Thoughts For Beginners

[New2vp]

Yes that is correct with my analysis. When you are on a streak (the Streak 3 which is 5 hands 5 hands), at some point it is worth switching to regular standard optimal play. There is not much gain to the multiplier if the player is going to make a suboptimal play to try to get a 3 of a Kind or Better hand for better future returns.

I estimated 10-Play 8-5 DDB would return 97.67% on the average of 50 years worth of constant play simulation, that takes into account of the total multipliers and such. I based on that to do the decision making and I ensured the simulation game parameters were correct.

But the reported figure is much lower at 97.24%

I am not sure if that figure is based on 2x,3x Streak 1 for 3 of a Kinds. But the 3 of a Kinds in the game I see online and at the live casino pays out 2x, 3x, and 4x. This could be a substantial difference which remains a mystery.For the 8-5 DDB game with the multipliers at videopoker.com, I calculate a single-line upper bound of 97.5780%, lower than your simulation percentage, but consistent with the Wizard's 97.24% for 3-play, being 0.34% higherMany of Koehler's 3-play numbers agree with the numbers posted by the Wizard but not all.  One that doesn't is 9-5 DDB (using the 3-play multipliers that have a short 2-hand streak after hitting trips).  He has 98.7923% while the Wizard is showing 98.40%.  Koehler's single-play with that pay schedule and set of multipliers is 99.1220%, a number that I cannot tie to.  I got 98.7373%, which again is 0.34% higher than 3-play number.  Perhaps this 0.34% margin is coincidence, but it gives me some confidence that my methodology is correct.I was able to tie to Koehler's 9-6 TDB (although I believe he mistakenly listed the straight payoff as 5 instead of 4).  His single line 99.3189% with 3-play being 99.0460%.  The 3-play number is a rounding error away from the Wizard's 99.04%.  My single line number was 99.3189128%, tying exactly to Koehler's single line within the precision that he reported.I could have made several mistakes as I'm using Excel, essentially calculating a strategy by hand for each possible bonus streak, then weighting them together based on a calculated expected frequency of occurrence.  I won't take the time any time soon to extrapolate this to 3-, 5-, or especially 10-play, so single line is the best that I can do.  That does allow me to have a reasonable playing strategy even If I have to take the Wizard's reported numbers for EV as correct.I'm not sure how to evaluate the simulation approach that you used.  Unless you replicate it many times, it is difficult to know what precision that you have.  Your result is a random variable with some variance away from the expected value, so it could be a little high ... or a little low.  If my number or the wizard's number for 8-5 DDB is right, then the result you got is higher than the upper bound.  But maybe they are both wrong.One thing that would also be hard to do with simulations would be to try different strategies and judge the one with the best result to be the best strategy, especially if they were close.  It is POSSIBLE to do this, but again variance will come into play, and it takes extra work to determine if the strategy with the better outcome was in fact a better strategy or whether it just meshed well with the set of random numbers that generated your simulations.I seem to recall that you went over the details of this earlier, but I can't recall them this late at night.(Edit: Sorry I posted this before I saw your last post.  Now I recall approximately how you went after your simulation.  It is curious if you got results higher than the theoretical upper bounds ... unless both the Wizard and I botched the calculation.  Since the Wizard simply was copying from IGT, he would have had to transcribe it wrong UNLESS IGT also messed up.  I suppose anything's possible)

[New2vp]

In Multi-strike you add the value of advancing to each winning hand.  This ends up with the result of not going for straights and flushes so much on the early levels.In Bonus Streak you add the value of advancing to each of the various streaks only to the outcomes that generate those streaks.  Since straights and flushes get you to streaks and pairs don't advance you to a streak, you end up with strategies that take more risks to get straights and flushes.  Yes trips advance to streaks, but strategy changes are more effective at increasing the number of straights and flushes than they are at generating significantly more 3oaks.So, in the sense of adding values, the approach is similar for the two game types.  However, the resulting strategies are very different.Also, it takes more complex math to calculate the Bonus Streak values than it does to calculate the Multi-strike values.  Koehler gives some examples of the necessary values, but it may not be enough to help people see the necessary strategy without a lot more work.

[alpax]

Interesting findings on your end. At the moment I need to catch some rest. I will get back to responding as soon as possible.

Short answer of the time being, the bell curve I got out of the results was somewhat consistent.

I first did the non-optimal hold trade offs to get into the 97.3-97.4% range for 8-5 DDB 10 Play.

I incorporated average/total multiplier tradeoffs for a low 97.6% range.

I did the select greedy plays which I never got to write about to get a little higher to the mid 97.6% range.

I might re-run the simulations again to verify.

I have an HTML output of all the hand combinations and an explanation on how I did the average multiplier decision making here

http://forum.videopoker.com/forum/forum ... p?TID=8680

[asteroid]

That is a terrific analytical approach to the streak game Alpax (IMHO). I figured since Multi-strike is a mature game, the strategic considerations were mature and well-advanced and could be leveraged for the bonus streak game in some way. I always played Deuces Wild with multi-strike since natural hands weren't required to advance to the next line, whereas it appears that only natural hands will result in multiplier streaks in this UX bonus streak game. With Super Times Pay, the juice required is only one more coin per line (versus double your hand in many of these newer games) and, as you say, the strategy remains the same as the regular (single line standard) game. [QUOTE=asteroid]

Alpax, I would imagine that the strategy considerations used for multi-strike videopokerin which the player is placing a priority of getting to the next line (multiplier) may have applicability in this Ultimate X bonus streak game. I have not delved into it due to the large bank roll required and the certainty that I could not play this game optimally even if I were rich.



I agree with you that is what I logically believed to be the proper approach to this game. In multistrike, you do what it takes to advance from level 1 to level 2 by simply getting a winning hand. The player pays 4 folds the normal wager than on single line games so it goes to waste if they fail to advance to level 3 where there are 4x multipliers (advancing to level 4 at 8x would make up for the other rounds where the player loses on level 1). The player eases a little at level 2 2x and goes for a little more of the higher EV play since they are getting double, and eases up more on level 3 since they are getting quadruple. If they reach the top level or get a free ride, they will switch to normal strategy.

I weighted the hold decision in Ultimate X Bonus Streak by the percentage of Three of a Kind or Better hand as well as the respective expected return of all 32 hold possibilities of all 2598960 card draws. As long as the player was not giving up too much EV, I went for the lesser return to gain chances to initiate the multipliers.

I do believe the 10-play returns are based off the fact that 3 of a Kind produces just 2x and 3x multipliers rather than the 2x, 3x, and 4x. Getting the third hand for a longer streak is HUGE. It would really be horrible if a player gets something good on the 2nd hand of a 3 of a Kind, it means their next hand is at 2x (start of a new streak) instead of the 12x. The whole dynamic changes.

I would not personally play this game as well not because of its cost to play; the variance is very high from the wideness of the bell curve after long simulation of play (after over 4000 hours of FAST play, you could be as much as 1% off the theoretical return). This game is tougher to master since there is so many situation to account for, a person must really really put in the time to master a sophisticated game which may not return much to the player in the long run. There are better returning video poker games out there like Super Times Pay which strategy is the same as regular single line poker.

I think we need to branch off from this thread if we were to discuss this further, its purpose was sort of served already.[/QUOTE]

[asteroid]

You've done a very nice job of quantifying the problem which needs to be solved for bonus streak New2vp. It is clear that IGT has come up with a very nice way to increase holds for the casino - they (IGT) know full well that no one but perhaps the most gifted autistic savant will play this game optimally (the population of optimal players is so small as to be insignificant), yet the bonus streak games conform to those regulations which state that the games must have a theoretical house edge that is less than the standard game (for example ddb).In Multi-strike you add the value of advancing to each winning hand.  This ends up with the result of not going for straights and flushes so much on the early levels.In Bonus Streak you add the value of advancing to each of the various streaks only to the outcomes that generate those streaks.  Since straights and flushes get you to streaks and pairs don't advance you to a streak, you end up with strategies that take more risks to get straights and flushes.  Yes trips advance to streaks, but strategy changes are more effective at increasing the number of straights and flushes than they are at generating significantly more 3oaks.So, in the sense of adding values, the approach is similar for the two game types.  However, the resulting strategies are very different.Also, it takes more complex math to calculate the Bonus Streak values than it does to calculate the Multi-strike values.  Koehler gives some examples of the necessary values, but it may not be enough to help people see the necessary strategy without a lot more work.

[alpax]

For the 8-5 DDB game with the multipliers at videopoker.com, I calculate a single-line upper bound of 97.5780%, lower than your simulation percentage, but consistent with the Wizard's 97.24% for 3-play, being 0.34% higherMany of Koehler's 3-play numbers agree with the numbers posted by the Wizard but not all.  One that doesn't is 9-5 DDB (using the 3-play multipliers that have a short 2-hand streak after hitting trips).  He has 98.7923% while the Wizard is showing 98.40%.  Koehler's single-play with that pay schedule and set of multipliers is 99.1220%, a number that I cannot tie to.  I got 98.7373%, which again is 0.34% higher than 3-play number.  Perhaps this 0.34% margin is coincidence, but it gives me some confidence that my methodology is correct.I was able to tie to Koehler's 9-6 TDB (although I believe he mistakenly listed the straight payoff as 5 instead of 4).  His single line 99.3189% with 3-play being 99.0460%.  The 3-play number is a rounding error away from the Wizard's 99.04%.  My single line number was 99.3189128%, tying exactly to Koehler's single line within the precision that he reported.I could have made several mistakes as I'm using Excel, essentially calculating a strategy by hand for each possible bonus streak, then weighting them together based on a calculated expected frequency of occurrence.  I won't take the time any time soon to extrapolate this to 3-, 5-, or especially 10-play, so single line is the best that I can do.  That does allow me to have a reasonable playing strategy even If I have to take the Wizard's reported numbers for EV as correct.I'm not sure how to evaluate the simulation approach that you used.  Unless you replicate it many times, it is difficult to know what precision that you have.  Your result is a random variable with some variance away from the expected value, so it could be a little high ... or a little low.  If my number or the wizard's number for 8-5 DDB is right, then the result you got is higher than the upper bound.  But maybe they are both wrong.One thing that would also be hard to do with simulations would be to try different strategies and judge the one with the best result to be the best strategy, especially if they were close.  It is POSSIBLE to do this, but again variance will come into play, and it takes extra work to determine if the strategy with the better outcome was in fact a better strategy or whether it just meshed well with the set of random numbers that generated your simulations.I seem to recall that you went over the details of this earlier, but I can't recall them this late at night.(Edit: Sorry I posted this before I saw your last post.  Now I recall approximately how you went after your simulation.  It is curious if you got results higher than the theoretical upper bounds ... unless both the Wizard and I botched the calculation.  Since the Wizard simply was copying from IGT, he would have had to transcribe it wrong UNLESS IGT also messed up.  I suppose anything's possible)



I was not able to interpret Koehler's work to be able to derive the return percentages that you were able to. I do not use the theories enough in real life to be able to retain the knowledge, I only use binomial distribution.

If you were able to get 97.578% for single line, and with Koehler able to prove that more lines will degrade the return, I think you are closer to what videopoker.com reported as 97.24% for 10-play. The original 8-5 DDB 10-play had a reported return of 97.35% and with a somewhat easier strategy, it will be the better choice.

I do not think there is just one mathematical model that can derive the return. There are 32 endpoints the user can take for every 5 card deal, and if there are 134,459 unique draws, and 12^10 multiplier states it would take a computer a very long time to know what is best.

I went with card holds that produce the highest percentage of 3 of a Kind or better outcomes, and went with optimal play only if I felt the sub optimal play was giving up too much EV.

Even if my return reported by the simulation efforts are incorrect, I can at least assure that the report I provided (the 20 suboptimal hold cases and when to play optimal) at least provides a strategy that will do better than someone just playing normally on this game.

I realize I am repeating myself, but I do wave the white flag on this game and will play 9-5 DDB (something I will not do) instead.

[asteroid]

Perhaps the multinomial distribution (the binomial distribution is just a special case of this) is what the IGT programming team used when designing and evaluating the returns for this game. [QUOTE=New2vp]

For the 8-5 DDB game with the multipliers at videopoker.com, I calculate a single-line upper bound of 97.5780%, lower than your simulation percentage, but consistent with the Wizard's 97.24% for 3-play, being 0.34% higherMany of Koehler's 3-play numbers agree with the numbers posted by the Wizard but not all.  One that doesn't is 9-5 DDB (using the 3-play multipliers that have a short 2-hand streak after hitting trips).  He has 98.7923% while the Wizard is showing 98.40%.  Koehler's single-play with that pay schedule and set of multipliers is 99.1220%, a number that I cannot tie to.  I got 98.7373%, which again is 0.34% higher than 3-play number.  Perhaps this 0.34% margin is coincidence, but it gives me some confidence that my methodology is correct.I was able to tie to Koehler's 9-6 TDB (although I believe he mistakenly listed the straight payoff as 5 instead of 4).  His single line 99.3189% with 3-play being 99.0460%.  The 3-play number is a rounding error away from the Wizard's 99.04%.  My single line number was 99.3189128%, tying exactly to Koehler's single line within the precision that he reported.I could have made several mistakes as I'm using Excel, essentially calculating a strategy by hand for each possible bonus streak, then weighting them together based on a calculated expected frequency of occurrence.  I won't take the time any time soon to extrapolate this to 3-, 5-, or especially 10-play, so single line is the best that I can do.  That does allow me to have a reasonable playing strategy even If I have to take the Wizard's reported numbers for EV as correct.I'm not sure how to evaluate the simulation approach that you used.  Unless you replicate it many times, it is difficult to know what precision that you have.  Your result is a random variable with some variance away from the expected value, so it could be a little high ... or a little low.  If my number or the wizard's number for 8-5 DDB is right, then the result you got is higher than the upper bound.  But maybe they are both wrong.One thing that would also be hard to do with simulations would be to try different strategies and judge the one with the best result to be the best strategy, especially if they were close.  It is POSSIBLE to do this, but again variance will come into play, and it takes extra work to determine if the strategy with the better outcome was in fact a better strategy or whether it just meshed well with the set of random numbers that generated your simulations.I seem to recall that you went over the details of this earlier, but I can't recall them this late at night.(Edit: Sorry I posted this before I saw your last post.  Now I recall approximately how you went after your simulation.  It is curious if you got results higher than the theoretical upper bounds ... unless both the Wizard and I botched the calculation.  Since the Wizard simply was copying from IGT, he would have had to transcribe it wrong UNLESS IGT also messed up.  I suppose anything's possible)



I was not able to interpret Koehler's work to be able to derive the return percentages that you were able to. I do not use the theories enough in real life to be able to retain the knowledge, I only use binomial distribution.

If you were able to get 97.578% for single line, and with Koehler able to prove that more lines will degrade the return, I think you are closer to what videopoker.com reported as 97.24% for 10-play. The original 8-5 DDB 10-play had a reported return of 97.35% and with a somewhat easier strategy, it will be the better choice.

I do not think there is just one mathematical model that can derive the return. There are 32 endpoints the user can take for every 5 card deal, and if there are 134,459 unique draws, and 12^10 multiplier states it would take a computer a very long time to know what is best.

I went with card holds that produce the highest percentage of 3 of a Kind or better outcomes, and went with optimal play only if I felt the sub optimal play was giving up too much EV.

Even if my return reported by the simulation efforts are incorrect, I can at least assure that the report I provided (the 20 suboptimal hold cases and when to play optimal) at least provides a strategy that will do better than someone just playing normally on this game.

I realize I am repeating myself, but I do wave the white flag on this game and will play 9-5 DDB (something I will not do) instead.[/QUOTE]

[ukaserex]

[QUOTE=onemoretry]

I've never registered for a Wizard of Vegas account so I cannot be a candidate to see Shackleford's analysis before it gets posted onto a site. Very broad range of situations and states to analyze for the game, and there are multiple game variants as well.



While it's not my intent to promote any site - I believe that although the site is a little crude in it's formatting, the people there - most of them are what I would call ...smart. Really sharp math-minded folks.

They have an appreciation for advantage play - but also within ethical constraints. That is, they play by the casino's rules. They will certainly milk any advantage they find, but again, within the rules. At least, that's my impression of the forum posters at Wizard of Vegas.

I wouldn't have found this site without that site. I dare say, you'd like some of those folks. You definitely speak their language as far as math goes.

[alpax]

While it's not my intent to promote any site - I believe that although the site is a little crude in it's formatting, the people there - most of them are what I would call ...smart. Really sharp math-minded folks.

They have an appreciation for advantage play - but also within ethical constraints. That is, they play by the casino's rules. They will certainly milk any advantage they find, but again, within the rules. At least, that's my impression of the forum posters at Wizard of Vegas.

I wouldn't have found this site without that site. I dare say, you'd like some of those folks. You definitely speak their language as far as math goes.

The Wizard of Vegas/Odds site is a heavily promoted gambling resource across many gambling related forums on the web, including here. There is no need to feel any shame to mention it, they got tools to really help people in their video poker skill. I've gained a ton of insight from Shackleford and give him all the credit for more than 98% of the gambling insights I have.

I am surprised myself that I did not create an account and participate. I've lurked there for several years. WoV is well rounded in all aspects of gambling, I was into slots at the time and there was not much for it except for the reality that it is a money burning game. I made video poker a primary focus a few years back so I participated in a more video poker focused forum.

I agree that there are many talented folks at WoV even though I heard there has been some of them are no longer participating. Successful gambling requires analytical skills to see casino mistakes to exploit.

I too would not have found this site if it was not through the Wizard of Odds. I think Mr. Dancer is participating there now so most people here in the past left here to lurk there.



Perhaps the multinomial distribution (the binomial distribution is just a special case of this) is what the IGT programming team used when designing and evaluating the returns for this game.[QUOTE=alpax]


Yup, the calculations were going to be too much for myself to handle so I resorted to simulations. Binomial is straight forward since you start with 5 cards and end with the outcome. This Ultimate X game goes from one state to another state to another state which will require some complex calculations. I can assure my efforts with Magic Draw and Split Card Poker are credible.

Koehler has now participated in the Wizard of Vegas forum thread regarding Ultimate X Bonus Streak. Someone by the handle of "drrock" has also posted something very very similar to what New2Vp has posted here. They are correcting the returns and they will work on a strategy in which everyone is anticipating for.