dddkkk1
Joined: Oct 11, 2019
• Posts: 12
October 16th, 2019 at 9:56:01 PM permalink
Quote: DogHand

...

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
...

Thanks everyone for the replies so far.

Also, I would like to know if there are additional hands to stand on based on the above table and the rules below:
\$20 minimum bet on the regular game, and \$1 is the only amount you can bet on the side bet,
6 - decks, S17, No Hole Card, double hard 9-11, DAS, split once, and the house edge for the regular game is 0.6612%

Below is one hand to get started and to see if I am correct with my reasoning/answers
note: some of my answers will be off slightly because I am using "infinite deck"

Deviating from basic strategy by standing on a 12 v 2 is the correct play, as deviating gives the player a total gain in EV of \$4.089 for that hand and playing correct basic strategy is worth \$3.131
Note: When hitting a 12 v 2 there is a 9/13 chance of not busting, when using "infinite deck" reasoning.

Numbers used for working out of 12 v 2 strategy deviation:
Total number of games: 1,000,000,000
Estimated number of times the dealer had any 2-up: 76,923,077
Total number of 8 card 21 with a dealer 2-up: 459
Estimated chance of an 8 card 21 with a dealer 2-up: 1/167,588

Is the above correct or not? If not can you show me the correct answer, and also answer the correct strategy for the hands below:
12 v 3,
12 v 4,
16 v A (I think traditional basic strategy is the correct play for this hand, but I am not sure)
and any other hands you can think of, if any, thanks.
Last edited by: dddkkk1 on Oct 16, 2019
charliepatrick
Joined: Jun 17, 2011
• Posts: 2057
October 16th, 2019 at 11:15:46 PM permalink
Very quick calculation (based on my list of dealer hands when looking at 6-deck Push22 - Stand soft 17 and no peek) gives pr of 8+ card 21 as .000 001 107 120 355. I'm guessing with Hit soft 17 the chances are bigger since you're turning some 17s into 21s. (My spreadsheet also gives .000 001 163 191 418 for 8 decks.)
DogHand
Joined: Sep 24, 2011
• Posts: 377
October 17th, 2019 at 4:38:31 AM permalink
Quote: dddkkk1

Thanks everyone for the replies so far.

Also, I would like to know if there are additional hands to stand on based on the above table and the rules below:
<snip>

dddkkk1,

The numbers I gave are based on the assumption that the dealer finishes her hand whether or not any player hands are still active. Your latest post in this thread has me wondering if my assumption is true or not. Can you clarify? For example, if you are playing heads up and you bust or get a BJ, does your sidebet automatically lose?

Dog Hand
charliepatrick
Joined: Jun 17, 2011
• Posts: 2057
October 17th, 2019 at 4:44:00 AM permalink
^ When analysing sidebets the usual assumption is (since it is a mathematical calculation) that dealer always completes their hand. Some casinos make this clear, other casinos, which would take your sidebet, might not. So it's best to check this with the casino beforehand.
dddkkk1
Joined: Oct 11, 2019
• Posts: 12
October 17th, 2019 at 5:47:06 AM permalink
Quote: DogHand

dddkkk1,

The numbers I gave are based on the assumption that the dealer finishes her hand whether or not any player hands are still active. Your latest post in this thread has me wondering if my assumption is true or not. Can you clarify? For example, if you are playing heads up and you bust or get a BJ, does your sidebet automatically lose?

Dog Hand

I asked the casino and they don't play out their hand when the player busts or gets a BJ

SOOPOO
Joined: Aug 8, 2010
• Posts: 6847
October 17th, 2019 at 8:55:41 AM permalink
Quote: dddkkk1

I asked the casino and they don't play out their hand when the player busts or gets a BJ

OK.... ALL the work the members did is useless now..... If this is online, and you are always playing one hand versus the house, then the player advantage certainly goes down a bit. Maybe doghand and the others will redo the math.....
gordonm888
Joined: Feb 18, 2015
• Posts: 2495
October 17th, 2019 at 12:56:00 PM permalink
Quote: dddkkk1

Also, I would like to know if there are additional hands to stand on based on the above table and the rules below:
\$20 minimum bet on the regular game, and \$1 is the only amount you can bet on the side bet,
6 - decks, S17, No Hole Card, double hard 9-11, DAS, split once, and the house edge for the regular game is 0.6612%

Below is one hand to get started and to see if I am correct with my reasoning/answers
note: some of my answers will be off slightly because I am using "infinite deck"

Deviating from basic strategy by standing on a 12 v 2 is the correct play, as deviating gives the player a total gain in EV of \$4.089 for that hand and playing correct basic strategy is worth \$3.131
Note: When hitting a 12 v 2 there is a 9/13 chance of not busting, when using "infinite deck" reasoning.

Numbers used for working out of 12 v 2 strategy deviation:
Total number of games: 1,000,000,000
Estimated number of times the dealer had any 2-up: 76,923,077
Total number of 8 card 21 with a dealer 2-up: 459
Estimated chance of an 8 card 21 with a dealer 2-up: 1/167,588

Is the above correct or not? If not can you show me the correct answer, and also answer the correct strategy for the hands below:
12 v 3,
12 v 4,
16 v A (I think traditional basic strategy is the correct play for this hand, but I am not sure)
and any other hands you can think of, if any, thanks.

Okay, I understand. The useful concept here is "Equity" of your hand.

When you have a \$10 BJ wager and a sidebet of \$1 and you are dealt 10-2 vs 2.

Equity of your hand if you STAND:
(1) about \$5.97 on you BJ hand, because it has an approximate EV of -0.403
(2) about \$5.97 (by coincidence) on your sidebet which has a 1/167,588 chance of winning one million

so your total STAND equity is \$5.97 +\$5.97 = \$11.94

Equity of your hand if you HIT and you are one-on-one with the dealer
(1) about \$6.34 on your BJ hand, because it has an approximate EV of -0.366
(2) because hitting a 10-2vs2 has a 31.07% chance of drawing TEN and busting, the equity of your sidebet is \$4.11= (1-0.3107)*\$5.97

so your Total HIT Equity is about \$6.34 + \$4.11 = \$10.45.

So, in situations in which the dealer will not draw to his upcard 2 when you Bust your 12, you should STAND. If the dealer will draw to his hand anyway,regardless of whether you BUST, then you should HIT.

I haven't yet done the math, but I imagine that you should stand on 12 versus 2-4 (and on 13v2) and on 14,15,16vA if you are betting \$5 (or \$10) on BJ and \$1 on a sidebet, and your chance of making the sidebet will become zero if you BUST your hand (because the dealer will not draw.)

I don't have time right now to do the analysis on all the other hands, maybe someone else will,
So many better men, a few of them friends, were dead. And a thousand thousand slimy things lived on, and so did I.
dddkkk1
Joined: Oct 11, 2019