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13 members have voted

Wizard
Administrator
Wizard
Joined: Oct 14, 2009
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March 7th, 2017 at 5:25:12 PM permalink
Quote: charliepatrick

When I analysed it quickly using infinite deck I recall there were only two squares where the strategy depended on whether you had an Odds bet still running. So it might be easier to have one strategy card. Note that I separated hitting from Doubling - the latter knows whether you've started Even or Odd!



You're right, there are very few differences. I'm surprised.

Quote:

(i) There seems to be a misalignment in the Basic Strategy For Even Starting Hands s17 as the double 11 row is marked 13.



You're right. Thanks for the correction. I just fixed it.

Quote:

(ii) I think it's worth mentioning whether you split or double with (say) 3,3 vs 16 or similar.



I'm not sure I see your point. D=double and P = split. They are also in different colors.

Quote:

(iii) The rules state the dealer stands on Soft 17 - so there's an argument to leave out that bit (or just say this is only in the UK at the moment).



Good point. I just eliminated that last rule about standing on soft 17, although that is the case with all placements so far.

Quote:

(iv) 17-21 could be handled as "Stiffs" catering for both hard and soft totals where the final dealer's total is known (although I can see card dependent strategies may be different if there were any close decisions).



Are you suggesting I just say those cases are obvious and leave them off the table? If I go down that road, people will ask me why I list obvious plays in the blackjack tables. I do because if I don't, people will write to me asking how to play hands like a hard 20 in blackjack.

Quote:

Note : I haven't checked my strategy and it comes out with a different House Edge, so there's probably something that I've missed.



MrCasinoGames was kind enough to give me his spreadsheet. You might ask him if you can have a copy, if the differences are keeping you up at night.
It's not whether you win or lose; it's whether or not you had a good bet.
MrCasinoGames
MrCasinoGames
Joined: Sep 13, 2010
  • Threads: 92
  • Posts: 885
March 7th, 2017 at 5:33:46 PM permalink
Quote: charliepatrick

When I analysed it quickly using infinite deck I recall there were only two squares where the strategy depended on whether you had an Odds bet still running. So it might be easier to have one strategy card. Note that I separated hitting from Doubling - the latter knows whether you've started Even or Odd!

(i) There seems to be a misalignment in the Basic Strategy For Even Starting Hands s17 as the double 11 row is marked 13.
(ii) I think it's worth mentioning whether you split or double with (say) 3,3 vs 16 or similar.
(iii) The rules state the dealer stands on Soft 17 - so there's an argument to leave out that bit (or just say this is only in the UK at the moment).
(iv) 17-21 could be handled as "Stiffs" catering for both hard and soft totals where the final dealer's total is known (although I can see card dependent strategies may be different if there were any close decisions).
Note : I haven't checked my strategy and it comes out with a different House Edge, so there's probably something that I've missed.


Hi charliepatrick,

Thanks for your inputs.

PM me if you would like a copy of the spreadsheet and report (By Charles R. Mousseau) on Open 21® Blackjack.
Stephen Au-Yeung (Casino Hold'em®) NewTableGames.com
Romes
Romes
Joined: Jul 22, 2014
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March 10th, 2017 at 7:29:29 AM permalink
Quote: MrCasinoGames

Hi Paradigm,

The Probability of a Odd Total on the initial 2 card dealt in a 6-Deck game is 47.4895%.
Notes: (An odd number + even number = odd number) or (A even number + an odd number = odd number).

Ah, my apologies for only doing half the equation...

P(Odd Hand) = P(1stOdd 2ndEven) + P(1stEven 2ndOdd)

P(1stOdd 2ndEven) = 23.67%

HOWEVER

P(1stEven 2ndOdd) = 23.67%

Thus, P(Odd Hand) = 23.67% + 23.67% = 47.34%

...Though, you still have to ALSO win the BJ hand to actually win the bet... Thus P(Winning Side Bet) = .4734 * .42 = .1988... So you lose the side bet 4/5 times, it's mandatory, and the big upside is a 2-1 pay on that 20% of the time (assuming you play proper basic strategy and don't have a higher loss rate in BJ).

Quote: Romes

*Edit: Numbers will change a bit for double exposure win rate, but I'd still think it comes out to quite a low number (<20%) to actually win both bets.

Hey I still wasn't that far off lol.
Playing it correctly means you've already won.
MrCasinoGames
MrCasinoGames
Joined: Sep 13, 2010
  • Threads: 92
  • Posts: 885
March 10th, 2017 at 10:09:28 PM permalink
Quote: Romes

Ah, my apologies for only doing half the equation...

P(Odd Hand) = P(1stOdd 2ndEven) + P(1stEven 2ndOdd)

P(1stOdd 2ndEven) = 23.67%

HOWEVER

P(1stEven 2ndOdd) = 23.67%

Thus, P(Odd Hand) = 23.67% + 23.67% = 47.34%

...Though, you still have to ALSO win the BJ hand to actually win the bet... Thus P(Winning Side Bet) = .4734 * .42 = .1988... So you lose the side bet 4/5 times, it's mandatory, and the big upside is a 2-1 pay on that 20% of the time (assuming you play proper basic strategy and don't have a higher loss rate in BJ).

Quote: Romes

*Edit: Numbers will change a bit for double exposure win rate, but I'd still think it comes out to quite a low number (<20%) to actually win both bets.

Hey I still wasn't that far off lol.


Hi Romes,
Thanks for your update.
Stephen Au-Yeung (Casino Hold'em®) NewTableGames.com
charliepatrick
charliepatrick
Joined: Jun 17, 2011
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March 15th, 2017 at 4:51:50 AM permalink
Quote: Wizard

...the differences are keeping you up at night...

Yes I'm still getting sleepless nights!

Side Bet probabilities

Running various simulations it seems the House Edge is lower for six decks than infinite decks and the side bet came out..
Even or OddWin/LosePercent
EvenLose
52.52%
OddWin
23.32%
OddTie
3.70%
OddLose
20.47%


Splitting Tens rules

I also seem to get that the rule for splitting tens has a fair influence on the House Edge whether
(i) you can split any two ten-valued cards or just ranked pairs (e.g. KK KQ KJ...TT or just KK QQ JJ TT)
(ii) you can resplit any many times as you wish
(iii) you can double if you receive an Ace on a picture card (I suspect Grosvenor will use their you can't double 21 rule).

Strategy e.g. vs 16 and other stiffs

When the dealer has 16 in normal Double Exposure you pile on money, for instance double 5 or 6 or any soft value ( https://wizardofodds.com/games/double-exposure/ ) so I should have expected the same. The only difference is with a starting odd total you also don't want to seriously affect the chances of the Side Bet winning, so you would't double 5 if that's your initial score but do if it's been created after a split. However you would always double 6 (2-4 not 3-3) vs 16 as the Side Bet has gone.

Thus I get it (infinite deck) that you are more aggressive with doubling and splitting.

MrCasinoGames
MrCasinoGames
Joined: Sep 13, 2010
  • Threads: 92
  • Posts: 885
March 20th, 2017 at 4:44:49 PM permalink
Quote: charliepatrick

Yes I'm still getting sleepless nights!

Side Bet probabilities

Running various simulations it seems the House Edge is lower for six decks than infinite decks and the side bet came out..

Even or OddWin/LosePercent
EvenLose
52.52%
OddWin
23.32%
OddTie
3.70%
OddLose
20.47%


Splitting Tens rules

I also seem to get that the rule for splitting tens has a fair influence on the House Edge whether
(i) you can split any two ten-valued cards or just ranked pairs (e.g. KK KQ KJ...TT or just KK QQ JJ TT)
(ii) you can resplit any many times as you wish
(iii) you can double if you receive an Ace on a picture card (I suspect Grosvenor will use their you can't double 21 rule).

Strategy e.g. vs 16 and other stiffs

When the dealer has 16 in normal Double Exposure you pile on money, for instance double 5 or 6 or any soft value ( https://wizardofodds.com/games/double-exposure/ ) so I should have expected the same. The only difference is with a starting odd total you also don't want to seriously affect the chances of the Side Bet winning, so you would't double 5 if that's your initial score but do if it's been created after a split. However you would always double 6 (2-4 not 3-3) vs 16 as the Side Bet has gone.

Thus I get it (infinite deck) that you are more aggressive with doubling and splitting.


Hi charliepatrick,

Thanks for your input.

You have been given very helpful and great info on Open 21® Blackjack.
Stephen Au-Yeung (Casino Hold'em®) NewTableGames.com

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