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**27 members have voted**

Last Sunday I was in a desperate search for a Dream Card machine downtown as part of my update of that page. While I failed in that mission, I saw a new video poker variant -- Ultimate X Poker -- Bonus Streak.

This is like conventional Ultimate X, except the player earns a multiplier stream of 2 to 5 multipliers for a three of a kind or better (or flush or better in deuces wild). If the player wins a multiplier in a hand that already has one, then the remaining multipliers jump to 12 but no new ones are added.

I've already been playing around with an analysis but I can't find a good rule of thumb to get the return greater than the return without the feature, In particular, in the 7/5 Bonus Poker Deluxe game I come up with following strategy:

Update 1/24/17: Strategy currently under revisions

I asked IGT for their returns but haven't heard back yet.

So, I invite my fellow math heads to sink their teeth into this game. The easier question should be to find a single strategy, or way to find one, that maximizes the return. The harder question is to find the optimal return.

The question for the poll is would you play Ultimate X Poker -- Bonus Streak? Multiple votes allowed (I mean it this time)

Here is a video of me playing.

Quote:rsactuaryI don't have much to offer analysis wise, but I am curious where you found said machines?

Observed one at Cosmo this week. Next to Barnyard Poker near Clique.

Quote:rsactuaryI don't have much to offer analysis wise, but I am curious where you found said machines?

The one I found was at the Fremont right by the pit, close to the doughnut shop.

I must say that I found the game very engaging to play.

Quote:rainmanI will be downtown 18th-21st I'll run a 100 through it since you said it was fun.

Be my guest. I'm not saying it is a good bet, but I enjoyed playing, which is the reason most of us gamble.

Quote:WizardThe one I found was at the Fremont right by the pit, close to the doughnut shop.

I must say that I found the game very engaging to play.

Ooh, doughnuts! Didn't know that was there. Not that I've eaten doughnuts in almost 2 years, but hey, a Homerette can dream, right?

I voted I'd play it. I think it would be especially fun on deuces, but I also said paytable dependent. I'll be very interested in any analysis, so thanks in advance, guys.

Quote:beachbumbabsOoh, doughnuts! Didn't know that was there. Not that I've eaten doughnuts in almost 2 years, but hey, a Homerette can dream, right?

It is a Dunkin Doughnuts outlet. Nothing special. I've yet to find a respectable doughnut place in Vegas.

Quote:I'll be very interested in any analysis, so thanks in advance, guys.

One could write a Ph.D., dissertation on the math of this game. However, the number of people who will play this by perfect strategy is 0%. The more realistic goal is to create the best strategy that balances simplicity and return. Hopefully some of the other math club members of the forum will stumble upon this thread and take an interest.

Quote:RogerKintThe bank I played required max bet to play off multipliers.

I should have mentioned that in my write up. Thanks.

Quote:WizardI should have mentioned that in my write up. Thanks.

I figured that out watching the video. Seems consistent with other ultx.

Dunking donuts? Never mind. Sad.

A real doughnut bakery open 24/7 would kill on Fremont street. Huge moneymaker.

Quote:WizardIt is a Dunkin Doughnuts outlet. Nothing special. I've yet to find a respectable doughnut place in Vegas.

You and me both. I stopped by a Pinkbox a while back getting lost from GVR to my house and it was awful. Donuts always looks good but more times then not I am quite disappointed in the taste. If anyone has any suggestions I would love to hear it.

Quote:djatcYou and me both. I stopped by a Pinkbox a while back getting lost from GVR to my house and it was awful. Donuts always looks good but more times then not I am quite disappointed in the taste. If anyone has any suggestions I would love to hear it.

Wouldn't have to be big. Could even be in a food truck. Should be open kitchen, counter, no tables necessary, walk up service. Make old fashioned donuts and holes with a dozen toppings, fresh. The smell alone will drive business to you.

Don't bother with raised unless you want to do a hot fresh Krispy Kreme thing, but what you're missing was the good recipe they used to use 50 years ago. Now it's all air and cheap shortening with a bitter aftertaste. But the good recipes are still around.

Quote:djatcYou and me both. I stopped by a Pinkbox a while back getting lost from GVR to my house and it was awful. Donuts always looks good but more times then not I am quite disappointed in the taste. If anyone has any suggestions I would love to hear it.

Only in Vegas would there be a strip club named Little Darlings and a donut shop named PinkBox.

Quote:beachbumbabsI figured that out watching the video. Seems consistent with other ultx.

How so? I'm confused.

Unless you're playing at the Cosmopolitan, 99.73% of UX games don't require a max bet to play off a multiplier.

Besides the one machine at Cosmo, I only know one other UX with minimum bet - Twin Pine (Northern California)Quote:RogerKintUnless you're playing at the Cosmopolitan, 99.73% of UX games don't require a max bet to play off a multiplier.

I was in Vegas for 3 weeks. M Resort and Cosmo have UXBS. Not sure where else (wasn't in Vegas to gamble).

In Southern California, early December 2016,

Harrahs added 3 UXBS, then Barona added 7 UXBS (one for $1, $2, $5, $10), and Viejas added 7 UXBS.

Haven't checked all the casinos in Jan yet.

It's really fun to get a whole bunch of 12Xs for 4-8 hands. :-)

I came up with a way to analyze UX, or at least for a single strategy. Essentially, you enter the base pay plus the return from multipliers for each hand (ie, 8/6 BPD a FH would be 8/2+11*0.985), or something wonky. I still can't figure out how to do it even though I started a thread showing how to do it. :( Then just keep doing it until the return is steady and not changing.

I think it's the same method JB used, or similar to it. Tringlomane has done it several times with different paytables.

With this game, it's a bit different, because another qualifying hand makes the rest of the next-hand multipliers go to 12x. You can still do it, I'd think, it'd just be a bit more challenging.

Perhaps the first step would be to just see how regular strategy fares in the UXBS. If that's an amount one is willing to give up in EV, then that's good enough. If it's not, then do more work!

Quote:RogerKintOnly in Vegas would there be a strip club named Little Darlings and a donut shop named PinkBox.

And a restaurant staffed with mostly cute young gals called the Pink Taco.

Yeah, the 12X promotion aspect is fun. I'd be curious how much of the return comes from the bump-up-to-12X.Quote:RSWith this game, it's a bit different, because another qualifying hand makes the rest of the next-hand multipliers go to 12x. You can still do it, I'd think, it'd just be a bit more challenging.

For 5-play in terms of 50-coin bet units, variance is 10.8372 (1084 for 5-coin bet units).

For 5-play in terms of 30-coin bet units, variance is 16.4579 (592 for 5-coin bet units).

Can anybody provide a sanity check on my numbers? Of course, the variance will change a small amount depending on the strategy employed.

Playing 10-coin is very volatile. I don't like getting no multipliers on pairs. But a sequence of high value hands turbocharges everything.

Quote:mamatFantastic game to vulture compared to regular UX.

My understanding is you can't vulture this one. If you bet less than 10 coins per hand, the multipliers disappear, then reappear next time 10 coins are bet.

Bonus Poker Deluxe:

Straight 2,5,8 2,5,8 2,3,4

The Straight only yields multipliers of 2,5 on 5-play. You can see this in your video around 4:00 mark, and also on the photo of the pay table on that same web page.

On that same page, the game photo labeled Bonus Poker appears to be 9/5/4 Double Bonus Poker.

You wrote: "While this will make sacrifices in the wins before the multipliers, it should result in an average multiplier per hand of 2.0854. I haven't verified it, but given the 7-5 pay table, it should result in a return of 98.58%, which is higher than the 96.25% without the feature. "

Did you make this error in your simulations, too? This would goose your EV by several percent. I get a much lower EV for 5-play BP compared to your 98.58%. The Bonus Streak multipliers are generous, but they only add a fraction of a percent to the EV any game I have looked at, so far.

Quote:WizardHere is a video of me playing.

Thank you for the video. I am intrigued by the 'streaks'.

Quote:APIndyThere is an error on the wizardofodds site for Bonus Streak: /games/video-poker/tables/ultimate-x-bonus-streak/

Bonus Poker Deluxe:

Straight 2,5,8 2,5,8 2,3,4

The Straight only yields multipliers of 2,5 on 5-play. You can see this in your video around 4:00 mark, and also on the photo of the pay table on that same web page.

On that same page, the game photo labeled Bonus Poker appears to be 9/5/4 Double Bonus Poker.

You wrote: "While this will make sacrifices in the wins before the multipliers, it should result in an average multiplier per hand of 2.0854. I haven't verified it, but given the 7-5 pay table, it should result in a return of 98.58%, which is higher than the 96.25% without the feature. "

Did you make this error in your simulations, too? This would goose your EV by several percent. I get a much lower EV for 5-play BP compared to your 98.58%. The Bonus Streak multipliers are generous, but they only add a fraction of a percent to the EV any game I have looked at, so far.

Thanks for the correction. Yes, that error would have messed up my analysis too. I will remove it until I get around to fixing it.

I have yet to see a UXBS machine in the wild.

Play hands where your expected multipliers for the whole sequence of hands is at least 2.1X (doesn't take into account 12X bump-up, possibly can play lower with lots of multiplier stacks - haven't done a full calculation to say exactly when to play).Quote:rsactuaryMy understanding is you can't vulture this one.

Same as regular UX when there is a minimum bet which doesn't allow betting 5...except the sequences of multipliers can rack up quickly with good hands.

I thought with video poker, if a losing first draw including low pairs were laid, that the odds favored throwing all in for a 5 draw. If I'm correct, could it be because it's a multi deal that that theory/technique doesn't hold up?

Thanks.

That game didn't do too well in that run either unfortunately from the looks of it.

Quote:sammydvWizard. I watched your vid playing the UPBS and I noticed that you were keeping non winning pairs quite a bit.

I thought with video poker, if a losing first draw including low pairs were laid, that the odds favored throwing all in for a 5 draw. If I'm correct, could it be because it's a multi deal that that theory/technique doesn't hold up?

Thanks.

Sorry for the tardy reply. I had no idea what I was doing at that sitting so pretty much followed conventional video poker strategy. I'm sure I made similar errors in my example page for the game.

I'm happy to say my page on Ultimate X Bonus Streak is pretty much done. The mathematician with VideoPoker.com was nice enough to send me the list of games, pay tables, bonus streaks, and returns. I probably would have never figured out this game by myself. Perhaps the most complicated casino game to analyze I've ever seen.

Quote:I'm happy to say my page on Ultimate X Bonus Streak[/linkis pretty much done. The mathematician with was nice enough to send me the list of games, pay tables, bonus streaks, and returns. I probably would have never figured out this game by myself. Perhaps the most complicated casino game to analyze I've ever seen.

If you have done any work on UX, then it is pretty easy to set a lower bound for the return on UXBS and create a decent strategy, especially for 10-play. In ordinary UX, the average multiplier for the next hand is 1x very often, and the average multiplier is fairly high on a lot of hands. In UXBS 10-play, the average multiplier for the next hand is 1x less than 8% of the time, and the average multiplier only fairly high after you flop a big hand. Only 13% of hands have an average multiplier of more than 3x.

I.e., the variance of the average multiplier for the next hand is much lower. More hands are played with a middle-of-the-road multipliers, so a simpler strategy works better for UXBS than for simple UX. It also works better for games where the flush pays more, since you are going for more flushes in UX, generally.

Are the expected returns from the mathematician Monte Carlo or closed form values?

Rule 4 has "the player" duplicated.

Quote:Rules, Item 4... then the player the player will win up to five multipliers...

Lucky, Director

Bureau of Redundancy Bureau

Quote:WizardI'm happy to say my page on Ultimate X Bonus Streak is pretty much done. The mathematician with was nice enough to send me the list of games, pay tables, bonus streaks, and returns. I probably would have never figured out this game by myself. Perhaps the most complicated casino game to analyze I've ever seen.

I can't understand how these pay tables can possibly be right. You are showing a massive decrease in multipliers for the 10-play versions.

Three-Play Return Table

Double Double Bonus 9-5 2,4 2,4,8 2,4,8,10,12 98.40%

Five-Play Return Table

Double Double Bonus 9-5 2,4 2,4,8 2,4,8,10,12 98.31%

Ten-Play Return Table

Double Double Bonus 9-5 2,3 2,3,4 2,3,4,8,12 98.36%

There must be a difference in the hands where these multiplier apply, otherwise the EV on the 10-play game would be around 86%.

Your old web page had: Three of a kind 2,4 2,4 2,3,4 for the STREAK1

I think the entry should look like this:

Ten-Play Return Table

Double Double Bonus 9-5 2,3,4 2,3,4 2,3,4,8,12 98.36%

Quote:APIndyI can't understand how these pay tables can possibly be right.

You're absolutely right. I made a typographical error in the 10-play table. Each game has two different streaks only. Please have another look. Thank you for the correction.

I offer a couple possible corrections to Dr. Koehler's paper, with one being a very minor typo. The 9-6 TDB game has the straight value of 5 listed instead of 4. I was able to replicate the 1-line EV for TDB 9-6-4, so I'm fairly certain that this should change. One I am not so certain about is the end value for the 9-5 DDB game. He is reporting an EV of 0.991220 for the 1-line version and 0.987923 for the 3-line version. I was able to replicate all of the EVs for the 5 or 6 1-line versions that I tried except this one. I could have made a mistake but can offer 0.987372531 as a possible answer. I do not presently have a facility for easily convolving video poker probabilities to multiple line versions, so I cannot offer any help on the 3-line version, but the Wizard's new page has 98.40%. I would note that the difference between my 1-line number and IGT's 3-line (0.34%) is fairly close to the difference in some other 1-line vs. 3-line comparisons, including the one that I am questioning. My calculations are essentially "by hand" in Excel, so there are lots of places where I could have erred.

Thanks in advance if you are able to provide any 364-state listing of biases and frequencies.

Well, between the Wiz, me and you, we’ve now accounted for everyone who ever looked at this paper. LOL!

First, thank you. You indeed spotted two actual errors. The TDB table in the paper should have had a 4 for the Straight value (the code did so the results given were ok). The DDB game listed streaks of 2,4,8,10,12 but my code had 2,4,8,11,12. After changing the values in my code, the 1-Line EV is 0.987373, so your answer is in agreement.

I’m sending you the 364 lines of steady-state values for the Deuces Wild game so as not to clog the blog. If there is a simple way to attach a text or excel file, I can make it publically available.

As for encoding the state, that isn’t the challenge. Rather it is the blow-up in size – the old curse of dimensionality. However, I am working on a new idea to shrink the state space to more manageable sizes (as was possible with Ultimate X).

At some point I’ll bother the Wiz to repost the paper with the changes and any new results that might come if I reduce the state space.

Again, thanks!

Quote:GaryJKoehlerHi Drrork,

Well, between the Wiz, me and you, we’ve now accounted for everyone who ever looked at this paper. LOL!

First, thank you. You indeed spotted two actual errors. The TDB table in the paper should have had a 4 for the Straight value (the code did so the results given were ok). The DDB game listed streaks of 2,4,8,10,12 but my code had 2,4,8,11,12. After changing the values in my code, the 1-Line EV is 0.987373, so your answer is in agreement.

I’m sending you the 364 lines of steady-state values for the Deuces Wild game so as not to clog the blog. If there is a simple way to attach a text or excel file, I can make it publically available.

As for encoding the state, that isn’t the challenge. Rather it is the blow-up in size – the old curse of dimensionality. However, I am working on a new idea to shrink the state space to more manageable sizes (as was possible with Ultimate X).

At some point I’ll bother the Wiz to repost the paper with the changes and any new results that might come if I reduce the state space.

Again, thanks!

I read it too! While I have a degree in math, it's been way too long since I did this kind of work.. so I got a little lost in it.

I do have a question.. and this is more for regular UX, instead of Bonus Streak UX. If I used a strategy that was perfect for the one line version of the game, but used that on the 3 line version, how much EV am I giving up?

The Wiz published something similar - he developed a strategy for several Ultimate-X games independent of the number of lines. It is on his Multiline Ultimate X page towards the bottom:

https://wizardofodds.com/games/video-poker/tables/ultimate-x/

He states

"Strategies are available from the following games. Despite the fact that optimal strategy depends on the exact multipliers for the current hand, just a single strategy per game has near optimal performance."

If you go to a particular game, he gives the EV using the strategy.

Your question might be different. If you are asking about using a perfect single-line strategy on multi-line games, then I'm not sure how one would do that. A single line strategy is dependent on the hand and on the current multiplier. What would you use for the current multiplier?

I estimate the number of people in the entire world who will use this strategy is zero. Nevertheless, it was a good mathematical challenge. However, nowhere close to the closed form analysis Gary Koehler did that considers the multiplier stream on every hand, not just an overall average. Either that or Lunar Poker would the most difficult games to analyze I've ever seen.

As always, I welcome your questions and comments.

Quote:WizardI'm happy to say that I developed a strategy for Ultimate X Bonus Streak, in particular, the 10-play 8-6 Jacks or Better version. The return is only 0.09% lower than optimal, and only 0.08% if you use a huge table of exceptions. I had to dust off my matrix algebra skills to do the math. Here is a link: Ultimate X Bonus Streak -- Jacks or Better Strategy. The strategy itself is temporarily located here.

I estimate the number of people in the entire world who will use this strategy is zero. Nevertheless, it was a good mathematical challenge. However, nowhere close to the closed form analysis Gary Koehler did that considers the multiplier stream on every hand, not just an overall average. Either that or Lunar Poker would the most difficult games to analyze I've ever seen.

As always, I welcome your questions and comments.

The "fudged" one (on /video-poker/strategy ) looks fairly straightforward, and nothing too out of the ordinary. Looks pretty similar to regular UX strategy.

Royal Flush 809.9981

Straight Flush 59.9981

Four of a Kind 34.9981

Full House 17.9981

Flush 9.6874

Straight 7.6874

Three of a Kind 6.6874

Two Pair 2

Jacks or Better 1

Nothing 0

I believe that both the Basic Strategy and the penalty-card Perfect Strategy indicated above will have higher EVs than the corresponding strategies referenced in your link. When I plugged your numbers into my spreadsheet, I got the following:

Basic: 97.579033%** with a multiplier of 2.02189919 for a final EV of 98.6475%

Perfect: 97.600200% with a multiplier of 2.02161956 for a final EV of 98.6552%

I included a couple more decimal places than what you identified to allow you to check my figures (and also to differentiate the final EVs because they are very close). These do appear to tie to the numbers in your link (except for the typo indicated by the double asterisk).

With the strategy I suggested above, I got the following:

Basic: 97.546574% with a multiplier of 2.02260937 for a final EV of 98.6493% (improved by 0.0018%)

Perfect: 97.550217% with a multiplier of 2.02270800 for a final EV of 98.6578% (improved by 0.0026%)

Tiny improvements to be certain, but I don't believe the strategies are any more complicated, both being strategies independent of the state of the various multiplier streaks. Also, if this is correct, it might suggest that a somewhat different methodology is in order for calculating such single strategies for other Ultimate X Bonus Streak games.

**On your link, you used the Perfect percentage in both the Basic and Advanced calculations. You probably wanted to say “0.975790 x 2.021899 / 2” instead of “0.976002 × 2.021899 / 2” in your Basic paragraph.

This is what four square has to say, with pix. HTH.Quote:djtacIf anyone has any suggestions I would love to hear it

WoV admins - more supporting reasons for a dining section.

https://foursquare.com/top-places/las-vegas/best-places-donuts

Quote:RogerKintI haven't seen rogue one but played this game last week. The bank I played required max bet to play off multipliers.

so this cant be vultured? :(

is it still +ev to play max bet with abandoned multipliers till no more multipliers?