BukWildSuperFly
BukWildSuperFly
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May 9th, 2017 at 12:48:41 PM permalink
I have a somewhat unusual question. Lets say that you wanted to describe blackjack hands without simply saying that the hand closest to 21 was the best hand. So you had to come up with a ranking system for blackjack hands much like the rankings for poker hands (2 pair beats 1 pair, but is beat by a straight, and so on). A blackjack hand consisting of a 7, a 4 and a king made up a tier 1 hand and that would beat a hand that was a 7, a 4 and a 9 (which would be a tier 2 hand).

My question is this, if you wanted to produce a book listing all of the possible combinations you would need to describe the blackjack game in this manner roughly how many pages would be in this book?

For this project posit these parameters:
-suits don't matter and therefore do not have to be listed
-face cards can be described simply as a "face card" and need not be specified
-7 card hands are declared instant winners
-a multideck shoe is used
-after hitting a hand greater than 21 the player can no longer draw cards

I'm sure I'm probably forgetting some other parameters I need to be adding. But if I'm not I would be curious how unwieldy such a book of blackjack hand rankings would be.
Last edited by: BukWildSuperFly on May 9, 2017
Romes
Romes
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May 9th, 2017 at 1:03:57 PM permalink
I use the following rankings:

Blackjack
"21"
"20"
"19"
"18"
"17"
...everything else "oh sh*t". Why not "bucket" the categories to their ranked result... so instead of "tier 1" for 21's, why not just call them 21's?
Playing it correctly means you've already won.
BukWildSuperFly
BukWildSuperFly
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May 9th, 2017 at 1:22:04 PM permalink
Sure, for the sake of simplicity, tiers could be bucketed by their totals "21" "20" etc.

Like poker hands, with it's "straights" and "full houses" and so on, these hands could be renamed at a later time; the "14" being a "TwinkleFizz" the "21" a "FacePalmOmega" and so on. But yes, for simplicity's sake the labeling could be anything.
billryan
billryan
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May 9th, 2017 at 1:30:33 PM permalink
I think he means starting hands.
I'd rather be dealt an eleven than an 18.
Pair of 5s over a ten ,seven.
eight,two over eight ,ten.
The difference between fiction and reality is that fiction is supposed to make sense.
Hunterhill
Hunterhill
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May 9th, 2017 at 1:35:36 PM permalink
I think you can get a good estimate by looking at the Wizards Blackjack Switch page.
The mountain is tall but grass grows on top of the mountain.
QFIT
QFIT
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May 9th, 2017 at 2:02:34 PM permalink
Well, depends on rules and strategy. But, more importantly, depends on the dealer upcard. Assuming six decks, DAS, S17 and basic strategy, here's the EV of all starting hands in % sorted by best to last hand:

150.0 ATv2-9
138.8 ATv10
104.0 ATvA
79.1 A9v8
79.0 TTv8
77.3 A9v7
77.2 TTv7
75.9 A9v9
75.6 TTv9
70.3 TTv6
70.2 A9v6
67.9 AAv6
67.5 11v6
67.2 A9v5
67.1 TTv5
65.9 A9v4
65.9 TTv4
64.9 A9v3
64.8 TTv3
64.2 A9v2
63.8 TTv2
63.3 AAv5
63.0 11v5
61.5 A8v7
61.5 19v7
59.8 55v6
59.6 A8v8
59.0 19v8
58.4 10v6
58.2 AAv4
57.9 11v4
53.7 55v5
53.1 AAv3
52.9 11v3
52.8 10v5
49.4 A8v6
49.3 19v6
48.4 AAv2
48.0 11v2
47.9 55v4
47.5 10v4
47.3 AAv7
46.4 11v7
46.3 99v6
44.3 A8v5
44.1 19v5
43.9 A9v10
43.8 TTv10
42.7 55v3
42.2 A8v4
42.1 10v3
42.0 19v4
40.7 A8v3
40.4 55v7
40.3 88v6
40.1 19v3
40.1 A7v7
40.0 99v7
40.0 10v7
39.7 18v7
39.5 99v5
38.8 A8v2
38.6 19v2
38.3 A7v6
37.2 55v2
36.9 10v2
35.9 AAv8
34.8 11v8
32.8 9v6
31.7 99v4
31.7 88v7
30.4 88v5
30.2 A7v5
29.2 55v8
29.0 10v8
28.8 A8v9
28.4 19v9
28.0 18v6
26.2 9v5
25.9 A6v6
25.3 99v3
24.7 A7v4
24.5 77v6
23.8 22v6
23.6 AAv9
22.8 99v8
22.6 11v9
22.4 88v4
21.3 33v6
20.0 18v5
19.7 9v4
19.7 99v2
19.6 A6v5
18.6 A2v6
18.6 A5v6
18.5 A3v6
18.2 A4v6
18.0 A7v3
17.6 9v7
17.4 18v4
17.0 22v5
16.9 44v6
15.9 77v5
15.7 66v6
15.4 88v3
15.2 33v5
15.2 TTvA
15.0 55v9
14.8 18v3
14.6 A9vA
14.5 10v9
14.0 A2v5
13.7 A3v5
13.2 A4v5
13.1 9v3
12.8 A5v5
12.5 A6v4
12.4 A7v2
12.1 18v2
12.1 A2v7
12.0 8v6
11.0 44v5
11.0 66v5
10.8 A7v8
10.4 18v8
10.3 A2v4
10.0 9v8
9.7 AAv10
8.6 44v7
8.5 11v10
8.4 8v7
8.3 88v2
8.2 A3v4
8.1 8v5
7.7 A3v7
7.7 9v2
7.5 77v4
7.3 A2v3
6.8 22v4
6.2 A4v4
5.9 A5v4
5.8 A6v3
5.5 A6v7
5.2 A2v8
5.1 A3v3
4.7 44v4
4.6 33v4
4.6 8v4
4.5 A2v2
3.7 A4v7
3.4 7v6
2.8 A4v3
2.1 A3v2
1.7 A3v8
1.1 44v3
0.9 8v3
0.9 22v7
0.8 A5v3
0.8 17v6
0.6 66v4
0.2 7v5
0.2 5v6
0.1 A6v2
-0.2 A4v2
-0.7 A5v7
-0.9 22v3
-0.9 6v6
-1.3 19v10
-1.5 A8v10
-1.7 5v5
-1.9 44v2
-2.1 8v2
-2.3 A5v2
-2.7 A4v8
-2.9 6v5
-3.0 88v8
-3.2 77v3
-3.5 A2v9
-3.9 7v4
-4.5 17v5
-4.9 33v3
-4.9 77v7
-5.1 33v7
-5.2 9v9
-5.3 10v10
-5.4 55v10
-5.9 8v8
-6.0 5v4
-6.0 44v8
-6.8 A5v8
-6.9 7v7
-7.1 6v4
-7.1 A6v8
-7.2 A3v9
-7.6 7v3
-7.9 17v4
-8.1 99v9
-8.1 22v2
-9.5 5v3
-9.8 A7v9
-10.2 66v3
-10.6 6v3
-11.0 7v2
-11.0 17v7
-11.1 19vA
-11.2 A4v9
-11.7 A8vA
-11.8 77v2
-11.8 17v3
-11.9 5v7
-12.9 5v2
-13.3 33v2
-14.2 6v2
-14.6 A6v9
-15.1 A5v9
-15.3 6v7
-15.4 17v2
-15.5 12v6
-15.5 13v6
-15.5 14v6
-15.5 15v6
-15.7 22v8
-15.8 16v6
-16.3 13v5
-16.3 12v5
-16.3 14v5
-16.4 15v5
-16.5 16v5
-16.9 A2v10
-18.5 18v9
-18.6 5v8
-19.8 66v2
-20.1 A3v10
-20.6 A7v10
-20.8 13v4
-20.9 14v4
-20.9 15v4
-20.9 44v9
-20.9 11vA
-20.9 16v4
-20.9 12v4
-21.0 8v9
-21.2 7v8
-21.5 12v7
-21.8 9v10
-21.9 33v8
-21.9 66v7
-22.0 6v8
-22.4 AAvA
-23.2 12v3
-23.5 A4v10
-23.5 99v10
-23.7 22v9
-23.8 18v10
-25.2 14v3
-25.2 15v3
-25.2 13v3
-25.3 16v3
-25.3 12v2
-25.4 10vA
-25.5 55vA
-25.5 A6v10
-26.6 5v9
-26.9 A5v10
-27.2 13v7
-27.5 12v8
-28.0 66v8
-28.7 7v9
-29.3 15v2
-29.4 6v9
-29.4 13v2
-29.4 16v2
-29.4 14v2
-29.5 33v9
-30.7 44v10
-30.8 8v10
-32.4 14v7
-32.7 13v8
-34.2 22v10
-34.4 12v9
-34.6 66v9
-35.2 A2vA
-35.7 9vA
-36.6 5v10
-36.7 15v7
-37.0 14v8
-37.3 7v10
-37.5 18vA
-37.5 99vA
-37.6 77v8
-37.6 A7vA
-37.6 A3vA
-38.5 17v8
-38.5 13v9
-38.7 88v9
-39.0 33v10
-39.0 6v10
-40.3 A4vA
-40.8 16v7
-41.6 15v8
-42.2 17v9
-42.6 12v10
-42.8 A5vA
-42.9 14v9
-43.0 66v10
-43.6 A6vA
-43.7 77v9
-44.7 44vA
-44.9 8vA
-45.3 16v8
-46.3 17v10
-46.7 13v10
-47.1 15v9
-48.6 22vA
-50.3 5vA
-50.4 16v9
-50.5 14v10
-51.4 77v10
-51.4 88v10
-52.3 6vA
-52.4 33vA
-52.8 7vA
-54.2 15v10
-55.2 12vA
-55.6 66vA
-56.0 88vA
-57.0 16v10
-58.4 13vA
-61.3 14vA
-61.9 77vA
-63.7 17vA
-64.1 15vA
-66.4 16vA
Last edited by: QFIT on May 9, 2017
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
QFIT
QFIT
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May 9th, 2017 at 2:22:35 PM permalink
Now, for a counter, the order changes. It's a bit more complex as you must take into account the betting. This is for the same rules, Hi-Opt II with full indices, spread 1-15 with optimal Kelly betting:

150.0 ATv2-9
138.8 ATv10
101.6 ATvA
80.0 A9v8
80.0 TTv8
78.5 A9v7
78.4 TTv7
77.9 AAv6
77.0 11v6
76.9 A9v9
76.6 TTv9
73.8 TTv6
73.3 AAv5
72.9 A9v6
72.7 11v5
69.9 TTv5
69.5 A9v5
69.2 55v6
67.8 10v6
67.7 AAv4
67.6 11v4
67.5 TTv4
67.4 A9v4
65.5 A9v3
65.4 TTv3
64.6 A9v2
64.1 TTv2
63.6 A8v7
63.6 19v7
63.3 55v5
62.8 AAv3
62.2 11v3
62.2 10v5
61.4 A8v8
60.9 19v8
57.6 99v6
57.5 AAv2
57.1 A8v6
57.0 55v4
56.9 11v2
56.7 10v4
54.7 AAv7
53.9 11v7
52.3 88v6
51.5 19v6
51.4 A8v5
51.0 99v5
50.8 10v3
50.4 55v3
47.7 55v7
47.6 10v7
46.5 A8v4
46.2 19v5
45.2 A7v6
44.7 55v2
44.7 10v2
44.0 99v7
43.7 19v4
43.4 A7v7
43.2 99v4
42.9 A8v3
42.8 18v7
42.8 AAv8
42.5 88v5
42.5 TTv10
42.5 A9v10
42.2 9v6
41.7 11v8
41.2 19v3
39.9 A8v2
39.4 19v2
38.8 88v7
37.7 A7v5
35.8 10v8
35.7 9v5
35.7 55v8
35.2 77v6
35.2 99v3
35.0 22v6
33.8 88v4
32.7 33v6
31.8 A7v4
31.0 18v6
30.8 A6v6
29.9 AAv9
29.1 9v4
29.0 99v2
28.8 22v5
28.7 11v9
28.2 A8v9
27.8 19v9
27.6 99v8
27.0 77v5
26.2 33v5
25.5 66v6
25.3 88v3
25.0 44v6
24.9 A6v5
24.3 A2v6
23.8 A7v3
23.2 18v5
22.5 A3v6
22.4 A5v6
22.2 A4v6
21.8 9v3
21.8 9v7
21.6 66v5
20.7 10v9
20.4 55v9
20.3 44v5
20.3 18v4
20.1 A2v5
20.1 8v6
18.8 A3v5
18.7 77v4
18.1 22v4
17.8 A4v5
17.6 A6v4
17.5 A7v2
17.3 A5v5
16.9 18v3
16.3 88v2
15.8 33v4
15.2 9v2
14.6 AAv10
14.6 8v5
14.1 A2v4
13.7 18v2
13.6 11v10
12.6 TTvA
12.5 A9vA
12.3 44v4
12.1 9v8
12.0 A3v4
11.1 A7v8
11.0 A4v4
10.8 18v8
10.8 44v7
10.4 8v7
10.4 66v4
10.2 A5v4
10.1 A6v3
9.7 8v4
9.1 A2v7
9.0 A2v3
7.9 22v3
7.4 7v6
6.9 77v3
6.6 A3v3
5.4 A2v2
5.3 44v3
5.0 8v3
4.7 A6v7
4.6 A4v3
4.5 17v6
4.2 7v5
4.0 A3v7
3.6 33v3
3.6 5v6
3.1 A6v2
3.0 A5v3
2.9 A3v2
2.5 6v6
1.9 5v5
1.8 A2v8
1.2 8v2
1.2 44v2
0.8 6v5
0.6 22v7
0.4 A4v2
0.1 7v4
0.0 A4v7
-0.5 17v5
-0.9 66v3
-1.1 88v8
-1.4 A5v2
-1.7 22v2
-2.2 5v4
-2.4 A3v8
-2.5 77v7
-3.4 6v4
-3.7 77v2
-3.9 17v4
-4.0 7v3
-4.1 A5v7
-4.4 19v10
-4.4 55v10
-4.5 10v10
-4.6 A8v10
-5.0 9v9
-5.6 33v2
-5.8 44v8
-5.8 8v8
-6.4 5v3
-6.8 7v7
-6.9 99v9
-6.9 A4v8
-6.9 A2v9
-7.2 33v7
-7.5 6v3
-8.2 7v2
-8.2 17v3
-9.2 17v7
-10.0 A6v8
-10.5 5v2
-10.9 A5v8
-11.0 12v6
-11.3 13v6
-11.3 14v6
-11.4 A3v9
-11.5 15v6
-11.6 12v5
-11.7 16v6
-11.8 13v5
-11.8 6v2
-11.8 14v5
-11.9 16v5
-11.9 15v5
-12.1 A7v9
-12.5 66v2
-12.5 17v2
-12.5 19vA
-12.9 A8vA
-14.3 5v7
-15.6 A4v9
-15.8 12v4
-15.8 11vA
-16.2 13v4
-16.3 14v4
-16.3 15v4
-16.3 16v4
-16.9 AAvA
-17.7 6v7
-17.8 A6v9
-18.2 22v8
-19.5 A5v9
-20.0 12v3
-20.4 A2v10
-20.6 18v9
-20.8 13v3
-21.0 15v3
-21.0 14v3
-21.0 16v3
-21.7 5v8
-22.5 8v9
-22.6 44v9
-22.8 A7v10
-22.8 9v10
-23.1 7v8
-23.1 55vA
-23.4 10vA
-23.9 12v2
-23.9 12v7
-24.1 A3v10
-24.8 66v7
-24.8 6v8
-24.9 33v8
-25.4 13v2
-25.7 14v2
-25.7 15v2
-25.8 16v2
-25.8 99v10
-26.1 18v10
-26.6 22v9
-27.4 A4v10
-28.4 A6v10
-29.6 5v9
-30.1 13v7
-30.1 12v8
-30.4 A5v10
-30.6 66v8
-30.8 7v9
-32.2 6v9
-32.2 44v10
-32.3 8v10
-32.4 33v9
-35.3 9vA
-35.7 14v7
-35.7 13v8
-36.7 99vA
-37.0 22v10
-37.1 12v9
-37.4 A2vA
-37.5 A7vA
-37.5 66v9
-37.6 18vA
-39.2 7v10
-39.3 5v10
-39.5 17v8
-39.7 15v7
-40.3 A3vA
-40.5 14v8
-40.6 88v9
-40.8 77v8
-41.2 33v10
-41.2 6v10
-41.5 13v9
-43.0 A4vA
-43.4 16v7
-43.4 17v9
-44.5 44vA
-44.7 8vA
-44.8 15v8
-45.0 A6vA
-45.3 12v10
-45.6 A5vA
-45.6 66v10
-46.3 14v9
-47.3 77v9
-47.5 17v10
-48.2 16v8
-49.6 13v10
-50.0 22vA
-50.3 15v9
-52.0 5vA
-52.9 7vA
-53.2 16v9
-53.6 14v10
-53.7 6vA
-53.9 33vA
-54.1 88vA
-54.3 88v10
-54.6 77v10
-56.5 12vA
-56.6 15v10
-56.8 66vA
-57.8 16v10
-59.9 13vA
-62.1 17vA
-63.0 14vA
-63.3 77vA
-65.6 15vA
-67.8 16vA
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
BukWildSuperFly
BukWildSuperFly
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May 9th, 2017 at 7:29:32 PM permalink
Actually, I'm not looking for a strategic ranking. I mean something much more simplistic (but needing more brute force). I'm simply looking for ALL the hands that could come up. ALL the hands that would add up to 21. ALL the hands that would add up to 20, and so on and so on. For the sake of explaining the rules of the game without saying that the hand closest to 21 wins. In the same way that you would explain a full house beats a flush.
QFIT
QFIT
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Joined: Feb 12, 2010
May 10th, 2017 at 3:52:14 AM permalink
I don't see how that's the same as full house beets a flush. You don't list all possible sets of cards that make a flush. In any case, don't think that would fit in a post.:)
"It is impossible to begin to learn that which one thinks one already knows." -Epictetus
BukWildSuperFly
BukWildSuperFly
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May 10th, 2017 at 9:48:20 AM permalink
Strangely enough, that's exactly want I'm looking for, a list of all of the possible hands. And no, it would not fit into a post. Not a post I would want to inflict upon this forum anyway. What I'm trying to figure out is if such a list would even fit into a small book. If someone could produce such a list for a nominal fee I would be interested.
Romes
Romes
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May 10th, 2017 at 10:09:28 AM permalink
If you don't want to say - no big deal... but now you've got my curiosity =P. What exactly do you want this list for?
Playing it correctly means you've already won.
charliepatrick
charliepatrick
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May 11th, 2017 at 2:05:56 PM permalink
I've worked out where you're coming from - the easiest way is
(1) Total - Blackjack score (where all scores under 21 beat any score over 21)
(2) Number of cards (except perhaps Natural Blackjack using AK is best hand, through to AT).
(3) Highest ranking cards in your hand (ignoring pairs, flushes, straights).
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