DDB Ultimate X strategy

[shadowman]

Good analysis, new2vp. I actually started writing a program to analyze this game but quit due to other things that came up. As you stated the strategy is variable based on the multiplier values.

[New2vp]

Thanks shadowman,  Good luck on the program.  I think it will be a relatively tough one.  I can estimate what should happen based on an extrapolation of single line play...and I think that would be fine for practical play.But to get things computer-perfect exact, you need to have 3 different strategies (3-play and 10-play are different as damule pointed out...and I simply ignored 5-play in my answer since no one brought it up) taking into account the probabilities of each multiplier sum that could come up with each hold.  Theoretically, you need a different strategy for each possible multiplier sum.  To make this usable for actual play, you would probably need to collapse some of these...or come up with many rules of thumb for common decisions.I noticed that the Wizard of Odds was content just to use IGT's numbers and didn't try to determine even the EVs on his own, let alone the strategies. 

[shadowman]

One of the possible methods is to devise a strategy for different ranges of multiplier values. It would not be perfect but would be fairly easy to do. Kind of a brute force method.


 
I had another idea that I have now totally forgotten in the year since I thought about it. Since I don't plan to start on this again I'm not going to spend any time trying to remember. 

[coyote9]

New2VP, that's very impressive.

Seems to me the game plays like All American or maybe Joker 2 pair at very low (1 or less) multipliers, 10-7 DB to 5 or 6x, then mostly DDB the rest of the way.

I think if you just played a standard 10-7 DB strategy, you probably don't lose all that much (a couple of pros found a $1 5-play at a Strip Casino that was offering 1.33% cashback sometime and smacked it pretty good), maybe .2-.4%.

Anyway, I am having trouble constructing an equation to analyze random hands. A typical situation would be with something like As Jh 7h 5h 4d. I know if you can solve for the current multiplier you will know when to hold the F3, the AJ and the A, but I can't figure out the equation. Any advice?

[New2vp]

Hey coyote!  Thanks for your kind words.  This game is more difficult than regular video poker, but when you spend a few minutes on what I posted below, I don't think the outcome of the math is that hard to apply.  Did you choose your screen name because you are Wile E.?I like your suggestion about All American or 10-7 DB strategy here.  That is very close.  In general, as I can see you know, you do want to give more attention to straights, flushes, and full houses at the lower multipliers and play closer to regular 9-6 DDB strategy at the higher multipliers.  When there is no multiplier, perfect strategy would be close to 10 / 7.5 / 5.5 DB strategy (if there was such a game) if you also valued the 2-pair hand at 1.5 instead of 1.0 and devalued the higher hands, quads and above by about 50%.  With a 2x multiplier, the strategy becomes more like 9.7 / 7 / 5 DB with 2-pair at 1.3, and devaluing the big hands by about 33%.  Both of these are quite close to 10-7 as you suggested.  That may be close enough for most, but I think you can get better without a lot of work by applying the formulae below.The Wizard of Odds said about Ultimate X, "One could get good, but not perfect, advice by using a video poker calculator, putting into the pay field for each hand cm*w+nm-1, where cm is the average current multiplier, w is the pay table win, and nm is the pay table multiplier for the next hand."If you want, you can improve on the Wizard's formula without making it too complicated, by plugging in another factor as follows:  Base Payoff * Current Multiplier + (Next Multiplier - 1)*Factor(j)*5.  Factor(j) is a number, usually slightly less than one, which is different for each game and different for each Next Multiplier.  For the 9-6 DDB game, Factor(j) ranges from approximately 0.9833 to 0.9879, with larger values applicable to final hands that have the higher Next Multipliers.  You won't be too far off if you use 0.9855 for each factor.  Explaining how these factors are calculated is beyond the scope of most with average college level mathematics backgrounds, so I'll not go into detail.  It requires some applications of matrix algebra, limits, and a bit more specialized video poker software than is on the market for precise determination.  There is an additional optimizing consideration that I have never seen posted by the "experts" that I'll leave totally out of the discussion for now.   Unlike many video poker games, there are slight differences in the strategies to be employed depending on whether you are playing single line Ultimate X, 3-play, 5-play, or 10-play.  In most cases, you will not lose much by ignoring the differences, but it is relatively easy to account for the differences by plugging in the different values based on the different multipliers for the final hands.When comparing the two formulas, the Wizard's formula is based on 1-coin payoffs and the improved formula is based on 5-coin payoffs.  You can divide all the numbers in the improved formula by 5 to compare the level of differences.You can get a very close approximation for 10-play DDB by determining a different strategy for each current multiplier:  1, 2, 3, 4, 8, 10, 12 by using the following table, where I have rounded the values to integers for ease of presentation:



DDB 9-6
 
 
Current
Average Multiplier


 
Base
Next multiplier
1
2
3
4
8
10
12


ROYAL FLUSH
4000
4
4015
8015
12015
16015
32015
40015
48015


STRAIGHT
FLUSH
250
4
265
515
765
1015
2015
2515
3015


4 ACES w
2,3,or 4
2000
4
2015
4015
6015
8015
16015
20015
24015


4 2,3,or4 w
A-4
800
4
815
1615
2415
3215
6415
8015
9615


4 ACES
800
4
815
1615
2415
3215
6415
8015
9615


4 2,3,or4
400
4
415
815
1215
1615
3215
4015
4815


4 5-K
250
3
260
510
760
1010
2010
2510
3010


FULL HOUSE
45
12
99
144
189
234
414
504
594


FLUSH
30
10
74
104
134
164
284
344
404


STRAIGHT
20
8
55
75
95
115
195
235
275


3 OF A KIND
15
4
30
45
60
75
135
165
195


TWO PAIR
5
3
15
20
25
30
50
60
70


JACKS OR
BETTER
5
2
10
15
20
25
45
55
65


NOTHING
0
1
0
0
0
0
0
0
0


 
 
 
 
 
 
 
 
 
 


As Jh 7h 5h
4d
Best Play
 
J75
J75
A
A
A
A
A

Certainly, you will want to summarize these strategies with some simpler rules rather than use 7 different strategy sheets.  Most of the time, the simplifications will be based on likely competing holds such as what you described in the object hand.  If the multiplier is less than or equal to x, then you make hold y; otherwise, hold z.  Some of the rules that involve 3 or more holds can get quite complicated.Unfortunately, there are many more than 7 strategy sheets necessary unless you confine your play to single line only.  The table above simplifies the number of strategies.  Since there are 10 final hands in 10-play and each hand's current multiplier could be different than the rest, the current average multiplier can take on other values with many of them being fractional.  So, to be a bit more precise, we would have to also have strategies for most of the multipliers down to the tenths:  1, 1.1, 1.2, 1.3, ..., 12.  Many of these are extremely rare and some (like 11.9) are impossible, so focusing on the most probable will produce a likely reasonable compromise between perfect strategy and practicality. In the hand that you indicated, you can see that for a current multiplier of 1 or 2, the best hold is J75, the 3-card flush; for all other current multipliers in the table, the best hold is the singleton ace.  We will see below that we will play the 3-card flush if the current average multiplier is 2.2 or below.If you want to get the decision point for a particular hand, you can use algebra and the hand distributions for the various holds to find the value of the current multiplier that makes two hands have equivalent expected values.  This procedure is parallel to that outlined in many video poker books (including that of one of vp.com's frequent posters, Frank Kneeland's The Secret World of Video Poker Progressives, p. 253) for finding breakpoints when playing a progressive game.  The math is a little complicated primarily because there are so many final hand values, but this can be programmed into a spreadsheet without too much difficulty:





 
          J75
              A
            AJ
    Factor
2.271068


ROYAL FLUSH
0
1
0
0.9852
9099.05


STRAIGHT
FLUSH
0
1
0
0.9852
582.5448


4 ACES w
2,3,or 4
0
11
0
0.9852
4556.914


4 2,3,or4 w
A-4
0
2
0
0.9852
1831.632


4 ACES
0
33
1
0.9852
1831.632


4 2,3,or4
0
0
0
0.9852
923.205


4 5-K
0
6
1
0.9844
577.6114


FULL HOUSE
0
288
18
0.9879
156.535


FLUSH
45
493
0
0.9876
112.5737


STRAIGHT
0
334
64
0.9871
79.96855


3 OF A KIND
9
4102
281
0.9852
48.84381


TWO PAIR
27
8874
711
0.9844
21.19975


JACKS OR
BETTER
129
43389
5022
0.9834
16.2723


NOTHING
871
120831
10117
 
0


 
 
 
 
 
 


Total
1081
178365
16215
 
 










EV
7.564228
7.564228
7.453745



Using that procedure, for the hand that you indicated, the breakpoint is 2.271.  With current multipliers at or below that number, choose J75; if the multiplier is above that number, choose A.  [The last column in the table above would be the numbers that you could plug into video poker software for each final hand if the current average multiplier were exactly 2.271068 to get a strategy if the software took non-integer values(9099 for a royal flush, 582.5 for a straight flush, etc.).]AJ will never be chosen because one of the other two holds will always be better.  AJ is better than A if the current multiplier is < 1.098, but at those values J75 is better than both of the other holds.  AJ is better than J75 if the multiplier is > 3.148, but in that range, A is better than than the other two.Best of luck.  It is a complicated but very interesting game! 

[coyote9]

New2VP, thanks for such an awesome analysis. The AJ>A does come up, usually with multiple S penalties or a SF penalty. I would assume the break number would be higher with a hand like this: AsJdTh4s2c. How much higher is subject to question. I don't know "how Wile E." I am, having been run over by the roadrunner many times lol, but your product certainly isn't made by Acme.Actually, I did see a single line UX at Cache Creek recently, on the new Five Star platform. Why have a bunch of multiline titles and set them to single line only makes no sense to me, but for many readers here, they get to play full play VP cheaply and work on their game at the same time. It may well be a win/win for both the casino and the player.

[farc]

Bob Damcer says he paid someone 500 dollars to analyze ultimate X. He says stay away it's too complicated. But when this baby hits, one thinks"What does Bob know?.

[coyote9]

New2VP, please ignore the private message I sent you today. Didn't Dancer teach an UX class at South Point in Vegas several months ago?

[New2vp]

New2VP, please ignore the private message I sent you today.It was easy to ignore; I never received it.

[onemoretry]

Bob Damcer says he paid someone 500 dollars to analyze ultimate X. He says stay away it's too complicated. But when this baby hits, one thinks"What does Bob know?.
I imagine that what Bob knows is that the big hits are few and far between, and that without one you had better have really deep pockets to enable you to keep playing.  And, even with an occasional big hit, it's easy to lose a lot at this game,  with its extremely complicated playing strategy.