Wizard
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Wizard
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August 9th, 2019 at 4:36:13 PM permalink
Here are my dealer probabilities in the base game with 999 decks, assuming no blackjack. The dealer up card is along the first row. I post this table because I think starting with the dealer probabilities is a good place to look for agreement.

Total 2 3 4 5 6 7 8 9 10 ace
Bust 0.345089 0.369178 0.392362 0.414774 0.437694 0.261368 0.244208 0.228113 0.229672 0.189154
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
2 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
3 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
4 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
5 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
6 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
7 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
8 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
9 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
10 0.000035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
11 0.000140 0.000035 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
12 0.001050 0.000490 0.000175 0.000035 0.000000 0.000000 0.000000 0.000000 0.000000 0.001011
13 0.002030 0.001190 0.000630 0.000280 0.000105 0.000035 0.000000 0.000000 0.000000 0.001769
14 0.003325 0.002170 0.001330 0.000735 0.000385 0.000175 0.000070 0.000035 0.000000 0.003286
15 0.005390 0.003465 0.002310 0.001435 0.000875 0.000455 0.000245 0.000140 0.000038 0.005460
16 0.008156 0.005531 0.003606 0.002415 0.001610 0.000910 0.000560 0.000350 0.000152 0.008190
17 0.128532 0.125274 0.121740 0.117957 0.114598 0.368443 0.128499 0.119956 0.120698 0.081727
18 0.134832 0.130878 0.126630 0.122511 0.114595 0.137671 0.359270 0.119938 0.120697 0.205127
19 0.129585 0.125974 0.122089 0.117957 0.114598 0.078498 0.128498 0.350730 0.120698 0.205128
20 0.123946 0.120727 0.117188 0.113398 0.110045 0.078499 0.069324 0.119956 0.370681 0.205131
21 0.117891 0.115088 0.111940 0.108503 0.105494 0.073945 0.069326 0.060783 0.037364 0.094015
Total 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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August 9th, 2019 at 5:31:54 PM permalink
I found a bug in my C++ program. After fixing it, I agree with myself with infinite decks. Changing the number of decks to one, I get a house edge of 2.89% in the base game. Interestingly, the house edge increases as the number of decks decreases.
It's not whether you win or lose; it's whether or not you had a good bet.
CrystalMath
CrystalMath
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August 9th, 2019 at 9:07:34 PM permalink
Quote: Wizard

Here are my dealer probabilities in the base game with 999 decks, assuming no blackjack. The dealer up card is along the first row. I post this table because I think starting with the dealer probabilities is a good place to look for agreement.



I am in 100% agreement with this table.
I heart Crystal Math.
Wizard
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Wizard
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CrystalMath
August 9th, 2019 at 9:15:04 PM permalink
Quote: CrystalMath

I am in 100% agreement with this table.



Thank you.
It's not whether you win or lose; it's whether or not you had a good bet.
CrystalMath
CrystalMath
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August 9th, 2019 at 9:25:21 PM permalink
Quote: Wizard

I've analyzed an infinite-deck version of the base game two ways. Here are the results of the house edge:

Spreadsheet: 2.66%
Looping program: 3.24%

So there is an error somewhere. I tend to trust the spreadsheet number more.



I get 2.656% with 1000 decks, which looks right in line with your spreadsheet.

I am now at 1.925% with 1 deck. I had an error accounting for the dealer peek, assuming a score of 17 or better.
I heart Crystal Math.
Wizard
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Wizard
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August 10th, 2019 at 6:39:58 AM permalink
Quote: CrystalMath

I am now at 1.925% with 1 deck. I had an error accounting for the dealer peek, assuming a score of 17 or better.



Thanks. I will look at my program again, as I get a higher number for one deck. I tend to think you're right.
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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CrystalMath
August 10th, 2019 at 9:41:40 AM permalink
Quote: CrystalMath

I am now at 1.925% with 1 deck.



I found a bug where I wasn't removing the initial three cards from the deck array. After correcting for that, we agree.

Thank you!
It's not whether you win or lose; it's whether or not you had a good bet.
Wizard
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Wizard
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MrCasinoGames
August 10th, 2019 at 1:26:28 PM permalink
As to the Stud Bonus side bet, I learned that a Twisted Stud is ranked as the LOWEST paying hand. For example, AA234 would pay as a high pair, not a Twisted Stud with 13 points. With that understanding, I redid my analysis and get a house edge of 2.49% on the side bet. My Twisted 21 page I believe to now have the correct rules and analysis.

I thank all who helped with this page, either doing math or helping determine the actual rules.
It's not whether you win or lose; it's whether or not you had a good bet.
charliepatrick
charliepatrick
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MrCasinoGames
August 10th, 2019 at 1:40:30 PM permalink
Personally I think they would be better off having the "Twisted Stud" paying 10 to 1 as I would be very annoyed to have AA234 while someone else has A2346 and gets paid more.

btw the figures I posted a few days ago were based on a quick look,
Table 1: I have updated the figures for the new rules and agree with wizard's.
Table 2: What would happen if any hand is paid for "Twisted Stud" if that's a better pay out and was 10 to 1.
HandThese rulesOther PermsPaysContribution
Super 16
7 932
7 932
20
166 572
Royal Flush
4
1 000
4 004
Straight Flush
36
500
18 036
Quads
624
200
125 424
Full House
3 744
75
284 544
Flush
5 108
15
81 728
Straight
10 200
6
71 400
Trips
54 912
4
274 560
Two Pairs
123 552
3
494 208
Pair of Jacks thru Kings
253 440
2
760 320
Pair of Aces
84 480
2
253 440
Pair of Twos
3 840
80 640
Pair of Threes
1 920
82 560
Pair of Fours
768
83 712
Pair of Fives
384
84 096
Pair of Sixes thru Tens
422 400
Nothing
1 020
1 301 520
7 932
2 591 028
0.305 199%
2 598 960
2 534 236
97.509 619%


...and these are what it would be if "Twisted Stud" were to pay 10 to 1.
HandThese rulesOther PermsPaysContribution
Super 16
23 256
23 256
10
255 816
Royal Flush
4
1 000
4 004
Straight Flush
36
500
18 036
Quads
624
200
125 424
Full House
3 744
75
284 544
Flush
5 108
15
81 728
Straight
1 020
9 180
6
64 260
Trips
3 264
51 648
4
258 240
Two Pairs
4 896
118 656
3
474 624
Pair of Jacks thru Kings
253 440
2
760 320
Pair of Aces
6 144
78 336
2
235 008
Pair of Twos
3 840
80 640
Pair of Threes
1 920
82 560
Pair of Fours
768
83 712
Pair of Fives
384
84 096
Pair of Sixes thru Tens
422 400
Nothing
1 020
1 301 520
23 256
2 575 704
0.894 819%
2 598 960
2 562 004
98.578 047%
AxelWolf
AxelWolf
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ForagerRS
August 10th, 2019 at 1:52:11 PM permalink
That rule change was implemented within hours of this discussion. Coincidence? You decide.
♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪

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