There is a side bet where you can bet that the dealer will get an "8 or more card 21".

Side bet and game info

Cost $1 to play side bet

Pays: $1,000,000

6-deck

1 What is the chance of the dealer getting an 8 or more card 21 when:

(a) the dealer stands soft 17

(b) the dealer hits soft 17

2. What are the chances when the dealer's up card is an:

(a) Ace, (b) two, and (c) three.

For "1(a)" I think the chance is about 1 in 1.08 million, but I am not sure.

Thanks for your time

Quote:dddkkk1Hi again,

There is a side bet where you can bet that the dealer will get an "8 or more card 21".

Side bet and game info

Cost $1 to play side bet

Pays: $1,000,000

6-deck

1 What is the chance of the dealer getting an 8 or more card 21 when:

(a) the dealer stands soft 17

(b) the dealer hits soft 17

2. What are the chances when the dealer's up card is an:

(a) Ace, (b) two, and (c) three.

For "1(a)" I think the chance is about 1 in 1.08 million, but I am not sure.

Thanks for your time

dddkkk1,

I ran four 1-billion-round CVData sims to check this sidebet. Below are the number of times it hit overall, as well as the number specifically for A-up, 2-up, 3-up, and (anything else)-up. Note that, if the number of hits were exactly 1,000, the bet would be EV-neutral.

Decks | H/S 17 | Total | A-up | 2-up | 3-up | other | EV | SD | N0 |
---|---|---|---|---|---|---|---|---|---|

8 | S | 1,081 | 232 | 429 | 254 | 166 | 8.1% | 1,040 | 164,761,621 |

8 | H | 1,636 | 510 | 588 | 307 | 231 | 63.6% | 1,279 | 4,044,541 |

6 | S | 1,051 | 202 | 459 | 212 | 178 | 5.1% | 1,025 | 404,075,739 |

6 | H | 1,573 | 511 | 555 | 309 | 198 | 57.3% | 1,254 | 4,790,928 |

As you can see, someone erred, as the SB is +EV for each configuration. As expected, the EV is higher for 8D than for 6D, and for H17 rather than S17. However, the SD is huge, so you'll need to bring a BIG bankroll ;-)

Hope this helps!

Dog Hand

P.S. A tip of the hat to miplet for his table-maker!

Quote:dddkkk1Hi again,

There is a side bet where you can bet that the dealer will get an "8 or more card 21".

Side bet and game info

Cost $1 to play side bet

Pays: $1,000,000

6-deck

1 What is the chance of the dealer getting an 8 or more card 21 when:

(a) the dealer stands soft 17

(b) the dealer hits soft 17

2. What are the chances when the dealer's up card is an:

(a) Ace, (b) two, and (c) three.

For "1(a)" I think the chance is about 1 in 1.08 million, but I am not sure.

Thanks for your time

I’ve had one 8 card 20 in my life followed by 4 blackjacks in a row crazy day that was

Quote:heatmapI’ve had one 8 card 20 in my life followed by 4 blackjacks in a row crazy day that was

That was just the guy in the back room who rigs the shuffle machines messing with you

For 8 decks, I calculate that the probability of an 8-card 21 is 1.498 E-06. So, that's a 49.8% edge for the player, but of course its on a bet with lottery-type odds.

For 6 decks, I calculate that the probability of an 8-card 21 is 1.42755 E-06. A 42.755% player edge.

Given the tax bite out a $1M payout, there is some question whether there is any real-life player advantage.

Edit: To be clear, these numbers are only for 8-card 21s; 9-11 card 21s are not included in the above numbers.

Here is a table of Effect of Removal (EOR) in %.

Card | 8 Decks EOR,% | 6 Decks EOR,% |
---|---|---|

T | 2.925 | 3.742 |

9 | 2.826 | 3.621 |

8 | 2.588 | 3.323 |

7 | 2.035 | 2.616 |

6 | 0.817 | 1.047 |

5 | -1.513 | -1.955 |

4 | 1.108 | 1.386 |

3 | -1.430 | -1.885 |

2 | -7.260 | -9.292 |

A | -10.869 | -13.826 |

These values are quite remarkable, aren't they? Certainly the largest EOR values I have ever calculated!

In the 6 deck game, if a single Ace is removed/dealt, the Player edge decreases by about 13.8%, from 42.755% to about 29.8%. If 4 Aces are removed, the sidebet becomes unfavorable: the House has an edge of 6.2%.

In the 6 deck game, if a single Ten is removed/dealt, the Player edge increases by about 3.74%. If 4 Tens are removed, the player edge rises from 42.755% to 58.403%. That's an increase of 15.64% so even accounting for the smaller number of cards remaining the EOR for 4 Tens is a bit more then 4X the EOR for 1 Ten. That is, the EOR for multiple cards is more than linear.

This is a mathematically extreme bet that I thought math nerds would find interesting. I feel its okay to post this info because I don't believe this is a credible AP opportunity due to the tax bite, the enormous bankroll and time required to grind out this side-bet, as well as the possibility of large losses from playing the wagers on the main BJ game for a million hands or so.