Fu Bacc

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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.

Hand	Stand	Hit	Close
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).

	0	1	2	3	4	5	6	7	8	9
9	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp
8	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp	TakeSp
7	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand
6	Stand	Stand	Stand	Stand	Stand	Stand	Stand	HHHHHS	Stand	Stand
5	HHHSS	HSSSS	Stand	Stand	Stand	HHHSS	Hit	HHHFF	Fold	Fold
4	Hit	Hit	Hit	Hit	Hit	Hit	Hit	FHHFFH	Fold	Fold
3	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
2	Hit	Hit	Hit	Hit	Hit	HHFFHH	Fold	Fold	Fold	Fold
1	Hit	Hit	Hit	Hit	Hit	HFFFH	Fold	Fold	Fold	Fold
0	Hit	FHHHHH	FFHHHH	FFFHHH	FFFHHH	Fold	Fold	Fold	Fold	FFFFFT

9	9		TakeSp
9	8		Stand
9	7		Stand
9	6		Stand
9	5		Stand
9	4		Stand
9	3		Stand
9	2		Stand
9	1		Stand
9	0		Stand
8	9		TakeSp
8	8		TakeSp
8	7		Stand
8	6		Stand
8	5		Stand
8	4		Stand
8	3		Stand
8	2		Stand
8	1		Stand
8	0		Stand
7	9		Stand
7	8		Stand
7	7		Stand
7	6		Stand
7	5		Stand
7	4		Stand
7	3		Stand
7	2		Stand
7	1		Stand
7	0		Stand
6	9		Stand
6	8		Stand
6	7	97	Hit
6	7	88	Hit
6	7	60	Hit
6	7	51	Hit
6	7	42	Hit
6	7	33	Stand
6	6		Stand
6	5		Stand
6	4		Stand
6	3		Stand
6	2		Stand
6	1		Stand
6	0		Stand
5	9		Fold
5	8		Fold
5	7	96	Hit
5	7	87	Hit
5	7	50	Hit
5	7	41	Fold
5	7	32	Fold
5	6		Hit
5	5	96	Hit
5	5	87	Hit
5	5	50	Hit
5	5	41	Stand
5	5	32	Stand
5	4		Stand
5	3		Stand
5	2		Stand
5	1	96	Hit
5	1	87	Stand
5	1	50	Stand
5	1	41	Stand
5	1	32	Stand
5	0	96	Hit
5	0	87	Hit
5	0	50	Hit
5	0	41	Stand
5	0	32	Stand
4	9		Fold
4	8		Fold
4	7	95	Fold
4	7	86	Hit
4	7	77	Hit
4	7	40	Fold
4	7	31	Fold
4	7	22	Hit
4	6		Hit
4	5		Hit
4	4		Hit
4	3		Hit
4	2		Hit
4	1		Hit
4	0		Hit
3	9		Fold
3	8		Fold
3	7		Fold
3	6		Fold
3	5		Hit
3	4		Hit
3	3		Hit
3	2		Hit
3	1		Hit
3	0		Hit
2	9		Fold
2	8		Fold
2	7		Fold
2	6		Fold
2	5	93	Hit
2	5	84	Hit
2	5	75	Fold
2	5	66	Fold
2	5	20	Hit
2	5	11	Hit
2	4		Hit
2	3		Hit
2	2		Hit
2	1		Hit
2	0		Hit
1	9		Fold
1	8		Fold
1	7		Fold
1	6		Fold
1	5	92	Hit
1	5	83	Fold
1	5	74	Fold
1	5	65	Fold
1	5	10	Hit
1	4		Hit
1	3		Hit
1	2		Hit
1	1		Hit
1	0		Hit
0	9	91	Fold
0	9	82	Fold
0	9	73	Fold
0	9	64	Fold
0	9	55	Fold
0	9	00	TakeSp
0	8		Fold
0	7		Fold
0	6		Fold
0	5		Fold
0	4	91	Fold
0	4	82	Fold
0	4	73	Fold
0	4	64	Hit
0	4	55	Hit
0	4	00	Hit
0	3	91	Fold
0	3	82	Fold
0	3	73	Fold
0	3	64	Hit
0	3	55	Hit
0	3	00	Hit
0	2	91	Fold
0	2	82	Fold
0	2	73	Hit
0	2	64	Hit
0	2	55	Hit
0	2	00	Hit
0	1	91	Fold
0	1	82	Hit
0	1	73	Hit
0	1	64	Hit
0	1	55	Hit
0	1	00	Hit
0	0		Hit

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%.

8d	0	1	2	3	4	5	6	7	8	9
9	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp
8	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp	TakeSp
7	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand
6	Stand	Stand	Stand	Stand	Stand	Stand	Stand	HHSSSS	Stand	Stand
5	Hit	Stand	Stand	Stand	Stand	Hit	Hit	Hit	Fold	Fold
4	Hit	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold
3	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
2	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
1	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
0	Hit	Hit	FFHHHH	Fold	Fold	Fold	Fold	Fold	Fold	FFFFFT

99d	0	1	2	3	4	5	6	7	8	9
9	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp
8	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	TakeSp	TakeSp
7	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand
6	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand	Stand
5	Hit	Stand	Stand	Stand	Stand	Hit	Hit	Hit	Fold	Fold
4	Hit	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold
3	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
2	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
1	Hit	Hit	Hit	Hit	Hit	Hit	Fold	Fold	Fold	Fold
0	Hit	Hit	Fold	Fold	Fold	Fold	Fold	Fold	Fold	FFFFFT

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.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

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.

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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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.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

gordonm888
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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.

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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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%

Wizard
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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!

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

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.

The race is not always to the swift, nor the battle to the strong; but that is the way to bet.

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).

	0	1	2	3	4	5	6	7	8	9
9	Stand	Stand	Stand	Stand	Stand	Stand	SSSDS	SSDSS	SDSSS	Stand
8	Stand	Stand	Stand	Stand	SSSSSD	Stand	SSSDSS	SSDSSS	Stand	DDSDDD
7	Stand	Stand	Stand	Stand	Stand	Stand	SSDSS	Stand	DSSSS	DSSSS
6	Stand	Stand	Stand	SSSSSD	Stand	Stand	Stand	DSSSSS	Draw	DSSSSS
5	Draw	Draw	Draw	Draw	Draw	Stand	Draw	Draw	Draw	Draw
4	Draw	Draw	Draw	Draw	Stand	Draw	Draw	Draw	Draw	Draw
3	Draw	Draw	Draw	Stand	Draw	Draw	Draw	Draw	Draw	Draw
2	Draw	Draw	Stand	Draw	Draw	Draw	Draw	Draw	Draw	Draw
1	Draw	Stand	Draw	Draw	Draw	Draw	Draw	Draw	Draw	Draw
0	Stand	Draw	Draw	Draw	Draw	Draw	Draw	Draw	Draw	Draw

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).
0 1 2 3 4 5 6 7 8 9
9 Stand Stand Stand Stand Stand Stand SSSDS SSDSS SDSSS Stand
8 Stand Stand Stand Stand SSSSSD Stand SSSDSS SSDSSS Stand DDSDDD
7 Stand Stand Stand Stand Stand Stand SSDSS Stand DSSSS DSSSS
6 Stand Stand Stand SSSSSD Stand Stand Stand DSSSSS Draw DSSSSS
5 Draw Draw Draw Draw Draw Stand Draw Draw Draw Draw
4 Draw Draw Draw Draw Stand Draw Draw Draw Draw Draw
3 Draw Draw Draw Stand Draw Draw Draw Draw Draw Draw
2 Draw Draw Stand Draw Draw Draw Draw Draw Draw Draw
1 Draw Stand Draw Draw Draw Draw Draw Draw Draw Draw
0 Stand Draw Draw Draw Draw Draw Draw Draw Draw Draw

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.

Wizard
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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)

gordonm888
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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

The race is not always to the swift, nor the battle to the strong; but that is the way to bet.

Wizard
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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.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)

gordonm888
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Joined: Feb 18, 2015

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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