,2 | 0.00036199 | 7 8 9 | 132 | 0.056122449 | 0.0000203158 |

3 | 3,3 | 0.000181 | 6 7 8 | 132 | 0.056122449 | 0.0000101582 |

3 | 6,6 | 0.00036199 | 3 4 5 A | 210 | 0.089285714 | 0.0000323205 |

3 | 7,7 | 0.00036199 | A 2 3 4 | 210 | 0.089285714 | 0.0000323205 |

3 | 8,8 | 0.00036199 | 2 3 | 42 | 0.017857143 | 0.0000064641 |

3 | 9,9 | 0.00036199 | 2 | 12 | 0.005102041 | 0.0000018469 |

4 | 2,2 | 0.00036199 | A 7 8 9 | 240 | 0.102040816 | 0.0000369378 |

4 | 3,3 | 0.00036199 | A 6 7 8 | 240 | 0.102040816 | 0.0000369378 |

4 | 4,4 | 0.000181 | A 5 6 7 | 240 | 0.102040816 | 0.0000184694 |

4 | 6,6 | 0.00036199 | A 3 4 5 | 210 | 0.089285714 | 0.0000323205 |

4 | 7,7 | 0.00036199 | A 2 3 4 | 210 | 0.089285714 | 0.0000323205 |

4 | 8,8 | 0.00036199 | 2 3 | 56 | 0.023809524 | 0.0000086188 |

4 | 9,9 | 0.00036199 | 2 | 12 | 0.005102041 | 0.0000018469 |

5 | 2,2 | 0.00036199 | A 7 8 9 | 240 | 0.102040816 | 0.0000369378 |

5 | 3,3 | 0.00036199 | A 6 7 8 | 240 | 0.102040816 | 0.0000369378 |

5 | 4,4 | 0.00036199 | A 5 6 7 | 210 | 0.089285714 | 0.0000323205 |

5 | 6,6 | 0.00036199 | A 3 4 5 | 210 | 0.089285714 | 0.0000323205 |

5 | 7,7 | 0.00036199 | A 2 3 4 | 240 | 0.102040816 | 0.0000369378 |

5 | 8,8 | 0.00036199 | 2 3 | 56 | 0.023809524 | 0.0000086188 |

5 | 9,9 | 0.00036199 | 2 | 12 | 0.005102041 | 0.0000018469 |

6 | 2,2 | 0.00036199 | A 7 8 9 | 240 | 0.102040816 | 0.0000369378 |

6 | 3,3 | 0.00036199 | A 6 7 8 | 210 | 0.089285714 | 0.0000323205 |

6 | 4,4 | 0.00036199 | A 5 6 7 | 210 | 0.089285714 | 0.0000323205 |

6 | 6,6 | 0.000181 | A 3 4 5 | 240 | 0.102040816 | 0.0000184694 |

6 | 7,7 | 0.00036199 | A 2 3 4 | 240 | 0.102040816 | 0.0000369378 |

6 | 8,8 | 0.00036199 | A 2 3 | 132 | 0.056122449 | 0.0000203158 |

6 | 9,9 | 0.00036199 | 2 | 12 | 0.005102041 | 0.0000018469 |

7 | 2,2 | 0.00036199 | 8 9 | 56 | 0.023809524 | 0.0000086188 |

7 | 3,3 | 0.00036199 | 7 8 | 42 | 0.017857143 | 0.0000064641 |

7 | 6,6 | 0.00036199 | 4 5 | 56 | 0.023809524 | 0.0000086188 |

7 | 7,7 | 0.000181 | 3 4 | 56 | 0.023809524 | 0.0000043095 |

7 | 8,8 | 0.00036199 | 2 3 | 56 | 0.023809524 | 0.0000086188 |

8 | 3,3 | 0.00036199 | 7 8 | 42 | 0.017857143 | 0.0000064641 |

8 | 7,7 | 0.00036199 | 3 4 | 56 | 0.023809524 | 0.0000086188 |

8 | 8,8 | 0.000181 | 2 3 | 56 | 0.023809524 | 0.0000043095 |

8 | 9,9 | 0.00036199 | 2 | 12 | 0.005102041 | 0.0000018469 |

9 | 8,8 | 0.00036199 | 2 3 | 56 | 0.023809524 | 0.0000086188 |

9 | 9,9 | 0.000181 | 2 | 12 | 0.005102041 | 0.0000009235 |

10 | 7,7 | 0.00132976 | 4 | 12 | 0.005102041 | 0.0000067845 |

10 | 8,8 | 0.00132976 | 3 | 12 | 0.005102041 | 0.0000067845 |

Totals | All Cards | 0.01780773 | 0.0008111438 |

The odds of you winning?. I have to go back to work.

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You want the truth! You can't handle the truth!

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