jeffb
Joined: Jun 16, 2022
• Posts: 4
June 16th, 2022 at 8:48:21 AM permalink
I've been playing Ultimate X Jacks or Better at the local casino for a while now, but I'm confused about how to make the right strategy. Wizard of Odds provides a strategy for the 8/6 version, but at my casino they are cheap and the game is only 7/5, so I have to make my own. On the Wizard's "Ultimate X Multi-Line" page the Wizard gives this advice:

Creating a strategy for a game not listed above is easy. Just follow these steps:

For each poker hand, determine: (adjusted win) = 2×(base win) + (multiplier) - 1. For example, if the base win for a full house is 8 and the multiplier is 12, then the adjusted win is 2 × 8 + 12 - 1 = 27.
Put each adjusted win in my video poker strategy maker.
Click "continue."

Of course I always bet 10 credits to activate the multipliers. So when I input the figures into the strategy maker should I input the figures for 1 credit bet or for 10 credits bet? (For example: Royal Flush 1 credit: (250 x 2) + (multiplier is 2) -1 = 501. OR Royal Flush 10 credits: (4000 x 2) + (multiplier is 2) - 1 = 8001.) As you might have guessed, using the 10 credit figures produces quite a different strategy than using the 1 credit figures. But either way, both produce a strategy that shows a return well over 100% For example, using the 1 credit figures and the Wizard's formula above I input the following: (the actual Pay Table amount is on the Left (x multiplier) / the value input into the strategy maker is on the Right)

RF 250 (x2) / 501
SF 50 (x2) / 101
4Kind 25 (x3) / 52
FH 7 (x12) / 25
Flush 5 (x11) / 20
Straight 4 (x7) / 14
3Kind 3 (x4) / 9
2Pair 2 (x3) / 6
JoB 1 (x2) / 3

The return shown under "Perfect Strategy Analysis" is 2.914716, or 291% If I use the 10 credit figures the return shown is well over 900%. That can't be right. What am I missing? Which set of numbers should I use to create the correct custom strategy? In spite of my confusion I managed to hit a Royal Flush a few weeks ago with a 4x multiplier at 10 cent bet, paid out \$1,600. Thanks
Dieter
Joined: Jul 23, 2014
• Posts: 4686
June 16th, 2022 at 10:06:38 AM permalink
https://wizardofodds.com/games/video-poker/tables/ultimate-x/

Link to WoO UX Mulitiline page.
May the cards fall in your favor.
Dieter
Joined: Jul 23, 2014
• Posts: 4686
June 16th, 2022 at 10:20:53 AM permalink
Quote: jeffb

RF 250 (x2) / 501
SF 50 (x2) / 101
4Kind 25 (x3) / 52
FH 7 (x12) / 25
Flush 5 (x11) / 20
Straight 4 (x7) / 14
3Kind 3 (x4) / 9
2Pair 2 (x3) / 6
JoB 1 (x2) / 3

My instinct says that the RF value should be 1601, and you should disregard the return percentage when calculating strategy. I do not think the calculator is equipped to handle the more complex return probabilities involved in Ultimate X, but using the formula to modify the paytable should produce a viable strategy.
May the cards fall in your favor.
jeffb
Joined: Jun 16, 2022
• Posts: 4
June 16th, 2022 at 9:02:08 PM permalink
I'm not sure how you arrive at 1601. This pay table is not the standard JoB pay table. The one credit Royal Flush pays only 250, not 400. I think you must have meant to say 501, so the strategy should be based on the one credit game, is that right? And if so, I'm just wondering how the strategy would account for the 4000 credit payout for the 5 or 10 credit game? I made a strategy using the 5/10 credit figures (Royal Flush = 8001) and the result was a much higher ranking for "2 to a Royal Flush" and "3 to a Royal Flush" (as you might expect), but wouldn't that be the more correct strategy? Or would you say that if one is really trying for the Royal Flush then use the 5/10 credit strategy, but if one is trying for smaller prizes use the one credit strategy? Thanks again.

I'll copy the entire pay table here:

1 credit: 250 / 50 / 25 / 7 / 5 / 4 / 3 / 2 / 1
2 credits 500/ 100/ 50 / 14 / 10 / 8 / 6 / 4 / 1
3 credits 750 / 150 / 75 / 21 / 15 / 12 / 9 / 6 / 3
4 credits 1000 / 200 / 100 / 28 / 20 / 16 / 12 / 8 / 4
5 credits 4000 / 250 / 125 / 35 / 25 / 20 / 15 / 10 / 5
10 credits, same as 5 credits with multipliers.
Dieter
Joined: Jul 23, 2014
• Posts: 4686
June 16th, 2022 at 9:04:45 PM permalink
I'm hoping a math guru can jump in here.

It looks like the intent of the WoO page's adjusted return method may have been to insert the sum of all currently active multipliers for the "(multiplier)", not the value from the multiplier table if the hand is achieved.

I can't believe it had to rattle around in my brain for half a day for that little epiphany to stop by.
May the cards fall in your favor.
Dieter
Joined: Jul 23, 2014
• Posts: 4686
June 16th, 2022 at 9:10:37 PM permalink
Quote: jeffb

I'm not sure how you arrive at 1601. This pay table is not the standard JoB pay table. The one credit Royal Flush pays only 250, not 400. I think you must have meant to say 501, so the strategy should be based on the one credit game, is that right? And if so, I'm just wondering how the strategy would account for the 4000 credit payout for the 5 or 10 credit game? I made a strategy using the 5/10 credit figures (Royal Flush = 8001) and the result was a much higher ranking for "2 to a Royal Flush" and "3 to a Royal Flush" (as you might expect), but wouldn't that be the more correct strategy? Or would you say that if one is really trying for the Royal Flush then use the 5/10 credit strategy, but if one is trying for smaller prizes use the one credit strategy? Thanks again.

I'll copy the entire pay table here:

1 credit: 250 / 50 / 25 / 7 / 5 / 4 / 3 / 2 / 1
2 credits 500/ 100/ 50 / 14 / 10 / 8 / 6 / 4 / 1
3 credits 750 / 150 / 75 / 21 / 15 / 12 / 9 / 6 / 3
4 credits 1000 / 200 / 100 / 28 / 20 / 16 / 12 / 8 / 4
5 credits 4000 / 250 / 125 / 35 / 25 / 20 / 15 / 10 / 5
10 credits, same as 5 credits with multipliers.

Yes, but you're not playing 1 credit, you're playing 10 credits.
Common practice in VP analysis is to normalize by dividing by the base bet - 5 credits, in this case. RF should pay 800 for 1; 2 pair should pay 2 for 1.

I think there is a problem in how multipliers are being handled; I have an idea, but I'm still hoping for a more qualified expert to tell me how I goofed.
May the cards fall in your favor.
jeffb
Joined: Jun 16, 2022
• Posts: 4
June 18th, 2022 at 9:41:21 AM permalink
Many thanks for your reply. I think I'm getting closer to the answer I'm seeking. But I'm still confused about why I'd use the 800 figure and not the 4000 figure. I've posted another question about this in the forum, but from a slightly different angle. You are welcome to delete this whole thread and reply to the new one if you want. Thanks again.
Dieter
Joined: Jul 23, 2014
• Posts: 4686
June 18th, 2022 at 11:08:34 AM permalink
I think if you use the x5 paytable and the 4000 for 5 (vs 800 for 1), you would need to multiply the values of the multipliers that you add in by 5 as well.

Normalizing the 4000 for 5 to 800 for 1 allows you to not scale the multipliers.

As you noted, the 1 coin paytable short-pays the royal flush at 250 for 1, which throws off the strategy, since you actually get 800 for 1 (at the 5 or 10 coins played). Correct that line, and the rest of the single coin paytable should already be normalized for you, unless the paytable author has done something unusually sneaky.

You are certainly not the first to be a bit perplexed by the established practices of video poker analysts.
May the cards fall in your favor.