My Initial Simulation on DDB Ult X Bonus Streak

[alpax]

This will be my first crack at evaluating the brand new Ultimate X Bonus Streaks game. I envision the scope of the game to be bigger than the other specialty games, thus this will be the first of 3 or 4 aspects I will analyze. Hopefully someone can figure this out quicker and save me the effort. It will not be a priority of mine to achieve the most optimal playing strategy, but rather to be better than the average player that plays Ultimate X.


I was inspired by a recent thread about simulating Video Poker.


I felt very confident that I have a good approach on how to simulate the outcome of playing this game for a large number of trials without having to actually spend time playing and keep track of the results. This will be a two part simulation that covers the following:


1. To research whether playing the standard 5 card draw approach would have adverse effects towards playing this game. The most recent specialty games released on videopoker.com have rather severe consequences to a player’s bankroll if not played with the proper adjustments to the strategy.


2. I made a hypothetical assumption on a previous thread that the best way to approach this game is to go for the card holds that offer the best chance at achieving Three of a Kind outcomes or better, thus I would personally evaluate the outcome of doing so.


There will be 100 simulation trials for each which took hours to complete.


Each trial will represent a player playing 6 entire month chunk of his or her life playing 24 hours a day at a fast pace of 500 hands per hour. In another perspective, the 4392 hours worth of play will represent 2 years worth of effort that a typical full time employee performs on their weekday job.


10 credits per play * 10 hands per round * 500 rounds per hour * 24 hours / day * 183 days in 6 months = 219600000 units wagered. I think this amount is beyond what vast majority of people will seek to play.


There is only one paytable available for DDB on Ultimate X Bonus Streaks, there are different set of multipliers for 3 and 5 play, but this will only focus on the 10 play multiplier set.


Experiment 1 - Approaching the game like normal standard video poker


The player will play the optimal hold for every hand dealt, neglecting the multipliers and the streaks of other hands. The simulation will keep track of bonus multiplier streaks for each of the 10 hands if they hit Three of a Kind or better.


When playing 8/5 DDB optimally on standard video poker, here are the outcomes (I validated it with VPW) as a REFERENCE POINT:



Outcome Distribution of the 100 Trials


Number of 95.90% to 96.00% Return: 0
Number of 96.00% to 96.10% Return: 1
Number of 96.10% to 96.20% Return: 1
Number of 96.20% to 96.30% Return: 1
Number of 96.30% to 96.40% Return: 6
Number of 96.40% to 96.50% Return: 11
Number of 96.50% to 96.60% Return: 17
Number of 96.60% to 96.70% Return: 14
Number of 96.70% to 96.80% Return: 16
Number of 96.80% to 96.90% Return: 14
Number of 96.90% to 97.00% Return: 7
Number of 97.00% to 97.10% Return: 5
Number of 97.10% to 97.20% Return: 5
Number of 97.20% to 97.30% Return: 2
Number of 97.30% to 97.40% Return: 0


The Average Units Won per trial from the 100 trials is 212342807 units for the return of 96.695%


Conclusion: The Player will stand to lose around 0.2% return in the long run if playing the game normally. This is a somewhat decent floor value, and standard video poker play can be seen as a solid foundation for strategy development


Experiment 2 - Approaching the holds that yield the best chances at bonus streaks


Out of the 32 possible ways to hold a dealt hand, this one will focus on the highest percentage that will produce the highest percentage of 3 of a Kind or better hits. The motive is to produce as big of streaks as possible for big wins. This is a completely greedy approach to the game.


An example situation: A ♥ K ♥ 10 ♥ 3 ♥ Q ♥


When dealt a 5 card flush with 4 to the Royal, conventional video poker strategy will highly suggest the player would drop the existing flush and go for the Royal Flush since its expected return is much higher. However the guarantee bonus streak will prevent this automated player from going for the Royal Flush. Hence the player will lose 67 credits in expected value.





Obviously going for the big hands in a normal game will yield ugly results in standard 8/5 DDB video poker game, a return of 88.5% with more than 8% in mistakes! I would already eat my words from seeing this, but the simulation had to be completed.


Simulation Results


Number of 88.90% to 89.00% Return: 0
Number of 89.00% to 89.10% Return: 1
Number of 89.10% to 89.20% Return: 0
Number of 89.20% to 89.30% Return: 4
Number of 89.30% to 89.40% Return: 7
Number of 89.40% to 89.50% Return: 8
Number of 89.50% to 89.60% Return: 12
Number of 89.60% to 89.70% Return: 18
Number of 89.70% to 89.80% Return: 15
Number of 89.80% to 89.90% Return: 9
Number of 89.90% to 90.00% Return: 12
Number of 90.00% to 90.10% Return: 4
Number of 90.10% to 90.20% Return: 4
Number of 90.20% to 90.30% Return: 3
Number of 90.30% to 90.40% Return: 2
Number of 90.40% to 90.50% Return: 1
Number of 90.50% to 90.60% Return: 0
Number of 90.60% to 90.70% Return: 0
Number of 90.70% to 90.80% Return: 0
Number of 90.80% to 90.90% Return: 0
Number of 90.90% to 91.00% Return: 0


The Average Units Won per trial from the 100 trials is 197036169 units for the return of 89.725%


Still an atrocious result, but this clearly shows knowing when to go for producing the multipliers still has its benefit. That was the big part of the decision making in the standard Ultimate X game.


Out of the 134459 unique five card hands, just 78707 of the highest EV holds also produce the best chance at getting 3 of a Kind. There would be about 60000 unique hands for the player to determine if it is a good time to go for Bonus producing outcomes or go for the highest expected value hold. That will be my next segment to analyze.


The Full House or better outcomes produces a 5 hand streak of multipliers, that might be a consideration for the next analysis, whether to go for less than optimal hold for the chance at the big streaks.

[Tedlark]

Nice work alpax.

[WhitneyReed]

My head hurts!😀

[asteroid]

Wonderful stuff Alpax. Extremely interesting and helpful.Cheers Asteroid.

[Come Back Kid]

Alpax, you're amazing!

[alpax]

My head hurts!😀

The biggest takeaway from this simulation was that playing this game as if it like a regular Video Poker game does not have too much impact.

Thank you Ted, asteroid, and Come Back Kid! I did anticipate some increased vested interest with the new Ultimate X game.

I did make a valuable breakthrough tonight, I am doing an ongoing look into the non optimal plays. I found a small set of strategy adjustments that improves the average return.

8/5 DDB is 96.79%, the simple adjustments I found improved the return from 96.695% to 96.818% which beats standard single line VP.

Will start the 2nd segment tonight with these findings.

[alpax]

Started 2nd Segment

Link

Going to take a break for now

[Vman96]

Interesting stuff so far. When I played it in the weekly contest, I was thinking its strategy will be pretty close to original Ultimate X. And it's a good sign that playing standard DDB only costs the player very little vs. a standard game. However, I wonder if something like pair of face cards vs. two pair may be worth breaking if a lot of multipliers are on board and would turn many future ones into 12X's.

[Galeygoo]

Wow, Al. Your tireless work is truly amazing. I wish/hope vp.com does something to accommodate you. Bravo!!! I thank you for your efforts; and mostly and embarrassed to say I really don't get it. lol (kind of) lol

[alpax]

However, I wonder if something like pair of face cards vs. two pair may be worth breaking if a lot of multipliers are on board and would turn many future ones into 12X's.

I was going to evaluate that very same situation the next time I am able to look at this.

I progressively did

Player willing to take up to 5% EV loss for at least 2% Bonus Gain
Player willing to take up to 7.5% EV loss for at least 3% Bonus Gain

Both yielded good results.

The two pair situation falls under

Player willing to take up to 10% EV loss for at least 4% Bonus Gain

I did not tinker with the multiplier situation yet for the next segment, but it could be the borderline decision. To play greedy when the streaks are there, or to play conservatively. It will be an interesting find.

My efforts will not be the optimal play.

Wow, Al. Your tireless work is truly amazing. I wish/hope vp.com does something to accommodate you. Bravo!!! I thank you for your efforts; and mostly and embarrassed to say I really don't get it. lol (kind of) lol

Thanks Galey! It is just volunteer work personally so Action Gaming/VP.com owes me nothing.

To help you better understand the purpose of the simulation, it is to see how much the game returns if you played it regularly. VP.com does not list out that information for us, I just have a computer play it through like it was the real game.

The returns are almost identical between a normal game and this UltX game in the long long run.