WoO Deuces Strategy question

Hello, Wiz! Really enjoying your forum, thanks for having me!

I put in some hours yesterday learning your Optimal Deuces Wild Strategy (remarkable; thanks for doing it), and I ended up with a question to which I THINK I know the answer but could be wrong. In the following table,

1 Deuce
1.Wild royal flush (25.0000)
2.5 of a kind (15.0000)
3.Straight flush (9.0000)
4.Four of a kind (5.8510637)
5.4 to a royal flush (3.4042554)
6.Full house (3.0000)
7.3 consecutive suited cards 5-6-7 or greater(2.21277)
8.3 of a kind (2.01758)
9.Straight (2.0000)
10.Flush (2.0000)
11.All other 4 to a straight flush (1.70213 to1.97872)
12.3 to a royal flush, highest card king or less(1.1424607)
13.2 consecutive suited cards, 6-7 or higher, + deuce(1.0952822)
14.3 to a royal flush, ace highest card, no penalty cards (1.0462534)
15.Deuce only (1.0328652)
16.3 to a royal flush, ace highest card, 1+ penalty card8 (1.0286771)
17.2 consecutive suited cards, 5-6 or lower, + deuce(1.0166513)
18.4 to an outside straight (1.0000)

All of the rankings except 13 and 17 imply that the deuce is part of the makeup of the hold, except that on number 7, it seems out-of-whack to consider the deuce as one of the 3 suited sequential cards. I may be wrong, and a 2 card outside SF hit may outrank a straight or a flush guaranteed multiple pay for the potential return in this game, but does a "+ deuce" belong on 7 as well, for a total hold of 4 cards with a natural sequence of 3?

Thanks again!

#7 does NOT refer to a deuce. Note #11 refers to all other 4 to a Straight Flush.

The 3 consecutive non-deuce cards (5 or greater) is important because when they are consecutive there are 7 outs to a straight flush, 4 suited cards and 3 deuces.

Examples:

6d 7d 8d 2s 8s

Hold: 6d 7d 8d 2s

6d 9d 8d 2s 8s

Hold: 8d 2s 8s

tringlomane,

I agree that they're important; no question. Just that the ranking of this hand, with 2 cards that must work in concert among those 7 outs in the draw and 41 non-winning cards, seems mis-ranked above 3 of a kind, with a sure 1-1 pay and 5 outs for 5 to 1 pay, and 4 add'l to that for 15 to 1, in the aggregate would be a lower ranking hold unless the deuce is added to those 3 for only 1 card hit for 9 to 1 pay. This potential puts the 3OAK above higher-paying sure things, straight and flush at 2 to 1, and I can see that, but not for a non-pay without double-hit requirement hand, no matter how promising. The percentage of getting one without the other would be significantly higher than getting both you need to complete the SF, so it's not a simple 7outs, it's 2 out of only 7. The thought of throwing away 2 offsuit straight cards or nonsequential flush cards in the hand in order to draw to a 9 to 1 pay seems like erroneous play to me. However, if you're only looking for 1 of 7, with the deuce to double-flex your options outside the sequence (fill either inside or outside), this seems a reasonable gamble. But I'm not the one who ran the numbers, and if that seeming anomaly is correct, I'll fly with it.

(edit in addition). The SF draw is not the only winning possibility; this hand can straight, flush, 3OAK or 4OAK as well, so that may be the edge that places it there. But I still think it's overvalued, even so, especially since there's #11, which I read as covering a 5 card SF spread including the Deuce, and 3-4 card spreads lower than the 5-6-7 of #7. This one, as it reads, to me implies that #7 actually does mean 3 in a sequence plus the deuce.

Appreciate your response; what you're saying is part of what I'm wondering about on the other side of the probabilities.

FWIW, I think your examples are making my point; you have 3 sequential PLUS a deuce, and in the nomenclature the Wiz used, the phrase "+ deuce" should probably be added to #7 for consistency with the other tables. But I wanted to verify that before I assumed it. In the current table, it literally can mean "the sequence inclusive of the deuce", like #3, Straight Flush, in the 1 deuce table, means 4 natural and 1 deuce in the hold
.

The deuce is added to the 3 consecutive suited cards; sorry if I made that unclear.

Your thinking is a little off when you say you have 4 additional outs to 15 to 1 (it's actually 15 for 1, or 14 to 1). You have 5 "runner runner" outs to 15 for 1, so it rarely will happen (<1%).

I felt like making myself think, so I did what this does by hand:
https://wizardofodds.com/games/video-poker/hand-analyzer/


6d 7d 8d 2s 8s

Hold: 6d 7d 8d 2s

7 outs to straight flush: pays 9

5 outs to regular flush (3d, Jd, Qd, Kd, Ad): pays 2

12 outs to regular straight: pays 2

8 outs to three of a kind (discarding 8s so thats a dead out): pays 1

15 bricks: pays 0

EV of straight flush draw:
(7/47)*9 + (5/47)*2 + (12/47)*2 + (8/47)*1 = 2.23404

Hold: 8d 2s 8s

5 of a kind (10 combos: 2c2d, 2c2h, 2d2h, 8c8h, 2c8c, 2c8h, 2d8c, 2d8h, 2h8c, 2h8h): pays 15

4 of a kind (210 combos: a 2 or 8 (5 cards) with a "brick" (42 cards)): pays 5

Full house [60 combos: 6 combos for 9 ranks not discarded (e.g. JcJd, JcJh, JcJs, JdJh, JdJs, JhJs); 3 combos for 2 ranks discarded (eg 6c6h, 6c6s, 6h6s)...note that getting a 2 or 8 doesn't make a full house]: pays 3

Total combos: 47 cards x 46 cards / 2 (order is irrelevant) = 1081 combos

No improvement: (1081 - 10 - 210 - 60 = 801 combos): pays 1

(10/1081)*15 + (210/1081)*5 + (60/1081)*3 + (801/1081)*1 = 2.017576

Now compare this to:
6d 8d 9d 2s 8s

Now we only have 6 outs to the straight flush (5d, 7d, Td, 2c, 2d, 2h)
6 outs to a regular flush (3d, 4d, Jd, Qd, Kd, Ad)
9 outs to a regular straight (offsuit 5s, 7s, and Ts)
3 of a kind outs remain the same: 8
Bricks: 47-29 = 18

(6/47)*9 + (6/47)*2 + (9/47)*2 + (8/47)*1 = 1.957447

The expected value of holding 8d 2s 8s is the same as above, 2.017576. So for 6d 8d 9d 2s 8s: 8d 2s 8s is the best play as per rule #8 overruling rule #11.

And after writing all this mess, I agree with you. I'm keeping it here for general knowledge sake though. Rule #7 should have + deuce attached to it since rule #13 is already written this way, and then the rules will have consistent wording.