Ultimate X strategy formulas
June 4th, 2026 at 2:39:58 PM
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Wizard,
Regarding the Strategy section on the page:
Ultimate X (single line)
Is the formula win+multiplier-1 just an estimate for strategy generation purposes? I can’t seem to get the EVs for each of the multiplier strategies provided for 8/6 JoB to come up to the total EV for the game, using the probability of each multiplier provided:
Total EV is 149.03%, supposed to by 98.57%.
(Note: when I use the analyzer for 8/6 jacks with the standard multipliers it comes up with 98.4971%. I assume this is because the text says for Ultimate X it uses “the results of the optimal single strategy” rather perfect play)
What am I missing? Is the formula simplified by a factor of 150% for the sake of using integers? If so is there an exact formula? I would think for single line it would be relatively straightforward(?) to calculate the exact EV for the various multipliers that would sum up to the EV of the game? Or is it still an iterative process like multiline? There is only 1 hand and 7 multipliers and 10 paytable states including zero win so only 70 total states instead of the very large numbers of states in multiline. I see in your analysis tables it shows the 70 states in a table to calculate the total EV. I’m not sure how you calculate the probability for each state tho. I can get close by multiplying the probabilities of the 2 hands eg royal flush x fill house (12x), but it doesn’t quite match. Do you have to iterate until the change is within a certain delta like Koehler discussed?
For multiline Ultimate X Strategy section on:
Ultimate X -- Multi-Line
Why is the formula different from single line? It is 2 x win + multiplier - 1, which is equivalent to win + (multiplier - 1)/2. So why is the effect of the multiplier on strategy watered down by 1/2? I would expect the same formula as single line. Either way I’m sure this is a rough estimate because calculating the exact EV and strategy for multiline UX is quite complicated, per the Koehler paper linked to on the above page.
JD
Regarding the Strategy section on the page:
Ultimate X (single line)
Is the formula win+multiplier-1 just an estimate for strategy generation purposes? I can’t seem to get the EVs for each of the multiplier strategies provided for 8/6 JoB to come up to the total EV for the game, using the probability of each multiplier provided:
| Multiplier | EV | Probability | P*EV/2 |
|---|---|---|---|
1 | 1.990482 | 56.29% | 0.5602211589 |
2 | 2.970095 | 19.93% | 0.2959699668 |
3 | 3.951610 | 12.53% | 0.2475683665 |
4 | 4.933877 | 7.24% | 0.1786063474 |
7 | 7.882715 | 1.38% | 0.0543907335 |
10 | 10.833378 | 1.50% | 0.0812503350 |
12 | 12.801031 | 1.13% | 0.0723258251 |
| Total | 100.00% | 1.4903327330 |
Total EV is 149.03%, supposed to by 98.57%.
(Note: when I use the analyzer for 8/6 jacks with the standard multipliers it comes up with 98.4971%. I assume this is because the text says for Ultimate X it uses “the results of the optimal single strategy” rather perfect play)
What am I missing? Is the formula simplified by a factor of 150% for the sake of using integers? If so is there an exact formula? I would think for single line it would be relatively straightforward(?) to calculate the exact EV for the various multipliers that would sum up to the EV of the game? Or is it still an iterative process like multiline? There is only 1 hand and 7 multipliers and 10 paytable states including zero win so only 70 total states instead of the very large numbers of states in multiline. I see in your analysis tables it shows the 70 states in a table to calculate the total EV. I’m not sure how you calculate the probability for each state tho. I can get close by multiplying the probabilities of the 2 hands eg royal flush x fill house (12x), but it doesn’t quite match. Do you have to iterate until the change is within a certain delta like Koehler discussed?
For multiline Ultimate X Strategy section on:
Ultimate X -- Multi-Line
Why is the formula different from single line? It is 2 x win + multiplier - 1, which is equivalent to win + (multiplier - 1)/2. So why is the effect of the multiplier on strategy watered down by 1/2? I would expect the same formula as single line. Either way I’m sure this is a rough estimate because calculating the exact EV and strategy for multiline UX is quite complicated, per the Koehler paper linked to on the above page.
JD
Last edited by: johndouglass on Jun 4, 2026
