dddkkk1
dddkkk1
Joined: Oct 11, 2019
  • Threads: 3
  • Posts: 12
October 14th, 2019 at 8:14:04 PM permalink
Hi 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
DogHand
DogHand
Joined: Sep 24, 2011
  • Threads: 1
  • Posts: 244
October 15th, 2019 at 9:39:29 AM permalink
Quote: dddkkk1

Hi 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.

DecksH/S 17TotalA-up2-up3-upotherEVSDN0
8S 1,081 232429254166
8.1%
1,040
164,761,621
8H 1,636 510588307231
63.6%
1,279
4,044,541
6S 1,051 202459212178
5.1%
1,025
404,075,739
6H 1,573 511555309198
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!
DeMango
DeMango
Joined: Feb 2, 2010
  • Threads: 26
  • Posts: 2156
October 15th, 2019 at 10:04:56 AM permalink
Would this be countable if many high cards have left the building?
unJon
unJon
Joined: Jul 1, 2018
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October 15th, 2019 at 10:09:58 AM permalink
Thereís probably a max table payout in the fine print.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 34
  • Posts: 2013
October 15th, 2019 at 3:24:32 PM permalink
Yes. Very dependent on aces and deuces (and fives?) with reasonably high EORs.
Last edited by: gordonm888 on Oct 15, 2019
Ace2
Ace2
Joined: Oct 2, 2017
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October 15th, 2019 at 8:20:21 PM permalink
Easiest way to solve should be with a Markov chain
heatmap
heatmap
Joined: Feb 12, 2018
  • Threads: 118
  • Posts: 773
October 16th, 2019 at 12:44:56 PM permalink
Quote: dddkkk1

Hi 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



Iíve had one 8 card 20 in my life followed by 4 blackjacks in a row crazy day that was
michael99000
michael99000
Joined: Jul 10, 2010
  • Threads: 9
  • Posts: 1686
Thanks for this post from:
Forager
October 16th, 2019 at 2:48:01 PM permalink
Quote: heatmap

Iíve 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
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 34
  • Posts: 2013
Thanks for this post from:
DeMango
October 16th, 2019 at 4:17:09 PM permalink
I have created a spreadsheet with all of the 8-card 21s listed for a H17 game.

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.
Last edited by: gordonm888 on Oct 16, 2019
heatmap
heatmap
Joined: Feb 12, 2018
  • Threads: 118
  • Posts: 773
October 16th, 2019 at 5:58:45 PM permalink
Quote: michael99000

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



the last blackjack was a push with the dealer so maybe ;-)

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