Ultimate X Poker -- Bonus Streak
Poll
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| | 12 votes (41.37%) | ||
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| | 3 votes (10.34%) | ||
| | 2 votes (6.89%) | ||
| | 3 votes (10.34%) |
29 members have voted
January 10th, 2017 at 5:42:14 PM
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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.
Last edited by: Wizard on Jan 24, 2017
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 10th, 2017 at 5:51:45 PM
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I don't have much to offer analysis wise, but I am curious where you found said machines?
January 10th, 2017 at 6:36:04 PM
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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.
January 10th, 2017 at 6:58:44 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 10th, 2017 at 7:18:32 PM
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I will be downtown 18th-21st I'll run a 100 through it since you said it was fun.
January 10th, 2017 at 7:26:53 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 10th, 2017 at 7:34:20 PM
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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.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 8:21:37 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 10th, 2017 at 9:04:45 PM
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I haven't seen rogue one but played this game last week. The bank I played required max bet to play off multipliers.
100% risk of ruin
January 10th, 2017 at 9:33:33 PM
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Quote: RogerKintThe bank I played required max bet to play off multipliers.
I should have mentioned that in my write up. Thanks.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 10th, 2017 at 10:22:56 PM
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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.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 10:24:40 PM
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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.
"Man Babes" #AxelFabulous
January 10th, 2017 at 10:33:20 PM
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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.
If the House lost every hand, they wouldn't deal the game.
January 10th, 2017 at 11:04:57 PM
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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.
100% risk of ruin
January 10th, 2017 at 11:21:49 PM
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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.
Last edited by: RogerKint on Jan 10, 2017
100% risk of ruin
January 10th, 2017 at 11:45:47 PM
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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. :-)
Last edited by: mamat on Jan 11, 2017
January 11th, 2017 at 12:15:29 AM
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Five Star UX machines at Tropicana require max bet. Although it's a single line game, so play until you lose a hand.
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!
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!
January 11th, 2017 at 6:42:57 AM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 11th, 2017 at 9:05:40 AM
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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.
January 11th, 2017 at 12:35:13 PM
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Played this last night at Cosmo I absolutely hate this game
No longer hiring, don’t ask because I won’t hire you either
January 23rd, 2017 at 12:23:18 PM
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I estimate a variance of 6.0224 for 10-play 9/6 JB UX BS in terms of 100-coin bet units. (A variance 6.0224 in terms of one 100-coin bet unit equates to a variance of 2,409 in terms of 5-coin bet units.)
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.
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.
January 23rd, 2017 at 12:41:11 PM
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You can also lose with the 12x promotion rule. If you flop a full house and get a sequence of 2,3,4,8,12 multipliers on every line, you lose a lot of value if you flop another full house on the 4th hand. Instead of getting a new sequence of 2,3,4,8,12, nothing happens because the next hands are all 12x already! This is an extreme case, but the sword cuts both ways.
January 23rd, 2017 at 12:57:08 PM
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Fantastic game to vulture compared to regular UX. Streaks can produce a lot of EV, especially with bump up to 12X.
Playing 10-coin is very volatile. I don't like getting no multipliers on pairs. But a sequence of high value hands turbocharges everything.
Playing 10-coin is very volatile. I don't like getting no multipliers on pairs. But a sequence of high value hands turbocharges everything.
January 23rd, 2017 at 4:22:08 PM
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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.
January 24th, 2017 at 12:58:59 PM
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There 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.
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.
January 24th, 2017 at 3:52:55 PM
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Quote: WizardHere is a video of me playing.
Thank you for the video. I am intrigued by the 'streaks'.
January 24th, 2017 at 4:14:47 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 24th, 2017 at 5:48:09 PM
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The 2,5,8 straight multiplier didn't mess up your analysis. It just means that you analyzed a multiplier table that IGT chose not to implement ;)
I have yet to see a UXBS machine in the wild.
I have yet to see a UXBS machine in the wild.
January 25th, 2017 at 12:21:25 AM
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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.
January 25th, 2017 at 6:54:45 AM
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You would need to hold out for a total of 2.2X or better 7/5 Bonus Deluxe. It is definitely negative EV if your plan is to play just one hand at 2.1X or lower. For example, I would not play 10-play with multipliers of 1x1x1x1x1x1x3x4x4x4x=21X.
January 26th, 2017 at 10:24:43 AM
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Wizard. 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.
That game didn't do too well in that run either unfortunately from the looks of it.
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.
February 9th, 2017 at 4:24:20 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 10th, 2017 at 4:36:55 AM
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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?
February 10th, 2017 at 6:57:19 AM
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I started work on a single-strategy return but my analysis is unfinished. The returns are closed form.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 10th, 2017 at 11:36:29 AM
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Wiz,
Rule 4 has "the player" duplicated.
Lucky, Director
Bureau of Redundancy Bureau
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
February 10th, 2017 at 3:54:18 PM
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The DD coffee is my favorite.
February 10th, 2017 at 7:02:45 PM
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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%
February 10th, 2017 at 7:38:04 PM
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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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 13th, 2017 at 6:02:02 PM
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I was pleased to see that you had another paper from Dr. Koehler on your game page for Bonus Streak. I know Dr. Koehler posts here from time to time. If possible, I would be interested in seeing a listing of what he terms the state biases and steady-state probabilities for the 3-Line version for one of the games that he has already analyzed. I would suggest one of the games with only 2 streak types, so that there are 12 1-line states, resulting in "only" 364 3-line states (rather than a 14-state version coming from a 3-streak type game that would need 560 3-line states). I was thinking that the 364 states could be compactly named by 12-digit numbers, with each digit being a placeholder for the 1-line state and the value in each digit being from 0 to 3 to indicate the possible number of each state; i.e., 000000000003, indicates all 3 hands being of 1-line state 1, 020010000000 indicating 2 hands with 1-line streak type 11 and the other one being of type 8, etc.
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.
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.
February 14th, 2017 at 3:49:04 AM
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Hi 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!
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!
February 14th, 2017 at 8:55:37 AM
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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?
February 14th, 2017 at 9:23:13 AM
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Ahha! Four people!!
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?
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?
February 22nd, 2017 at 12:05:27 PM
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I'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.
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 23rd, 2017 at 1:56:57 AM
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I played this game recently, it totally sucks balls most of the time, just like regular UX. But it's pretty fun, especially IF you hit some good hands.
The "fudged" one (on /video-poker/strategy ) looks fairly straightforward, and nothing too out of the ordinary. Looks pretty similar to regular UX strategy.
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.
February 24th, 2017 at 7:04:07 PM
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Wiz, Could you check this strategy that I developed using your Strategy Calculator?
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.
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.
Last edited by: drrock on Feb 24, 2017
February 24th, 2017 at 7:45:34 PM
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I don't need to do the math to know my strategy could have been improved upon a little. However, I didn't want to fuss with doing a third iteration for only a benefit of 0.002%. Consider the number of people who will actually use this strategy, ever, in the entire world, is probably zero. I did it more as an exercise in matrix algebra and game theory than for actual use.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
February 25th, 2017 at 9:22:19 AM
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Ok, thanks for the free forum. Sorry if I misunderstood and took the calculation too far.
March 4th, 2017 at 2:07:12 PM
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Have done well searching for abandoned multipliers on bonus point days. Definitely an edge to be found. First question is how to figure out what the base payout is, with optimal strategy, from their pay table. I just guess 97%, but could be lower, especially on the 1-cent games. Then how much is lost by using an Ultimate X / Intuition hybrid strategy, instead of a chart / calculator?
March 4th, 2017 at 6:02:26 PM
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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
Eat real food . . . and you won't need medicine (or a lot less!)
April 3rd, 2017 at 8:37:58 AM
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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?
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
