21 Duel Blackjack
Poll
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| | 1 vote (14.28%) | ||
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| | 1 vote (14.28%) | ||
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7 members have voted
June 19th, 2017 at 11:42:49 AM
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Okay, I hope you people are happy. I wrote a 612-line program to analyze 21 Duel Blackjack, not to mention time processing the results in Excel and writing up the page. Well, I guess I did just mention it. Anyway, please click the link to my new page on the game and let me know what you think. As usual, I welcome all questions, comments, and corrections.
Unfortunately, after I spent all weekend and much of today analyzing the game I get a different house edge than claimed by the game. Mine is almost zero (0.075%) while Playtech, the game maker, claims 1.62%. I'm not sure if that is for the house edge or element of risk, but either way, we disagree. Hopefully one of the other math wizards on the site will rise to the occasion and provide a much-needed third opinion.
You can play for free through our sister site Latest Casino Bonuses.
The question for the poll is would you play 21 Duel Blackjack?
Unfortunately, after I spent all weekend and much of today analyzing the game I get a different house edge than claimed by the game. Mine is almost zero (0.075%) while Playtech, the game maker, claims 1.62%. I'm not sure if that is for the house edge or element of risk, but either way, we disagree. Hopefully one of the other math wizards on the site will rise to the occasion and provide a much-needed third opinion.
You can play for free through our sister site Latest Casino Bonuses.
The question for the poll is would you play 21 Duel Blackjack?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 19th, 2017 at 2:08:14 PM
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Just added an example to the page.
The above is just the starting situation. The player has a 9 starting card and can add either a 2 or a 9. Which would you pick?
The above is just the starting situation. The player has a 9 starting card and can add either a 2 or a 9. Which would you pick?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 19th, 2017 at 2:19:15 PM
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I'm not familiar with the strategy, but I'd assume pick the 2 and hit on 11? Eh, conventional wisdom says 19 is better than the average hand, and if the dealer can't draw more than 3 cards then I'd assume that makes 19 even stronger though. I've talked myself in to taking the K instead.
Playing it correctly means you've already won.
June 19th, 2017 at 2:21:21 PM
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Quote: RomesI'm not familiar with the strategy, but I'd assume pick the 2 and hit on 11? Eh, conventional wisdom says 19 is better than the average hand, and if the dealer can't draw more than 3 cards then I'd assume that makes 19 even stronger though. I've talked myself in to taking the K instead.
That is correct. It is also confirmed by the strategy table for a starting 9 on my page for the game.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 19th, 2017 at 3:52:04 PM
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This seems like a fairly symmetric game - with player and house having equal starting positions and game-play rules that are not greatly dissimilar.
The House advantages are
-player can bust first and lose, correct? And that happens less often than in conventional BJ because of the ability of the player to choose which of the 2 common cards to play, and the limitation of having a maximum of 3 cards with which to make a hand.
- if dealer has a bad hand and doesn't qualify, its a push
The player advantages are the flexibility to
- stand on a hard 12-16 when it is warranted.
- fold on a bad hand (similar to a surrender bet in conventional BJ if you think of the standard bet in this game as being 2 Ante units.)
Not hard to believe that the HE might be small.
The House advantages are
-player can bust first and lose, correct? And that happens less often than in conventional BJ because of the ability of the player to choose which of the 2 common cards to play, and the limitation of having a maximum of 3 cards with which to make a hand.
- if dealer has a bad hand and doesn't qualify, its a push
The player advantages are the flexibility to
- stand on a hard 12-16 when it is warranted.
- fold on a bad hand (similar to a surrender bet in conventional BJ if you think of the standard bet in this game as being 2 Ante units.)
Not hard to believe that the HE might be small.
Last edited by: gordonm888 on Jun 19, 2017
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 19th, 2017 at 5:38:12 PM
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Quote: gordonm888The House advantages are
-player can bust first and lose, correct? And that happens less often than in conventional BJ because of the ability of the player to choose which of the 2 common cards to play, and the limitation of having a maximum of 3 cards with which to make a hand.
- if dealer has a bad hand and doesn't qualify, its a push
The player advantages are the flexibility to
- stand on a hard 12-16 when it is warranted.
- fold on a bad hand (similar to a surrender bet in conventional BJ if you think of the standard bet in this game as being 2 Ante units.)
Not hard to believe that the HE might be small.
I agree exactly how you put it. Yes, if the player busts first, he loses, as in regular blackjack. Also correct that busting is not very common in this game as you tend to start with good hands and can have at most three cards.
Normally Internet casino software companies just steal land casino games and when they do make up one on their own, it is something bizarre. However, this seems like a pretty good game concept. I could easily see it working in a land casino. Some rule would need to be tweaked to give the house a bigger edge. Probably raising the dealer qualifying point.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 19th, 2017 at 5:41:49 PM
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Pushing on a low dealer hand has got to be a strong house advantage. I have to think that many more of these hands would have been losers rather than winners, plus the house has already collected antes and bets on the busted hands, so pushing the non-qualifying hands is an overall house win.
How often will the dealer not qualify?
Also, Blackjacks only pay even money in this game, assuming the dealer qualifies.
How often will the dealer not qualify?
Also, Blackjacks only pay even money in this game, assuming the dealer qualifies.
Simplicity is the ultimate sophistication - Leonardo da Vinci
June 19th, 2017 at 5:44:57 PM
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Quote: Wizard...I could easily see it working in a land casino. Some rule would need to be tweaked to give the house a bigger edge. Probably raising the dealer qualifying point.
Memorizing the pecking order of the hands in the "House Way" would be a procedural challenge for the dealers.
Simplicity is the ultimate sophistication - Leonardo da Vinci
June 19th, 2017 at 5:51:01 PM
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Quote: AyecarumbaMemorizing the pecking order of the hands in the "House Way" would be a procedural challenge for the dealers.
Oh, I think they could handle it. I feel sorry for the ones who are supposed to learn the house way for Asia Poker. That thing is about 20 pages long.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 19th, 2017 at 6:53:23 PM
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Interesting game, but probably a nightmare to remember a strategy at the table.
I've had a quick look without checking my logic much and get totally different figures (HE=2.652 for s17 and 2.661% for h17), thus there's a bug in my code somewhere and/or a misunderstanding of the rules.
Interestingly I get you fold 13% of the times, e.g. when you can see 3 aces. So I'll look into that one in more detail later in the week (as it's getting late here!)
I've had a quick look without checking my logic much and get totally different figures (HE=2.652 for s17 and 2.661% for h17), thus there's a bug in my code somewhere and/or a misunderstanding of the rules.
Interestingly I get you fold 13% of the times, e.g. when you can see 3 aces. So I'll look into that one in more detail later in the week (as it's getting late here!)
Player's card, community cards
01 01 01
02 01 04
02 01 05
02 01 06
02 01 07
02 01 10
02 02 02
02 02 03
02 03 10
02 04 10
02 05 10
02 06 10
03 01 05
03 01 09
03 01 10
03 02 02
03 02 10
03 03 10
03 04 10
03 05 10
04 01 08
04 01 09
04 01 10
04 02 10
04 03 10
04 04 10
05 01 07
05 01 08
05 01 09
05 01 10
05 02 10
05 03 10
05 07 10
05 08 10
05 09 10
05 10 10
06 01 07
06 02 09
06 02 10
06 06 10
06 07 10
06 08 10
06 09 10
06 10 10
07 05 10
07 06 10
07 07 10
June 20th, 2017 at 6:43:30 AM
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The error could also be mine so please keep plugging away.
For three aces I get an EV by hitting either hand of -0.788821.
For three aces I get an EV by hitting either hand of -0.788821.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 20th, 2017 at 7:11:36 AM
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I still get wildly different figures, but for AAA this is what I get from a simple infinite deck analysis.
(The other way gets a difference of .1% HE between 6 and 9999 decks, so my next approach is to look at infinite decks as an approximation and get it close to 9999 decks.)
(The other way gets a difference of .1% HE between 6 and 9999 decks, so my next approach is to look at infinite decks as an approximation and get it close to 9999 decks.)
| W | T | L | DNQ | EV | |||
| 21 | 104 | 57 | 8 | 1.278 107 | |||
| 20 | 86 | 18 | 57 | 8 | 0.390 533 | ||
| 19 | 68 | 18 | 75 | 8 | -0.035 503 | ||
| 18 | 50 | 18 | 93 | 8 | -0.461 538 | ||
| 17 | 32 | 18 | 111 | 8 | -0.887 574 | ||
| 16 | 24 | 8 | 129 | 8 | -1.195 266 | ||
| 15 | 16 | 8 | 137 | 8 | -1.384 615 | ||
| 14 | 8 | 8 | 145 | 8 | -1.573 964 | ||
| 13 | 8 | 153 | 8 | -1.763 314 | |||
| 12 | 161 | 8 | -1.857 988 | ||||
| 11 | 161 | 8 | -1.857 988 | ||||
| Hitting | EV (Hit) | Best EV | |||||
| 21 | 700 | 332 | 1061 | 104 | -0.281 293 | 1.278 107 | St |
| 20 | 646 | 215 | 1232 | 104 | -0.486 117 | 0.390 533 | St |
| 19 | 592 | 215 | 1286 | 104 | -0.584 433 | -0.035 503 | St |
| 18 | 538 | 215 | 1340 | 104 | -0.682 749 | -0.461 538 | St |
| 17 | 484 | 215 | 1394 | 104 | -0.781 065 | -0.781 065 | h |
| 16 | 460 | 185 | 1448 | 104 | -0.852 071 | -0.852 071 | h |
| 15 | 436 | 185 | 1472 | 104 | -0.895 767 | -0.895 767 | h |
| 14 | 412 | 185 | 1496 | 104 | -0.939 463 | -0.939 463 | h |
| 13 | 388 | 185 | 1520 | 104 | -0.983 159 | -0.983 159 | h |
| 12 | 388 | 161 | 1544 | 104 | -1.005 007 | -1.005 007 | h |
June 20th, 2017 at 8:30:17 AM
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Here are some infinite-deck results for the case of three aces. First, here is my probability distribution for the dealer's final hand:
Here is the same table for the player.*
Looking at every combination of both hands, here is my table for the player's net win *:
So, this agrees with neither of our figures. Let me see where I have gone wrong...
* Corrected (6/20/17 4:51 PM PST)
| Dealer | Total |
|---|---|
| 12 | 0.047337278 |
| 13 | 0.047337278 |
| 14 | 0.047337278 |
| 15 | 0.047337278 |
| 16 | 0.047337278 |
| 17 | 0.106508876 |
| 18 | 0.106508876 |
| 19 | 0.106508876 |
| 20 | 0.106508876 |
| 21 | 0.337278107 |
| Total | 1 |
Here is the same table for the player.*
| Player | Probability |
|---|---|
| 12 | 0.307692308 |
| 13 | 0.076923077 |
| 14 | 0.076923077 |
| 15 | 0.076923077 |
| 16 | 0.076923077 |
| 17 | 0.076923077 |
| 18 | 0.076923077 |
| 19 | 0.076923077 |
| 20 | 0.076923077 |
| 21 | 0.076923077 |
Looking at every combination of both hands, here is my table for the player's net win *:
| Win | Probability | Return |
|---|---|---|
| 2 | 0.176604461 | 0.353208921 |
| 1 | 0.047337278 | 0.047337278 |
| 0 | 0.073281748 | 0 |
| -2 | 0.702776513 | -1.405553027 |
| Total | 1 | -1.005006827 |
So, this agrees with neither of our figures. Let me see where I have gone wrong...
* Corrected (6/20/17 4:51 PM PST)
Last edited by: Wizard on Jun 20, 2017
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 20th, 2017 at 10:54:05 AM
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I found an error in how I was scoring some soft hands. I now show that hitting the AAA situation has an EV of -1.009, so folding is indeed better. The difference between that and -0.983158853 for infinite decks may be due to the effect of elimination with six decks.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 20th, 2017 at 12:09:44 PM
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After fixing that problem my return for the game only drops a little to -0.0015654.
Here is the new player ace strategy:
Note, if AAA shows as a hit, then you may need to clear your browsing data.
Here is the new player ace strategy:
Note, if AAA shows as a hit, then you may need to clear your browsing data.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 20th, 2017 at 3:37:42 PM
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The "basic" strategy seems ok on paper, but it would be a pain to fumble thru 10 cards to figure out in the 2 seconds the dealer gives you.
Pass.
Pass.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
June 20th, 2017 at 4:43:09 PM
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Quote: WizardHere are some infinite-deck results for the case of three aces..
Here is the same table for the player.
Player Probability 12 0.076923077 13 0.307692308 14 0.076923077 15 0.076923077 16 0.076923077 17 0.076923077 18 0.076923077 19 0.076923077 20 0.076923077 21 0.076923077
If the player is going to hit his soft hand then all the values have 1/13 except the one you're already on has 4/13 (as there are four tens). Thus your table above seems to have started with Soft 3 not Soft 2! Indeed I get -.9831 for player having 2 seeing AA.
June 20th, 2017 at 4:53:52 PM
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Quote: charliepatrick
If the player is going to hit his soft hand then all the values have 1/13 except the one you're already on has 4/13 (as there are four tens). Thus your table above seems to have started with Soft 3 not Soft 2! Indeed I get -.9831 for player having 2 seeing AA.
D'oh! After fixing that, I get an infinite-deck EV for that situation of -1.005006827.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 20th, 2017 at 7:43:44 PM
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Quote: WizardI agree exactly how you put it. Yes, if the player busts first, he loses, as in regular blackjack. Also correct that busting is not very common in this game as you tend to start with good hands and can have at most three cards.
Normally Internet casino software companies just steal land casino games and when they do make up one on their own, it is something bizarre. However, this seems like a pretty good game concept. I could easily see it working in a land casino. Some rule would need to be tweaked to give the house a bigger edge. Probably raising the dealer qualifying point.
Wizard,
This game is not invented by casino software companies. It is invented by two Polish guys, over 10 years ago.
I have met with them a few times.
Stephen Au-Yeung (Legend of New Table Games®) NewTableGames.com
June 20th, 2017 at 9:13:11 PM
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Quote: WizardI found an error in how I was scoring some soft hands. I now show that hitting the AAA situation has an EV of -1.009, so folding is indeed better. The difference between that and -0.983158853 for infinite decks may be due to the effect of elimination with six decks.
lol, with a composition-dependent model I had calculated EV = -0.95394829 for hitting the AAA, and I thought it must be correct because it agreed with the Wizard's strategy charts. I now have no conviction that my calculation is correct - but I admit to feeling sorry for any player who is playing this game because its very hard to figure out the basic strategy.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 21st, 2017 at 2:19:21 AM
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Quote: MrCasinoGamesWizard,
This game is not invented by casino software companies. It is invented by two Polish guys, over 10 years ago.
I have met with them a few times.
"Back in the day" this would be a delightful launching point for a "Pollock" joke - somebody mentioned in another thread that you don't seem to hear them anymore.
Ethnic jokes are definitely unacceptable to more and more of the polite public these days. I suppose there are younger folk who didn't know Poles used to be so picked on.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
June 21st, 2017 at 6:13:04 AM
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I've used a different way to look at each combination of cards and get the following results for AAA. Strategy 2 is best (and equal to s4) to pick Common card A and then "Hit".
I think this will mean some marginal decisions on infinite deck might flip when six decks are considered.
21 Duel : Number of decks=6. s17
P1: 1 CA: 1 CB: 1
S1: W:0 T:0 L:338715153216 D:16105858560 B:0 J:0
S2: W:62736486912 T:26177557824 L:249801108480 D:16105858560 B:0 J:0
S3: W:0 T:0 L:338715153216 D:16105858560 B:0 J:0
S4: W:62736486912 T:26177557824 L:249801108480 D:16105858560 B:0 J:0
EV: -1.0090253189459413 St: AHit
21 Duel : Number of decks=999999. s17
P1: 1 CA: 1 CB: 1
S1: W:0 T:0 L:8.572868256940735e+42 D:4.259809239132098e+41 B:0 J:0
S2: W:1.5892369162560742e+42 T:6.594514206852045e+41 L:6.324179919999459e+42 D:4.259809239132098e+41 B:0 J:0
S3: W:0 T:0 L:8.572868256940735e+42 D:4.259809239132098e+41 B:0 J:0
S4: W:1.5892369162560742e+42 T:6.594514206852045e+41 L:6.324179919999459e+42 D:4.259809239132098e+41 B:0 J:0
EV: -1.0050068516333703 St: AHit
June 21st, 2017 at 8:17:05 AM
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Quote: MrCasinoGamesWizard,
This game is not invented by casino software companies. It is invented by two Polish guys, over 10 years ago.
I have met with them a few times.
Can you expand on what placements it has had. I actually think this is a pretty good game concept.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 21st, 2017 at 8:28:11 AM
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Quote: WizardCan you expand on what placements it has had. I actually think this is a pretty good game concept.
Hi Wizard,,
As far as I know, This game is not in any live casino, it is only play in online casino power by Playtech.
They have an exclusive agreement with Playtech for online casinos.
P.S. I have not hear from them for over 10 years.
Stephen Au-Yeung (Legend of New Table Games®) NewTableGames.com
June 21st, 2017 at 10:22:41 AM
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Quote: MrCasinoGamesHi Wizard,,
As far as I know, This game is not in any live casino, it is only play in online casino power by Playtech.
They have an exclusive agreement with Playtech for online casinos.
P.S. I have not hear from them for over 10 years.
Thanks.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 21st, 2017 at 10:59:32 AM
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Quote: charliepatrickI've used a different way to look at each combination of cards and get the following results for AAA. Strategy 2 is best (and equal to s4) to pick Common card A and then "Hit".
I think this will mean some marginal decisions on infinite deck might flip when six decks are considered.
To expand on what I said earlier, and correct an error that I found in my composition-dependent calculation:
I evaluated the case of two common aces and a player ace. I split this case into ten "subcases" when the player's facedown card is an A, 2, 3 ... T, but not known until after the player's decision. For each of the subcases I calculated the probability of the subcase, and the probability of the dealer's outcome (12, 13 . . . 21) given six decks and the removal of the 4 cards (3 aces and the player's facedown card) from the 6 deck shoe.
I calculate that the best strategy is to FOLD, and that HIT has an EV = -1.009025319.
Last edited by: gordonm888 on Jun 21, 2017
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 21st, 2017 at 12:55:59 PM
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Quote: gordonm888I calculate that the best strategy is to FOLD, and that HIT has an EV = -1.009025319.
That's close to what I got. I used a random simulation. For selection the left ace I got -1.009154 and for the right ace -1.00868. Given that my numbers have some inherent error, I think it is safe to say we don't disagree.
I'm sure somebody will ask why I wasted time analyzing both cards when they are the same. In general, I like to keep the complexity of code to a minimum, even at the expense of the program doing extra calculations it doesn't need to do.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 21st, 2017 at 9:52:17 PM
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I've cracked it and got their 1.618626% based on an average of 1.9 bets with a House Edge of 3.075%. One of my mistakes was to assume that the Player could make a Blackjack but all 21s are treated equally so can still be tied by the other party.
I get slightly different strategy - for instance with a 7 and looking at Ace and 3 you hit the 10 rather than go for the safer 18.
| P (Folds) | Bust | DNQ | Win | Tie | Lose | |
| 9.997 846% | 4.977 483% | 4.662 110% | 35.734 990% | 15.000 219% | 29.627 351% | |
| -1 | -2 | 1 | 2 | 0 | -2 | |
| -9.997 846% | -9.954 967% | 4.662 110% | 71.469 981% | 0.000 000% | -59.254 703% | -3.075 424% |
| 1 | 2 | 2 | 2 | 2 | 2 | |
| 9.997 846% | 9.954 967% | 9.324 220% | 71.469 981% | 30.000 438% | 59.254 703% | 1.900 022 |
| -1.618 626% |
I get slightly different strategy - for instance with a 7 and looking at Ace and 3 you hit the 10 rather than go for the safer 18.
| Upcard = 1 | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| A | F | |||||||||
| 2 | RH | H | ||||||||
| 3 | RH | RH | H | |||||||
| 4 | RH | RH | RH | H | ||||||
| 5 | RH | RH | RH | RH | H | |||||
| 6 | RH | RS | RS | RS | RH | H | ||||
| 7 | RS | RS | RS | RS | RS | RS | S | |||
| 8 | RS | RS | RS | RS | RS | RS | RS | S | ||
| 9 | RS | RS | RS | RS | RS | RS | RS | RS | S | |
| 10 | RS | RS | RS | RS | RS | RS | RS | RS | RS | S |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 2 | ||||||||||
| A | H | |||||||||
| 2 | LH | H | ||||||||
| 3 | LH | RH | H | |||||||
| 4 | LH | RH | RH | H | ||||||
| 5 | F | RH | RH | RH | H | |||||
| 6 | F | RH | RH | RH | RH | H | ||||
| 7 | RH | RH | RH | RH | RH | RH | H | |||
| 8 | RH | RH | RH | RH | RH | RH | RH | H | ||
| 9 | RH | RH | RH | RH | RH | RH | RH | RH | H | |
| 10 | F | RH | RH | RH | F | F | LH | LH | LH | H |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 3 | ||||||||||
| A | H | |||||||||
| 2 | LH | H | ||||||||
| 3 | LH | RH | H | |||||||
| 4 | LH | RH | RH | H | ||||||
| 5 | F | RH | RH | RH | H | |||||
| 6 | RH | RH | RH | RH | RH | H | ||||
| 7 | RH | RH | RH | RH | RH | RH | H | |||
| 8 | RH | RH | RH | RH | RH | RH | RH | H | ||
| 9 | F | RH | RH | RH | RH | LH | LH | LH | H | |
| 10 | F | RH | RH | F | F | LH | LH | LH | LH | H |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 4 | ||||||||||
| A | H | |||||||||
| 2 | LH | H | ||||||||
| 3 | LH | RH | H | |||||||
| 4 | LH | RH | RH | H | ||||||
| 5 | RH | RH | RH | RH | H | |||||
| 6 | RH | RH | RH | RH | RH | H | ||||
| 7 | RH | RH | RH | RH | RH | RH | H | |||
| 8 | F | RH | RH | RH | LH | LH | LH | H | ||
| 9 | F | RH | RH | RH | LH | LH | LH | LH | H | |
| 10 | F | RH | F | F | LH | LH | LH | LH | LH | H |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 5 | ||||||||||
| A | H | |||||||||
| 2 | LH | H | ||||||||
| 3 | LH | RH | H | |||||||
| 4 | LH | RH | RH | H | ||||||
| 5 | RH | RH | RH | RH | H | |||||
| 6 | RH | RH | RH | RH | RH | H | ||||
| 7 | F | RH | LH | LH | LH | LH | H | |||
| 8 | F | RH | LH | LH | LH | LH | LH | H | ||
| 9 | F | RH | RH | LH | LH | LH | LH | LH | H | |
| 10 | F | F | LH | LH | LH | LH | F | F | F | F |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 6 | ||||||||||
| A | H | |||||||||
| 2 | LH | H | ||||||||
| 3 | LH | RH | H | |||||||
| 4 | RH | RH | RH | H | ||||||
| 5 | RH | RH | RH | RH | H | |||||
| 6 | LH | LH | LH | LH | LH | H | ||||
| 7 | LH | LH | LH | LH | LH | LH | H | |||
| 8 | LH | LH | LH | LH | LH | LH | LH | H | ||
| 9 | LH | LH | LH | LH | LH | LH | LH | LH | H | |
| 10 | LH | RS | LH | LH | LH | F | F | F | F | F |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 7 | ||||||||||
| A | S | |||||||||
| 2 | LS | H | ||||||||
| 3 | RH | RH | H | |||||||
| 4 | RH | RH | RH | H | ||||||
| 5 | LS | LH | LH | LH | H | |||||
| 6 | LS | LH | LH | LH | LH | H | ||||
| 7 | LS | LH | LH | LH | LH | LH | H | |||
| 8 | LS | LH | LH | LH | LH | LH | LH | H | ||
| 9 | LS | LH | LH | LH | LH | LH | LH | LH | H | |
| 10 | LS | RS | LH | LH | F | F | F | RS | RS | S |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 8 | ||||||||||
| A | S | |||||||||
| 2 | LS | H | ||||||||
| 3 | LS | RH | H | |||||||
| 4 | LS | LH | LH | H | ||||||
| 5 | LS | LH | LH | LH | H | |||||
| 6 | LS | LH | LH | LH | LH | S | ||||
| 7 | LS | LH | LH | LH | LH | LH | H | |||
| 8 | LS | LH | LH | LH | LH | LH | LH | H | ||
| 9 | LS | LH | LH | LH | LH | RS | RS | RS | S | |
| 10 | LS | LH | LH | RS | RS | RS | RS | RS | RS | S |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 9 | ||||||||||
| A | S | |||||||||
| 2 | LS | H | ||||||||
| 3 | LS | LH | H | |||||||
| 4 | LS | LH | LH | H | ||||||
| 5 | LS | LH | LH | LH | S | |||||
| 6 | LS | LH | LH | LH | RS | S | ||||
| 7 | LS | LH | LH | LH | LH | LH | H | |||
| 8 | LS | LH | LH | LH | RS | RS | RS | S | ||
| 9 | LS | LH | RS | RS | RS | RS | RS | RS | S | |
| 10 | LS | LH | RS | RS | RS | RS | RS | RS | RS | S |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
| Upcard = 10 | ||||||||||
| A | S | |||||||||
| 2 | LS | H | ||||||||
| 3 | LS | LH | H | |||||||
| 4 | LS | LH | LH | H | ||||||
| 5 | LS | LH | RS | RS | S | |||||
| 6 | LS | RS | RS | RS | RS | S | ||||
| 7 | LS | RS | RS | RS | RS | RS | S | |||
| 8 | LS | RS | RS | RS | RS | RS | RS | S | ||
| 9 | LS | RS | RS | RS | RS | RS | RS | RS | S | |
| 10 | LS | RS | RS | RS | RS | RS | RS | RS | RS | S |
| A | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
June 22nd, 2017 at 3:59:53 AM
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fyi - Here are the figures for Player = 7 , Common cards = Ace and Three.
| Dealer | DNQ | W | T | L | |
| Player Stands 18 (7 using A) | |||||
|---|---|---|---|---|---|
| Combinations | 4 488 | 27 897 | 3 936 | 58 851 | -0.603 329 |
| Player Hits 10 (7 using the 3) | |||||
| Contribution to payout | 38 093 856 768 | 468 511 727 616 | 0 | -902 148 046 848 | |
| Combinations | 38 093 856 768 | 234 255 863 808 | 84 390 100 992 | 451 074 023 424 | |
| 27648 | 1 377 816 | 8 472 796 | 3 052 304 | 16 314 888 | -0.489 646 |
June 24th, 2017 at 4:48:05 PM
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I get practically the same house edge when considering my total EV at the decision point. If you saw before this edit, I'm tripping lol. You did this at the beginning of a 6 deck shoe? Not sure where there's a tiny difference.
Total EV: -0.03057238581536694
Total Fold: 0.0999784573895143
Average Bet: 1.9000215426104858
EV per Bet: -0.016090546938411443
Total EV: -0.03057238581536694
Total Fold: 0.0999784573895143
Average Bet: 1.9000215426104858
EV per Bet: -0.016090546938411443
| Outcome | Probability |
|---|---|
| P Fold | 0.0999784573895143 |
| P Bust | 0.049774832854983055 |
| D Bust | 0.05820703884381545 |
| Dealer NQ | 0.04663967908342749 |
| P Win | 0.2991435832330912 |
| Tie | 0.15006381561860496 |
| P Lost | 0.2961925929765635 |
Last edited by: lightningbolts on Jun 24, 2017
June 24th, 2017 at 6:33:23 PM
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Nice work charlie and lightningbolts. Interesting, how the game distributor quoted an EV/average bet rather than an EV/unit Bet, - because when the casino posts the tables stakes, i.e., the minimum and maximum bet, they sure as heck refer to the ante as the "Bet" size.
What I wonder with all of these strategy results is "What were the close decisions?" Clearly, player A+AA HIT vs. FOLD is a very close decision. The decision charlie posted information on, the player 7+A3, was not super close, with an EV difference of about 0.11 between 7A and 73. But were there any other close decisions in the basic strategy?
What I wonder with all of these strategy results is "What were the close decisions?" Clearly, player A+AA HIT vs. FOLD is a very close decision. The decision charlie posted information on, the player 7+A3, was not super close, with an EV difference of about 0.11 between 7A and 73. But were there any other close decisions in the basic strategy?
Last edited by: gordonm888 on Jun 24, 2017
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
June 25th, 2017 at 2:37:23 AM
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Running the spreadsheet for four decks gives a fold for 2 (A4) (HE = 3.075%)
Six decks -0.997916 Four decks -1.001762.
btw There seemed lots of chances to make almost untraceable mistakes - for instance I got player bust hands wrong (they were being counted as both bust and player beats dealer) and my misunderstanding whether player BJs automatically won. I used the 7 (A3) example as it seemed wizard was having some difficulty, perhaps similar to me, and this one is good at testing whether the dealer is picking the best starting hand for their various first cards and has the case where the player stands on 18 or hits 10.
Six decks -0.997916 Four decks -1.001762.
btw There seemed lots of chances to make almost untraceable mistakes - for instance I got player bust hands wrong (they were being counted as both bust and player beats dealer) and my misunderstanding whether player BJs automatically won. I used the 7 (A3) example as it seemed wizard was having some difficulty, perhaps similar to me, and this one is good at testing whether the dealer is picking the best starting hand for their various first cards and has the case where the player stands on 18 or hits 10.
June 25th, 2017 at 9:11:38 AM
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lol your first mistake was using a microsoft product. But seriously, writing a program is less error prone
June 25th, 2017 at 9:53:39 AM
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^ Usually for these types of things I use a spreadsheet for infinite deck analysis and then develop a program to handle finite decks. Hopefully the results converge as the number of decks increases.
In this case I was getting different results and decided to use a brute force method. This used all 550 ways of starting with 10 player cards with 55 possible pairs of community cards. Then for each of these 1000 ways of having the dealer's 1st card, dealer's 2nd card, player's 2nd card.
As you saw I check a few of the results (e.f. AAA, 7(A3) ) using a spreadsheet but with a different approach.
In this case I was getting different results and decided to use a brute force method. This used all 550 ways of starting with 10 player cards with 55 possible pairs of community cards. Then for each of these 1000 ways of having the dealer's 1st card, dealer's 2nd card, player's 2nd card.
As you saw I check a few of the results (e.f. AAA, 7(A3) ) using a spreadsheet but with a different approach.
June 25th, 2017 at 10:16:20 AM
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Oh I like this...I'll often enumerate then simulate as a check. I didn't simulate because our numbers matched up very closely.
