## Poll

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**28 members have voted**

That's not so good. Lots of hands with multipliers are -EV. One reason this game is currently VERY nice to vulture (even in high competition areas) is that non-mathematician vultures (and copycats) haven't figured out how to play (They sometimes use simple rules like "only play 10x-12x's").Quote:100xOddsis it still +ev to play max bet with abandoned multipliers till no more multipliers?

Look at

(1) current multipliers: If 2.1-2.2x or higher, play. If 2.0x-2.1x or lower, look at #2.

(2) sequence of multipliers: Looking at the current hand and next 1-4 hands combined, do any of the four combined averages reach 2.1x-2.2x or higher? If so, play.

e.g. The current hand is 1.6x, but the next hand is 3.0x, so the average of two hands is 2.3x...so play 2 hands.

(3) If both #1 & #2 are both 2.0x-2.1x or lower, don't play & look at another game.

This isn't quite accurate, as stacks of 3-4 multipliers have a higher chance to be converted to 12x's if you land a good hand.

Thus, there is probably a lower profitable level to play with large stacks of multipliers on a 10-play.

...possibly 1.6x-2.1x. I don't know exactly where.

Would be interesting if someone wanted to do the analysis...

It is really fun on this game to get dealt trips or higher. Sometimes you get sequences of multipliers which go on quite long (10-20 hands).

Quote:JohnzimboMy only dealt royal lifetime was on videopoker.com. Dammit.

I've got 2 "real" ones. Spin Poker for 9 at once and single line. This game just got instated here. Tempting but I'll pass. ☺

Quote:Mission146None for me, yet. I've gotten two on complete throwaways, but those were both on multi-line games, so got them on one of the lines. I do have dealt Four Deuces w/Joker on that game, which I almost never play. $500 on a $0.25 total bet, so that was neat. Haven't played that one since.

I've only played DW+J on the Hoyle Casino cd-rom for the pc. I think I've only hit that hand once but drew to it.

Quote:IbeatyouracesI've only played DW+J on the Hoyle Casino cd-rom for the pc. I think I've only hit that hand once but drew to it.

It was strange, the Joker was even in the middle, so that's as perfect as that hand could get. Figured I'll never top that, so unless there's a way to find one at an advantage (and it's rare to find at all, so I doubt it) why ever play again?

Quote:Mission146None for me, yet. I've gotten two on complete throwaways, but those were both on multi-line games, so got them on one of the lines. I do have dealt Four Deuces w/Joker on that game, which I almost never play. $500 on a $0.25 total bet, so that was neat. Haven't played that one since.

for me, Royal with least # of cards = 2

best dealt hand was quads (2,3,4) with kicker.

both times resulted in w2-g

:)

best redraw with 1 card (ace) was quad aces with kicker.

2nd best was holding 1 Ace and getting 3333A.

both this year.

also, that's the 2nd time in my life getting Aces with kicker. (don't play ddb that often.)

irony: have same of # of Royals in ddb as Aces with kicker

Therefore, being results oriented, I say AAA and give yourself the extra chance for the 4th A.

don't know if its +ev but played it.

uggg.. hate putting in 10 coins for ult x. :)

(and whiffed both for a total of -$25)

Quote:beachbumbabsI had that exact hand yesterday. Held AAA2. Bricked it.

Therefore, being results oriented, I say AAA and give yourself the extra chance for the 4th A.

I held the AAA2 as well and didn't hit either (not expected to).

First was a 10 hand Deuces Wild Bonus 50 cent play. Abandoned mults were 12/12, 2/2/4 and 2/2/4 with seven singles. Deal was 2d 7h 4h 2c 2s - Straight Flush. Passed up temptation to hold the deuces and took the SF for $575 win on the $50 bet plus the 2-4-7-10-12 stacked multipliers on seven hands and 12, 12/12, 12/12 on the other three.

Going into the fifth subsequent hand, with eight 12x mults and three singles, I was dealt Jd, 3s, 3d, Jh, 2d - Full House for a $725 win on that hand.

Intermediate big wins were on dealt four to a flush for $217.50, three Queens for $250.

Played out the stacked 2/2/4 on all hands after the FH and netted another $20.

I had put in a $100 to start, didn't realize that it wasn't max bet on the first push (only 5) and lost $15 when dealt pair of 5s. I cashed out $1,692.50 after the nine total hands played.

If I'd just quit playing slots, I'd have taken home another $800 last night (lost that plus the $100 I walked in with) after a $540 haul the night before.

I'll be checking the forums here for more tips and strategy for sure.

I think it's easy to say that if the average multiplier on the next hand is more than 2x, then vulture. Remember that a hand with no multiplier really has a multiplier of 1x.

I would hazard to say it's positive at exactly 2x and maybe even at 1.9x, because of the value of future multipliers with a pat 3K or better.

However, let's look more than one hand in advance. Like this one.

The next hand as an average multiplier of 1.5, which is not immediately +EV. However, the hand after that, assuming no improvement, has an average multiplier of 1.9. The hand after that is also at 1.9x, but has two chances to improve.

Would you vulture this hand and why?

As far as vulturing, I almost never find anything at all let alone worth playing.

I see the hustlers come by and they never find anything.

I think Gary Koehler's full Markov approach is overkill to resolve this question.Quote:WizardThe next hand as an average multiplier of 1.5, which is not immediately +EV. However, the hand after that, assuming no improvement, has an average multiplier of 1.9. The hand after that is also at 1.9x, but has two chances to improve.

Would you vulture this hand and why?

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What I would like to have (if I actually had any interest in vulturing UXBS) is a set of coefficients to multiply the stream of current and future multipliers to see if it is playable in the current state. Suppose I guess a set of coefficients C1, C2, C3, C4, C5. I then calculate the weighted average multiplier, Mw, of the next five hands. For example for your screen shot:

Mw = (C1 * 1.9 + C2 * 1.9 + C3 * 1.9 + C4 * 1.0 + C5 * 1.0) / 5

If the resulting weighted average multiplier Mw > 2.0, the game is considered playable.

Now, I can run tests of my initial Cs. I select a strategy that is appropriate to the specific VP game with a neutal multiplier. This strategy won't be a very good strategy if the multiplier for the next hand is very high or very low. However, I am seeking to get a method that works well for marginal cases where the next hand has a marginal multiplier near 2.0X.

I can run a MC simulation that starts in any state and then runs until I have a boundary case with Mw in the range 2.0 < Mw < 2.5. Then, I run the simulation forward until Mw < 2.0. I capture the net win/loss of this mini-session. I can create a graph of EV versus the initial Mw. I expect that EV versus Mw this will be a monotonically increasing graph. Now, I can see if my coefficients are close to predicting the correct point to stop playing for optimal vulture EV.

I can adjust C1 up or down to make the simulated vulture EV zero when Mw = 2.0. Then, I vary C2 (while keeping the other coefficients fixed) to optimize the EV. Using this optimal C2, I readjust C1 to produce zero EV. likewise, I optimize C3, C4, and C5.

After a few iterations, I expect that the coefficients will converge. Now, I can just do some simple math to see if the game is in a +EV state. I then play until it is not a +EV state.

If I demand a positive EV rather than a non-negative EV, I can just do the coefficient optimization targeting that positive EV number. It may turn out that the EV isn't very sensitive to C5. Also, M5 will often be 1.0. This might mean we can drop the last term of the equation. Or maybe, just count the number of 12xs on the fifth hand to make a simple adjustment if there are multipliers on the fifth hand.

I would be a little concerned that the promotion of multipliers to 12x adds a nonlinear effect. Small future multipliers are actually worth more than their face value.

For the record, my analysis only has the full Markov solution for 3-line Bonus Streak. The 5-Line and 10-Line cases have state spaces far too large for my computing platform.Quote:MentalI think Gary Koehler's full Markov approach is overkill to resolve this question.

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What Mental suggests is interesting.

Quote:MentalWhat I would like to have (if I actually had any interest in vulturing UXBS) is a set of coefficients to multiply the stream of current and future multipliers to see if it is playable in the current state. Suppose I guess a set of coefficients C1, C2, C3, C4, C5. I then calculate the weighted average multiplier, Mw, of the next five hands. For example for your screen shot:

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Thanks, good post.

My simulator for the game is coming along well. Then I'll start playing around with strategies to simulate. I'll consider this approach.

Great! I know how tedious it is to program streaks of multipliers. I hope it goes smoothly.Quote:WizardQuote:MentalWhat I would like to have (if I actually had any interest in vulturing UXBS) is a set of coefficients to multiply the stream of current and future multipliers to see if it is playable in the current state. Suppose I guess a set of coefficients C1, C2, C3, C4, C5. I then calculate the weighted average multiplier, Mw, of the next five hands. For example for your screen shot:

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Thanks, good post.

My simulator for the game is coming along well. Then I'll start playing around with strategies to simulate. I'll consider this approach.

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I am revising my suggestion to subtract a base value form the total of multipliers on each line. These base values will represent the neutral value for the Nth game multipliers.

This means I would have 10 parameters to optimize and the final formula would be more complicated:

C1 * (M1 - M1b) + C2 * (M2 - M2b) + C3 * (M3 - M3b) + C4 * (M4 - M4b) + C5 * (M5 - M5b)

The upside is the the resulting base values are targets when looking for a playable game. The C coefficients indicate how sensitive the EV is to a surplus or deficit of multipliers at each subsequent game. A big surplus in earlier games is more important than a similar deficit in later games. I would expect that many borderline cases that come up in real life would have similar profiles. It might be more practical to have a few typical borderline-playable profile memorized rather than doing complicated math in your head. Of course, a spreadsheet formula with the formula would be pretty simple.

Yup, that's what high variance looks like in multiplier VP.Quote:Sandybestdog.... I’ve hit big many times and you are almost always still down. I finally did hit a 12x royal ($12000). I’ve hit many other jackpots. I have about 30x where I’ve been dealt 4 to the royal with multipliers where one more card would have been $20k, $40k or even $100k. But it just seems like a drain when you’re not hitting anything. It is amazing how many times you have a full screen of 4x or 7x and you don’t even get your money back on that spin. Also you’ll get the hands with the long streak of multipliers and go 4-5 hand in a row and hit nothing on it..

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Vulture if one or more of the following are true:

- Total multipliers on the next hand are 21 or more.
- Total multipliers for the next two hands are 34 or more.
- Total multipliers for the next three hands are 43 or more.

This, I think, is good stuff and the first time I've published on it.

As an example, I posted the screenshot above earlier in this thread, asking if you would vulture it. The combined multipliers the next two hands are exactly 34, so you should vulture it.

Quote:WizardVulture if one or more of the following are true:

- Total multipliers on the next hand are 21 or more.
- Total multipliers for the next two hands are 34 or more.
- Total multipliers for the next three hands are 43 or more.

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Nice work! This is a nice simple strategy and very useful information for someone.

I like to squeeze every last bit of info out of a set of progressive meters, but I am not into checking UX or UXBS. The structure of the game raises a lot of interesting EV questions, but I suspect you are not giving up much by just adding multipliers. If there were random streams of multiplier, there might be pathological cases that throw this off, but the multiplier are not random. I suspect that most multiplier streams in the real UXBS game have a similar structure after you average over 10 hands.

Quote:MentalNice work! This is a nice simple strategy and very useful information for someone.

I like to squeeze every last bit of info out of a set of progressive meters, but I am not into checking UX or UXBS. The structure of the game raises a lot of interesting EV questions, but I suspect you are not giving up much by just adding multipliers. If there were random streams of multiplier, there might be pathological cases that throw this off, but the multiplier are not random. I suspect that most multiplier streams in the real UXBS game have a similar structure after you average over 10 hands.

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Thank you!

The multiplier streams are defined in the rules. I'll be the first to admit this strategy is just a basic strategy, but I think it will balance ease of use and power well.

I'm working on a 3-play and 5-play strategy now.

Quote:WizardI am taking a fresh look at Ultimate X Poker Bonus Streak. My previous work was on a long-term strategy and return. However, I would like to turn my attention to when to vulture the game (shut up Wiz!).

I think it's easy to say that if the average multiplier on the next hand is more than 2x, then vulture. Remember that a hand with no multiplier really has a multiplier of 1x.

I would hazard to say it's positive at exactly 2x and maybe even at 1.9x, because of the value of future multipliers with a pat 3K or better.

However, let's look more than one hand in advance. Like this one.

The next hand as an average multiplier of 1.5, which is not immediately +EV. However, the hand after that, assuming no improvement, has an average multiplier of 1.9. The hand after that is also at 1.9x, but has two chances to improve.

Would you vulture this hand and why?

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No.

It might be good mathematically (I don't know on this one), but you can get absolutely punished for chasing on this game. For me, the very next hand is either +EV (independent of next multipliers, potential to boost multipliers or potential to get new multipliers) or it is not +EV. I guess I would also look and see if the average for KNOWN multipliers will come out to more than 2x, per hand, but that doesn't happen without the first set of hands being at least an average of 2x all that often.

Play if any of the following are true:

- Total multipliers next hand are 11 or more.
- Total multipliers next two hands are 18 or more.
- Total multipliers next three hands are 26 or more.

As to Mission's point, sometimes, like in the screenshot I provided, you have to suffer a negative bet or two to get to a positive one that makes up for the negative ones. My strategy does rely on averages that future multipliers will go up to 12. As with any play, respect your bankroll and don't over-bet it.

Play if any of the following are true:

- Total multipliers next hand are 7 or more.
- Total multipliers next two hands are 10 or more.

There doesn't appear to be any situation where you need to count the next 3 multipliers, where either of the first two rules are already enough to vulture.

Consider the situation where the three streams are 2-4-8, 1-1-1, 1-1-1. Counting just the first two multipliers in each hand there are 10, which is enough to vulture.

Though I once asked for pretty much exactly the type of strategy you’ve now published, I somehow missed its April publication. I’ve been successfully vulturing this game for years now, but using a very conservative strategy of pretty much requiring 2X or better multipliers on all future hands.

The problem with doing this is I always knew I’d been leaving money on the table. The two hard questions were:

1. At what sub-2X level are streaks profitable

2. What strategy adjustments should be made

There are also some unexpected nuances I’ve discovered through playing:

1. A streak has surprising value in its *length* beyond the actual numbers in the streak

2. Except in fresh long streaks, “busting” existing numbers is not as valuable as it appears.

3. Multipliers overall are not as valuable to vultures because not all future multipliers are playable

3. 10-play is the least likely to have a playable streak, yet holds the highest potential (e.g., full streaks left)

Long streaks are great if you have enough of them make it worthwhile (so often you find only 1 or 2 hands with a full streak at 5- or 10-play that are not playable). Most of the extra value comes from the ability to bust all remaining hands to 12X by hitting something early in the streak.

“Short streaks” of one are also have an advantage: you can earn an entirely new, full streak. If there’s even one more hand in the streak to go, you can’t. This is worst late in a streak with an existing high multiplier. If you’re on the last hand (12x) of a streak and get dealt a good hand, you get nothing extra.

So, for example, a single 4X line at Triple Play — at 6X — does not meet your 7X requirement, yet I am almost certain it is playable. Whereas a combination of streaks of 2 with multipliers that also total 2X bet may not be, because of #2 and #3 above.

I saw your post for UXBS strategy for the one game — DDB, right? I appreciate that someone of your ability took the time to create this — I’ve definitely needed it, but creating it myself wasn’t realistic. Unfortunately, your strategy is for, play-through. What I need is one for vultures that takes into account #3 above — I’ll only be playing positive multipliers, not average ones.

I will be trying out your strategy in coming months and will try to keep a separate accounting for it. I have a system for tracking my estimated EV for this game which is primitive, but the best I could do without better info.

This game is a big chunk of my gaming activity lately, so any further help would be much appreciated.

😸

If you start a game that has more multipliers than Mike's criteria, you can easily estimate the extra advantage. You have not said what your EV threshold is. Do you want a certain percentage advantage based on coin in or a certain expected profit over each complete sequence?Quote:TabbycatI saw your post for UXBS strategy for the one game — DDB, right? I appreciate that someone of your ability took the time to create this — I’ve definitely needed it, but creating it myself wasn’t realistic. Unfortunately, your strategy is for, play-through. What I need is one for vultures that takes into account #3 above — I’ll only be playing positive multipliers, not average ones.

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Every extra multiplier on the next hand earns you about 4.9 coins above breakeven. That would be enough for me. I have a high tolerance for losses if a situation is +EV. Maybe you want more margin of safety. If you find a setup that exceeds Mike's cutoffs due to extra multipliers on the far off hands, you need to discount those extra coins a bit. You might never play those hands because you are playing so tight.

It seems really unlikely that most of the potential plays that you come across are only at Mike's cutoff or 1-2 multipliers higher. Most cases will be fairly strong plays that are no-brainers. I think Mike's criteria are a little tight myself. A more sophisticated model should be able to extract more EV from the optionality of quitting early if the first hand doesn't turn out well.

Quote:MentalA more sophisticated model should be able to extract more EV from the optionality of quitting early if the first hand doesn't turn out well.Quote:TabbycatI saw your post for UXBS strategy for the one game — DDB, right? I appreciate that someone of your ability took the time to create this — I’ve definitely needed it, but creating it myself wasn’t realistic. Unfortunately, your strategy is for, play-through. What I need is one for vultures that takes into account #3 above — I’ll only be playing positive multipliers, not average ones.

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Agreed — that would be useful for me.

I would play any hand that’s positive. If I need action and thought I could get enough, I’d play breakeven cases in some casinos. Finding near-breakeven setups is quite common, and now Mike’s criteria promises more of them. I would not have considered his Ten Play example with the 2-3-4X streaks, but if he’s right then I will get many more play opportunities — just what I was hoping for.

My biggest problems are getting any action on my card and hiding wins, as I’m winning too consistently. Eventually that’s going to be a problem.

Normally in DB you'd of course ditch the queens, but in Bonus Streak does the guarantee of starting 5 long streaks outweigh the EV of going after four aces?

Quote:ChicagoSkinnyDoes the guarantee of starting 5 long streaks outweigh the EV of going after four aces?

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Without an actual AP (or even play-through) strategy for UXBS I can only estimate.

I will attempt this for 8-5 DDB, 3- or 5-play since this is the most common schedule I find. The earned multipliers are 2-4 for trips and 2-4-8-10-12 for full house or better (note that multipliers for 10-play are different).

Without the bonus, holding the two pair instead of just the aces costs 31% of one bet. (Though you have made a second bet to activate the bonus, it doesn’t affect your payout here.) In return, you get a full house 8.5% of the time, 6.5 times more often than when holding just the aces. Since the full 2-4-8-10-12 streak is much more valuable than the 2-4 one earned from making trips on 11.4% of draws, it seems pretty clear that it’s a good tradeoff. I would like to know the exact value of a 2-4-8-10-12 streak at this game, but Wiz has only published it for 2-3-4-7-12 (and I’m not sure for which pay table). He gave that value as 23.1 bets, so this streak should be worth considerably more.

Those streak values assume playing through, i.e. using up all the multipliers you earn. That’s not the case as an AP, because many of those multiplier combinations won’t be enough to make the play positive to the end. To complicate it further, as you go from 3- to 5- to 10-play, fewer multiplier combos are positive — and the most common examples are many of the 2-4 short streaks earned from trips, further tipping the edge toward holding two pair.

Again, what’s needed besides an AP-based play strategy is a value for at least the longest streaks with an adjustment for only continuing to play when the game remains positive.

Quote:WizardI just published my page at WoO on Vulturing Ultimate X Bonus Streak. This includes strategies for both Double Double Bonus and Deuces Wild.link to original post

I thought you had posted detailed **play** strategies for UXBS DW and DDB (I’d copied one page).

Are they now gone or moved elsewhere?

Found them before but don’t see them now.

I only have pay tables for Deuces Wild and jacks or better right now. I can fully solve the 3-line problem in a couple of minutes and the 5-line problem in a couple of hours. I may add a few types of games later.

I am not allowed to post links as I am new but if you can figure this out you can use the app. "bonusstreak dot azurewebsites dot net"

Is the EV in your calculator based on the 5-coin base bet or the entire 10-coin bet?

I will definitely be trying it out in the wild.

For some reason I never read Gary's paper.

I’ll have a look at it.

I am a big fan of Gary's work on Bonus Streak. I went to your site and really like your calculator app. If you don't mind my asking, what language is your VP engine written in?Quote:HankI read Gary Koehler's Bonus streak analysis paper. I wanted to take on the challenge of solving the 5 line problem. In addition to solving the 3 and 5-line problems, I implemented his approach to vulture decisions. I created an interactive front UI for solutions. The UI can calculate the optimal hand as well as the expected EV for any streak multipliers. It is useful for testing any of the ideas discussed here. See how the hand to hold depends on which multipliers you have and your goal of long-term vs short-term play.

I only have pay tables for Deuces Wild and jacks or better right now. I can fully solve the 3-line problem in a couple of minutes and the 5-line problem in a couple of hours. I may add a few types of games later.

I am not allowed to post links as I am new but if you can figure this out you can use the app. "bonusstreak dot azurewebsites dot net"

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Do you have a lot of experience in Markov chains and programming?

Quote:TabbycatHank,

Is the EV in your calculator based on the 5-coin base bet or the entire 10-coin bet?

I will definitely be trying it out in the wild.

For some reason I never read Gary's paper.

I’ll have a look at it.

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All the percent and ev numbers you see are based on 10 coin play. For example, if the vulture ev for a set of multipliers shows 100% you have even odds of getting your money back.

Quote:MentalI am a big fan of Gary's work on Bonus Streak. I went to your site and really like your calculator app. If you don't mind my asking, what language is your VP engine written in?

Do you have a lot of experience in Markov chains and programming?

The solver is written in C# using SIMD instructions and parallel processing. The UI is an angular app.

This was my first Marov chain application, but I have a Math degree and a lot of programming experience. I originally wrote the solver because I wanted to see how efficiently I could write the 5-line solution utilizing a normal CPU. I was considering a GPU-based solution but the CPU version is fast enough. I will consider playing with the 10-line solution via GPU.

Thanks.Quote:HankQuote:MentalI am a big fan of Gary's work on Bonus Streak. I went to your site and really like your calculator app. If you don't mind my asking, what language is your VP engine written in?

Do you have a lot of experience in Markov chains and programming?

The solver is written in C# using SIMD instructions and parallel processing. The UI is an angular app.

This was my first Marov chain application, but I have a Math degree and a lot of programming experience. I originally wrote the solver because I wanted to see how efficiently I could write the 5-line solution utilizing a normal CPU. I was considering a GPU-based solution but the CPU version is fast enough. I will consider playing with the 10-line solution via GPU.

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Until you mentioned it, I did not realize I have access to SIMD vector instructions via the GCC compiler. I am writing a graphics program for screen scraping right now, and I might try to use this to speed things up.