Bug in Wizard's Video Poker Strategy Calculator?

Hi,

I was checking Wizard's Video Poker Strategy Calculator for 9/5 Jacks or Better, and I think I may have found a bug. In the FAQ, he says:

Quote:

The basic strategy is designed to be as accurate as possible when exceptions are not used, however, there are two ways to interpret or accomplish this task:

1. Make the basic strategy return as much as possible, regardless of how many exceptions it ends up having; or

2. Make the basic strategy have as few exceptions as possible, regardless of how much the strategy returns.

The video poker strategy calculator uses the first method, which results in a strategy that returns as much as possible for the player who chooses to disregard exceptions.

But I don't think that's the case for the strategy generated that game. Near the end of the results, the strategy says:

2 to a Royal Flush	TJ
2 to a Straight	QK
3 to a Straight Flush	234; 235; 245; 346; 356; 457; 467; 568; 578; 679

But this strategy can be improved to return even more (with even less exceptions). It just suffices to change that part to:

2 to a Royal Flush	TJ
3 to a Straight Flush	679
2 to a Straight	QK
3 to a Straight Flush	234; 235; 245; 346; 356; 457; 467; 568; 578

This is because in a hand of 679QK, where the 6, 7, and 9 are of the same suit but the Queen and the King are of different suits, the right play in 9/5 Jacks or Better is always holding the 679. Am I missing something here, or does the strategy generator have a bug?

(I understand 6♣7♣9♣Q♦K♥ is listed later in the exceptions, but my questions is why list it in the exceptions when it can be part of the strategy itself?)

I think I found another problem in the same strategy. Right now, the strategy generated by the Wizard's website says:

3 to a Straight Flush	78T; 79T
2 to a Royal Flush	TJ
2 to a Straight	QK
3 to a Straight Flush	234; 235; 245; 346; 356; 457; 467; 568; 578; 679

Apart from moving 679 above QK, we should also move 578 above suited TJ, like this:

3 to a Straight Flush	578; 78T; 79T
2 to a Royal Flush	TJ
3 to a Straight Flush	679
2 to a Straight	QK
3 to a Straight Flush	234; 235; 245; 346; 356; 457; 467; 568

I wrote some code to do an analysis, and while Wizard's strategy returns 98.448243%, the above modification returns 98.448248%. I know it's a tiny difference, but I really think something could be wrong with the Wizard's strategy generator.

I found yet another problem in the same generated strategy (JoB 9/5)!

This time it's about moving "3 to a Straight Flush" hands 456, 567, and 678 above suited JA. The strategy generated by the Wizard's tool currently has somewhere around the center:

3 to a Straight Flush	9JK; 9QK
2 to a Royal Flush	JA; JQ; JK; QK
3 to a Straight Flush	456; 567; 678; 789; 89T

Now, we can improve it by changing it to:

3 to a Straight Flush	9JK; 9QK
2 to a Royal Flush	JQ; JK; QK
3 to a Straight Flush	456; 567; 678
2 to a Royal Flush	JA
3 to a Straight Flush	789; 89T

If my strategy evaluation code is correct, this further improves the return from my latest 98.448248% above to 98.448266%.

Decided to check the strategy generated by "Video Poker for Winners" (VPW) for JoB 9/5, and it has way more problems than the Wizard's. VPW's strategy claims to return 98.44817%, while it's actual return is lower. How much lower? It depends!

The major offender seems to be bundling AH (which means either AK, AQ, or AJ) in the same line as KQ near the bottom of the strategy, while KQ is the better hand and they can occur together in hands such as A♥K♦Q♣8♦7♠.

So depending on which of the hands AH and KQ you hold, the return of the strategy changes. My strategy evaluation code selects the hand listed first in such scenarios. So it thinks the return of VPW's strategy is 98.443681%, which is quite different from 98.44817% that VPW claims. In short, the return claimed by VPW is not even verifiable.

It's starting to look like one needs to write their own software instead of trusting the strategy generators...

Here's the strategy generated by VPW if you don't have the software:
1 ROYAL FLUSH
2 STRAIGHT FLUSH
3 FOUR of a KIND
4 RF4
5 FULL HOUSE
6 FLUSH
7 THREE of a KIND
8 STRAIGHT
9 TWO PAIR
10 SF4
11 HIGH PAIR J-A
12 RF3
13 FL4 2h; 1h; 0h
14 ST4 3h0i KQJT
15 Low Pair 2-T
16 ST4 2h0i QJT9; 1h0i JT98; 0h0i 2345-789T
17 SF3 2h1i 'QJ9'; 1h0i 'JT9'; 2h2i 'QJ8'
18 ST4 4h1i AKQJ
19 SF3 2h2i 'KH9'; 1h1i 'QT9'-'J98'
20 RF2 'KH'; 'QJ'
21 SF3 0h0i '345'-'89T'
22 RF2 'AH'
23 ST4 3h1i AHHT-KQJ9
24 HC3 KQJ
25 HC2 QJ
26 SF3 1h2i 'KT9'-'J87'; A-low 'A23'-'A45'
27 HC2 KJ
28 RF2 'JT'
29 SF3 0h1i '234','235'-'79T'
30 HC2 AH; KQ
31 RF2 'KT'; 'QT'
32 HC1 J-A
33 SF3 0h2i '236'-'69T'
34 Draw 5 new cards

I went and checked the Wizard's generated strategy for JoB 8/5 too, and there are similar improvements that can be made.

By moving "3 to a Straight Flush" hands 456, 567, and 678 above suited JA, moving "3 to a Straight Flush" hand 7TJ above unsuited JQ, and moving "3 to a Straight Flush" hand 679 above unsuited JK, the basic strategy can be improved from 97.296908% to 97.296934%.

Here are my proposed fixes to the Wizard's generated basic strategy for JoB 8/5:

1. Change:
2 to a Royal Flush JA; JQ; JK; QK
3 to a Straight Flush 456; 567; 678; 789; 89T

to:
2 to a Royal Flush JQ; JK; QK
3 to a Straight Flush 456; 567; 678
2 to a Royal Flush JA
3 to a Straight Flush 789; 89T

2. Change:
2 to a Straight JQ
3 to a Straight Flush A23; A24; A25; A34; A35; A45; 568; 578; 689; 78J; 79J; 7TJ; 89Q; 8TQ; 9TK
2 to a Straight JK
2 to a Royal Flush TJ
3 to a Straight Flush 234; 235; 245; 346; 356; 457; 467; 679; 78T; 79T

to:
3 to a Straight Flush 7TJ
2 to a Straight JQ
3 to a Straight Flush A23; A24; A25; A34; A35; A45; 568; 578; 679; 689; 78J; 79J; 89Q; 8TQ; 9TK
2 to a Straight JK
2 to a Royal Flush TJ
3 to a Straight Flush 234; 235; 245; 346; 356; 457; 467; 78T; 79T

Well, it looks like I'm talking to myself here, but I went and took a look at Triple Bonus Poker 9/5 too (pay table: 1/1/3/4/5/9/50/120/240/100/250).

The Wizard's basic strategy returns 99.800828%, while it can be improved to 99.801482%, still staying "basic". VPW has a better basic strategy than the the Wizard's in this case, 99.801479%, just a tiny bit less than the best basic strategy I could find.

Here are the fixes to Wizard's basic strategy. In the middle of the strategy, change:

4 to a Straight 2345; 3456; 4567; 5678; 6789; 789T
3 to a Straight Flush 345; 456; 567; 678; 789; 89T; 89J; 8TJ; 8JQ; 9TQ; 9JK; 9QK
4 to a Straight TJKA; TQKA; JQKA
2 to a Royal Flush JQ; KA
4 to a Straight TJQA
2 to a Royal Flush JA; QA
3 to a Straight Flush 234; 235; 245; 346; 356; 457; 467; 568; 578; 679; 689; 7TJ; 8TQ; 9TK
2 to a Royal Flush JK
3 to a Straight Flush 78T; 79T
2 to a Royal Flush QK
4 to a Straight 9JQK
3 to a Straight Flush A23; A24; A25; A34; A35; A45; 78J; 79J; 89Q

to:
3 to a Straight Flush 8JQ; 9JK; 9QK
4 to a Straight 2345; 3456; 4567; 5678; 6789; 789T; JQKA
3 to a Straight Flush 345; 456; 567; 678; 789; 89T; 89J; 8TJ; 9TQ
2 to a Royal Flush JQ
3 to a Straight Flush 346; 356; 457; 467; 568; 578; 679; 689
2 to a Royal Flush JK
3 to a Straight Flush 78T; 79T
2 to a Royal Flush QK
4 to a Straight TJQA; TJKA; TQKA; 9JQK
2 to a Royal Flush JA; QA; KA
3 to a Straight Flush A23; A24; A25; A34; A35; A45; 234; 235; 245; 78J; 79J; 7TJ; 89Q; 8TQ; 9TK

There's quite some moving around, and I'm not sure if all the changes are necessary, or it could be improved even further, but that's the best basic strategy I could come up with. If anyone can come up with something better, I can evaluate their strategy using the code I wrote.

I think the problem lies in games where flush pays 5. My guess is that "3 to a Straight Flush" hands become complicated with such payouts, and for some reason the existing software messes up somehow.

You should PM the Wizard to take a peek at this thread. I think he just hasn’t gotten around to it yet.

Quote: unJon

You should PM the Wizard to take a peek at this thread. I think he just hasn’t gotten around to it yet.

Thanks. I just PMed him.

And just because no one was posting doesn't mean it wasn't being read. Most of us try not to post when we really don't have anything to say. What you are doing is interesting (and impressive, well done!). I lost my VP strategy evaluation spreadsheet to a recent Hard Drive crash, so i can't check your work, but I suspect someone will eventually.

Quote: gordonm888

And just because no one was posting doesn't mean it wasn't being read. Most of us try not to post when we really don't have anything to say. What you are doing is interesting (and impressive, well done!). I lost my VP strategy evaluation spreadsheet to a recent Hard Drive crash, so i can't check your work, but I suspect someone will eventually.

Recuva!

From the makers of CCleaner... best file recovery program that ive only ever used because its free!

I was asked to look at this thread. Let me just say that the video poker strategy maker is not 100.000% perfect. I feel strongly in saying it is the best one out there and any cost due it it's errors are very small, probably under 0.01% in EV.

Plus, the person who made it, JB, has moved onto other projects and interests so I'm afraid it is what it is.

Anyone is welcome to send a PM to JB, but I doubt he will read it. I haven't seen him post here in years.

Quote: Wizard

I was asked to look at this thread. Let me just say that the video poker strategy maker is not 100.000% perfect. I feel strongly in saying it is the best one out there and any cost due it it's errors are very small, probably under 0.01% in EV.

Plus, the person who made it, JB, has moved onto other projects and interests so I'm afraid it is what it is.

Anyone is welcome to send a PM to JB, but I doubt he will read it. I haven't seen him post here in years.

Thanks you very much for your answer.

Would it be possible for you to share a little more about the algorithm used to determine the order of the various hands in the generated strategies? I mean beyond what you have posted at "My Methodology for Video Poker Analysis" and the "Video Poker Strategy Calculator FAQ". My guess is that a greedy algorithm is used and when cycles exist in the order of the hands, things can go wrong. My preliminary analysis tells me it's actually an NP-hard problem, but I'm not sure.