gordonm888
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July 27th, 2021 at 6:21:47 PM permalink
Yes, I agree. 23v0 HIT EV = 0.5471486.

On my spreadsheet, on the line where the player's 32 draws a zero, I neglected to designate the 3 and 2 as removed from the deck when calculating the dealer's probabilistic outcomes.

I appear to have made the same error everytime the player has a 32 in his hand. I'll need to recalculate all those cases.

EDIT: Okay, here is the corrected chart. Thanks for helping me to catch that glitch.

Last edited by: gordonm888 on Jul 27, 2021
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ssho88
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July 27th, 2021 at 8:45:17 PM permalink
Quote: gordonm888

Yes, I agree. 23v0 HIT EV = 0.5471486.

On my spreadsheet, on the line where the player's 32 draws a zero, I neglected to designate the 3 and 2 as removed from the deck when calculating the dealer's probabilistic outcomes.

I appear to have made the same error everytime the player has a 32 in his hand. I'll need to recalculate all those cases.

EDIT: Okay, here is the corrected chart. Thanks for helping me to catch that glitch.



I just randomly check and found that 4,0 vs 7, I got HIT ev = -1.0701440, and Fold ev = -1, so my ΔEV = 0.070144, compare to your 0.075 . . .


and 22 vs 7 should HIT( ev= -0.942683456) instead of FOLD( ev= -1) ?
Last edited by: ssho88 on Jul 27, 2021
charliepatrick
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July 27th, 2021 at 10:04:29 PM permalink
Yes I agree with your (4,0) vs 7 and (2,2) vs 7. Here's some of the other close decisions.
HandStandHitClose
P:9 6 D:1
-.411 564 626
-.411 039 948
.000 524 678
P:8 7 D:1
-.298 469 388
-.300 531 915
.002 062 527
P:7 3 D:3
-2.863 945 578
-1.005 029 671
.005 029 671
P:6 4 D:4
-2.867 346 939
-.992 980 171
.007 019 829
P:5 0 D:1
-.403 061 224
-.411 021 856
.007 960 631
P:2 1 D:7
-1.889 455 782
-1.008 051 093
.008 051 093
P:7 3 D:4
-2.846 938 776
-1.008 141 554
.008 141 554
P:4 1 D:7
-1.323 129 252
-1.009 679 404
.009 679 404
P:5 0 D:8
-1.270 408 163
-1.009 697 496
.009 697 496
P:3 2 D:7
-1.320 578 231
-1.013 496 888
.013 496 888
P:9 6 D:8
-1.268 707 483
-1.013 569 257
.013 569 257
P:9 1 D:1
-2.870 748 299
-1.014 039 658
.014 039 658
P:8 6 D:7
-1.678 571 429
-.985 236 648
.014 763 352
P:9 5 D:6
-1.692 176 871
-.983 970 184
.016 029 816
P:9 6 D:0
-.328 231 293
-.310 500 796
.017 730 496
P:8 7 D:0
-.328 231 293
-.310 066 580
.018 164 713
P:3 2 D:0
-.528 911 565
-.547 148 647
.018 237 082
P:8 7 D:8
-1.248 299 320
-1.018 381 821
.018 381 821
P:8 7 D:2
-.410 714 286
-.429 222 753
.018 508 467
P:4 1 D:0
-.528 911 565
-.547 474 309
.018 562 744
P:3 2 D:5
-.482 993 197
-.502 985 237
.019 992 039
P:4 1 D:5
-.482 993 197
-.503 419 453
.020 426 256
P:7 7 D:7
-1.663 265 306
-.978 506 296
.021 493 704
P:2 1 D:6
-1.917 517 007
-1.022 072 659
.022 072 659
P:8 2 D:4
-2.845 238 095
-1.024 659 864
.024 659 864
P:9 6 D:2
-.405 612 245
-.430 453 032
.024 840 787
P:8 2 D:3
-2.846 938 776
-1.026 595 745
.026 595 745
P:8 2 D:2
-2.874 149 660
-1.026 849 037
.026 849 037
P:6 6 D:4
-2.081 632 653
-.971 088 435
.028 911 565
P:9 1 D:2
-2.852 040 816
-1.032 674 772
.032 674 772
P:8 3 D:2
-2.472 789 116
-.966 131 133
.033 868 867
P:5 0 D:2
-.404 761 905
-.438 703 141
.033 941 236
P:3 1 D:7
-1.633 503 401
-1.034 664 930
.034 664 930
P:7 4 D:5
-2.462 585 034
-1.035 243 885
.035 243 885
P:3 0 D:6
-1.915 816 327
-1.035 280 069
.035 280 069
P:4 2 D:7
-.867 346 939
-.831 904 038
.035 442 901
P:9 1 D:3
-2.846 938 776
-1.039 622 232
.039 622 232
P:1 0 D:5
-2.460 034 014
-.957 247 793
.042 752 207
P:0 0 D:5
-2.874 149 660
-1.043 204 516
.043 204 516
P:3 3 D:7
-.955 782 313
-1.032 132 002
.044 217 687
P:4 0 D:6
-1.646 258 503
-.954 895 788
.045 104 212
P:3 2 D:1
-.510 204 082
-.557 207 990
.047 003 908
P:8 3 D:5
-2.460 884 354
-1.048 179 910
.048 179 910
P:9 1 D:4
-2.850 340 136
-1.051 563 178
.051 563 178
P:9 2 D:5
-2.462 585 034
-.947 803 590
.052 196 410
P:8 3 D:3
-2.397 959 184
-.947 206 542
.052 793 458
P:0 0 D:4
-2.853 741 497
-.943 370 965
.056 629 035
P:2 2 D:7
-1.566 326 531
-.942 683 456
.057 316 544
P:5 1 D:7
-.880 952 381
-.823 364 452
.057 587 929
P:8 3 D:4
-2.379 251 701
-.938 648 864
.061 351 136
P:6 0 D:7
-.882 653 061
-.818 081 488
.064 571 573
P:4 1 D:9
-1.340 986 395
-1.274 732 233
.066 254 161
P:7 4 D:4
-2.404 761 905
-.933 745 839
.066 254 161
P:6 5 D:4
-2.455 782 313
-.933 347 807
.066 652 193
P:5 0 D:0
-.496 598 639
-.429 439 861
.067 158 778
P:7 3 D:2
-2.850 340 136
-.932 696 483
.067 303 517
P:7 4 D:3
-2.438 775 510
-.931 900 420
.068 099 580
P:0 0 D:3
-2.850 340 136
-.931 357 649
.068 642 351
P:4 0 D:7
-1.637 755 102
-1.070 144 015
.070 144 015
ssho88
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July 27th, 2021 at 10:25:17 PM permalink
So some basic strategies may change and need to be updated
charliepatrick
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July 28th, 2021 at 5:11:42 AM permalink
Quote: ssho88

So some basic strategies may change and need to be updated

I haven't double checked but creating the table from the spreadsheet I get the following. Where there are multiple decisions they have been ordered by highest card (see the bigger table).
0123456789
9StandStandStandStandStandStandStandStandStandTakeSp
8StandStandStandStandStandStandStandStandTakeSpTakeSp
7StandStandStandStandStandStandStandStandStandStand
6StandStandStandStandStandStandStandHHHHHSStandStand
5HHHSSHSSSSStandStandStandHHHSSHitHHHFFFoldFold
4HitHitHitHitHitHitHitFHHFFHFoldFold
3HitHitHitHitHitHitFoldFoldFoldFold
2HitHitHitHitHitHHFFHHFoldFoldFoldFold
1HitHitHitHitHitHFFFHFoldFoldFoldFold
0HitFHHHHHFFHHHHFFFHHHFFFHHHFoldFoldFoldFoldFFFFFT


99TakeSp
98Stand
97Stand
96Stand
95Stand
94Stand
93Stand
92Stand
91Stand
90Stand
89TakeSp
88TakeSp
87Stand
86Stand
85Stand
84Stand
83Stand
82Stand
81Stand
80Stand
79Stand
78Stand
77Stand
76Stand
75Stand
74Stand
73Stand
72Stand
71Stand
70Stand
69Stand
68Stand
6797Hit
6788Hit
6760Hit
6751Hit
6742Hit
6733Stand
66Stand
65Stand
64Stand
63Stand
62Stand
61Stand
60Stand
59Fold
58Fold
5796Hit
5787Hit
5750Hit
5741Fold
5732Fold
56Hit
5596Hit
5587Hit
5550Hit
5541Stand
5532Stand
54Stand
53Stand
52Stand
5196Hit
5187Stand
5150Stand
5141Stand
5132Stand
5096Hit
5087Hit
5050Hit
5041Stand
5032Stand
49Fold
48Fold
4795Fold
4786Hit
4777Hit
4740Fold
4731Fold
4722Hit
46Hit
45Hit
44Hit
43Hit
42Hit
41Hit
40Hit
39Fold
38Fold
37Fold
36Fold
35Hit
34Hit
33Hit
32Hit
31Hit
30Hit
29Fold
28Fold
27Fold
26Fold
2593Hit
2584Hit
2575Fold
2566Fold
2520Hit
2511Hit
24Hit
23Hit
22Hit
21Hit
20Hit
19Fold
18Fold
17Fold
16Fold
1592Hit
1583Fold
1574Fold
1565Fold
1510Hit
14Hit
13Hit
12Hit
11Hit
10Hit
0991Fold
0982Fold
0973Fold
0964Fold
0955Fold
0900TakeSp
08Fold
07Fold
06Fold
05Fold
0491Fold
0482Fold
0473Fold
0464Hit
0455Hit
0400Hit
0391Fold
0382Fold
0373Fold
0364Hit
0355Hit
0300Hit
0291Fold
0282Fold
0273Hit
0264Hit
0255Hit
0200Hit
0191Fold
0182Hit
0173Hit
0164Hit
0155Hit
0100Hit
00Hit
gordonm888
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July 28th, 2021 at 10:47:46 AM permalink
The only change is to 2,2 vs 7.

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
gordonm888
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July 28th, 2021 at 11:05:14 AM permalink
Thanks for your review of my work.





Charlie, can you simply sum up your table to get a House Edge?
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
charliepatrick
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July 28th, 2021 at 11:35:12 AM permalink
Quote: gordonm888

...Charlie, can you simply sum up your table to get a House Edge?

Quote: ssho88

...Based on Gordon’s [as at 24th July] basic strategy and combination analysis, the house edge is 3.0516%.

The spreadsheet added it up (before I added logic to combine the results for similar decisions) and it still gets 3.0496%. As this would compare to the earlier number quoted, I think we can assume it's in the region of 3.05%.

Interestingly, OK for a laugh, the House Edge with 8 decks is 3.567%, 99 decks 3.612%.
8d0123456789
9StandStandStandStandStandStandStandStandStandTakeSp
8StandStandStandStandStandStandStandStandTakeSpTakeSp
7StandStandStandStandStandStandStandStandStandStand
6StandStandStandStandStandStandStandHHSSSSStandStand
5HitStandStandStandStandHitHitHitFoldFold
4HitHitHitHitHitHitHitFoldFoldFold
3HitHitHitHitHitHitFoldFoldFoldFold
2HitHitHitHitHitHitFoldFoldFoldFold
1HitHitHitHitHitHitFoldFoldFoldFold
0HitHitFFHHHHFoldFoldFoldFoldFoldFoldFFFFFT

99d0123456789
9StandStandStandStandStandStandStandStandStandTakeSp
8StandStandStandStandStandStandStandStandTakeSpTakeSp
7StandStandStandStandStandStandStandStandStandStand
6StandStandStandStandStandStandStandStandStandStand
5HitStandStandStandStandHitHitHitFoldFold
4HitHitHitHitHitHitHitFoldFoldFold
3HitHitHitHitHitHitFoldFoldFoldFold
2HitHitHitHitHitHitFoldFoldFoldFold
1HitHitHitHitHitHitFoldFoldFoldFold
0HitHitFoldFoldFoldFoldFoldFoldFoldFFFFFT
Wizard
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August 5th, 2021 at 1:40:48 PM permalink
Sorry I'm late to the party. I was on vacation when this thread came out.

First, thank you Gordon, Charlie, and ssho88 for your outstanding work.

Second, given this has already been analyzed three times with perfect or very close agreement, does anyone object if I use your figures and strategy at WoO? With full credit to all three of you, of course.
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gordonm888
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August 5th, 2021 at 3:08:37 PM permalink
Okay by me.

The tiny difference between Charlie's calculation of house edge and ssho88's simulation is that ssho88 used my original strategy which had the wrong decision for 22v7, whereas Charlie's calculated number now includes the correct decision for 22v7.

So my suggestion would be to quote the house edge value that Charlie calculated, but of course to give credit to both ssho88 and charlie.
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ssho88
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August 5th, 2021 at 7:25:06 PM permalink
Quote: charliepatrick

Quote: ssho88

...Based on Gordon’s [as at 24th July] basic strategy and combination analysis, the house edge is 3.0516%.

The spreadsheet added it up (before I added logic to combine the results for similar decisions) and it still gets 3.0496%. As this would compare to the earlier number quoted, I think we can assume it's in the region of 3.05%.



Yes I agree with you that the revised( HIT 22 vs 7) house edge = -3.04956069%




I am thinking to simulate the game as below :-

1) 5 players, card counter sit at box 5, first 4 players play with perfect basic strategy.
2) Card counter at box 5 will adjust(combinations analysis) his strategy according to the all seen cards of first 4 players and dealer's up card.
3) Find the element of risk.
Last edited by: ssho88 on Aug 5, 2021
Wizard
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August 5th, 2021 at 9:27:53 PM permalink
Is the player allowed to bet the Tie only? If so, has anyone worked out the EV of that? I assume the strategy would be to take a third card unless there is already a tie in points.
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August 5th, 2021 at 10:00:14 PM permalink
The way the rules are written, it says that betting the Tie Bet is one of three possible ways for the player to play - so it does sound as if the Tie Bet can be played as your only bet.

The Tie Bet only pays 7:1, so the Return is going to be terrible.

I think I agree with the Tie Bet strategy you stated.
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ssho88
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August 5th, 2021 at 10:24:51 PM permalink
Quote: Wizard

Is the player allowed to bet the Tie only? If so, has anyone worked out the EV of that? I assume the strategy would be to take a third card unless there is already a tie in points.




If the Tie Bet can be played as your only bet, and based on your strategy ( HIT when first 2 cards total <> dealer's up card, STAND when first 2 cards total = dealer's up card), the TIE house edge I calculated is 14.86%

HE = (1,559,988,736 * 7 - 1* 13,098,145,664)/14,658,134,400 * 100 = -14.86%
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August 6th, 2021 at 6:11:56 AM permalink
Quote: ssho88

If the Tie Bet can be played as your only bet, and based on your strategy ( HIT when first 2 cards total <> dealer's up card, STAND when first 2 cards total = dealer's up card), the TIE house edge I calculated is 14.86%

HE = (1,559,988,736 * 7 - 1* 13,098,145,664)/14,658,134,400 * 100 = -14.86%



Thank you! Good work!
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ssho88
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August 6th, 2021 at 7:38:14 AM permalink
Quote: Wizard

Thank you! Good work!



With further study, I found that your proposed strategy for TIE can be improved further.

With below strategy :-

1) When player first 2 cards total = dealer's up card. STAND.
2) When player first 2 cards total <> dealer's up card, and player first 2 cards total >=6, STAND
3) When player first 2 cards total <> dealer's up card, and player first 2 cards total <=5, HIT

The TIE house edge = -10.41%

This may still not be the optimum strategy, I guess the experts here definitely can improve it further through card composition analysis.
unJon
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August 6th, 2021 at 8:15:28 AM permalink
Quote: ssho88

With further study, I found that your proposed strategy for TIE can be improved further.

With below strategy :-

1) When player first 2 cards total = dealer's up card. STAND.
2) When player first 2 cards total <> dealer's up card, and player first 2 cards total >=6, STAND
3) When player first 2 cards total <> dealer's up card, and player first 2 cards total <=5, HIT

The TIE house edge = -10.41%

This may still not be the optimum strategy, I guess the experts here definitely can improve it further through card composition analysis.



Reasoning from first principals I think a simple strategy would do better if your #2 and 3 were based on dealer upcard rather than player upcard. Could be wrong though.
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charliepatrick
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August 6th, 2021 at 8:49:13 AM permalink
I haven't checked it but I used the same spreadsheet that I had for the basic game but looked at the higher chances of getting a Tie given Standing or Hitting; it results in a House Edge of 10.303% (assuming payout is 7/1 or 8 for 1).
By and large it agrees with the earlier one but has some exceptions (e.g. hit 44 vs 4, hit 61 vs 6).
0123456789
9StandStandStandStandStandStandSSSDSSSDSSSDSSSStand
8StandStandStandStandSSSSSDStandSSSDSSSSDSSSStandDDSDDD
7StandStandStandStandStandStandSSDSSStandDSSSSDSSSS
6StandStandStandSSSSSDStandStandStandDSSSSSDrawDSSSSS
5DrawDrawDrawDrawDrawStandDrawDrawDrawDraw
4DrawDrawDrawDrawStandDrawDrawDrawDrawDraw
3DrawDrawDrawStandDrawDrawDrawDrawDrawDraw
2DrawDrawStandDrawDrawDrawDrawDrawDrawDraw
1DrawStandDrawDrawDrawDrawDrawDrawDrawDraw
0StandDrawDrawDrawDrawDrawDrawDrawDrawDraw
ssho88
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August 6th, 2021 at 9:22:29 AM permalink
Quote: charliepatrick

I haven't checked it but I used the same spreadsheet that I had for the basic game but looked at the higher chances of getting a Tie given Standing or Hitting; it results in a House Edge of 10.303% (assuming payout is 7/1 or 8 for 1).
By and large it agrees with the earlier one but has some exceptions (e.g. hit 44 vs 4, hit 61 vs 6).

0123456789
9StandStandStandStandStandStandSSSDSSSDSSSDSSSStand
8StandStandStandStandSSSSSDStandSSSDSSSSDSSSStandDDSDDD
7StandStandStandStandStandStandSSDSSStandDSSSSDSSSS
6StandStandStandSSSSSDStandStandStandDSSSSSDrawDSSSSS
5DrawDrawDrawDrawDrawStandDrawDrawDrawDraw
4DrawDrawDrawDrawStandDrawDrawDrawDrawDraw
3DrawDrawDrawStandDrawDrawDrawDrawDrawDraw
2DrawDrawStandDrawDrawDrawDrawDrawDrawDraw
1DrawStandDrawDrawDrawDrawDrawDrawDrawDraw
0StandDrawDrawDrawDrawDrawDrawDrawDrawDraw




Good work!
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August 6th, 2021 at 10:46:04 AM permalink
Thanks for catching this. I tossed in bed last night (literally, I really did), worrying about whether player should stand on Tie Wager when total >5, and also about 44vs4 and 33vs3. It is great to log on today and see that you guys were way ahead of me. Well done!
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
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August 8th, 2021 at 6:38:03 AM permalink
Quote: gordonm888

Okay by me.



I just finished a first draft of my new page on Fu Bacc. Please have a look. As always, I welcome all comments, questions, and especially corrections.

I hope the attribution is acceptable by all. If anyone prefers to be known by any other name, please let me know.

Thank you for your outstanding work on this game!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
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August 8th, 2021 at 5:23:15 PM permalink
One slight correction. You've posted the first (Or second?) Strategy chart I came up with, but we updated it a couple of pages back and I've reproduced the updated version here:



The only difference on this chart is that 22v7 has been changed to HIT rather than FOLD.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
unJon
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August 8th, 2021 at 5:40:01 PM permalink
Quote: gordonm888

One slight correction. You've posted the first (Or second?) Strategy chart I came up with, but we updated it a couple of pages back and I've reproduced the updated version here:



The only difference on this chart is that 22v7 has been changed to HIT rather than FOLD.



You could save a row by collapsing 2,2 with 8,6/7,7
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August 8th, 2021 at 6:08:14 PM permalink
Quote: gordonm888

One slight correction. You've posted the first (Or second?) Strategy chart I came up with, but we updated it a couple of pages back and I've reproduced the updated version here:



Thanks. I'll hold off updating it again, pending your answer to unjon's question.
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August 9th, 2021 at 8:19:35 AM permalink
Format change on Basic Strategy Chart, with correct strategy for 22v7.

So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
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August 9th, 2021 at 9:33:46 AM permalink
Quote: gordonm888

Format change on Basic Strategy Chart, with correct strategy for 22v7.



Thanks. I just updated the strategy on the Fu Bacc page.

I think we can call it a good on this game. Thanks again, Charlie, Gordon, and Shoe for all your outstanding work!
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
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August 9th, 2021 at 9:41:00 AM permalink
You might want to write an introduction. I think it's still in placeholder status.
Have you tried 22 tonight? I said 22.
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August 9th, 2021 at 11:12:33 AM permalink
Quote: Gialmere

You might want to write an introduction. I think it's still in placeholder status.



Thanks! You're right.
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Gialmere
Gialmere
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  • Posts: 2921
Joined: Nov 26, 2018
November 3rd, 2021 at 8:59:55 PM permalink
Have you tried 22 tonight? I said 22.
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