Winning Streak Poker

I just wrote up a page on Winning Streak Poker. This is another one of the new games from WMS on their MyPoker machines. WMS was nice enough to give me the optimal strategy returns for every available game and pay table. It isn't often I write about a page without analyzing it, but due to the complexity of the game, this was one of those times. However, I still explain the rules and show a nice series of examples from a five-hand winning streak, which took a while to attain. The photos were taken at an ISO speed of 1600, thanks to the advice in the Advice on taking pictures of video screens thread, so they are nice and crisp.

So, as always, I welcome corrections, comments, and questions. This game was a bit hard to explain, so let me know if anything didn't make sense.

If any of the other mathematicians on the site would like to take a crack at analyzing this game, by all means, please have at it. I'm open to paying for the analysis, as well as giving full credit. Just imagine the fame and glory. The women will be very impressed *ahem*.

I think you only won 78 credits total on the streak: 20 for the 2 pair (2*10) that got bumped off, 50 for the flush (5*10), 5 for the pair of kings (1*5), 2 for the pair of kings (1*2),and 1 for the pair of kings (1*1). That is the total in the picture above and matches your beginning balance of $9.60 and ending of $17.40.

Payments are based on the highest level that a hand attains. If it rolls off before the streak ends, then it's paid at the 10x level before the next hand starts. Otherwise, all wins are paid when the streak ends. In other words, Miplet is right:-)

Thanks guys for those corrections. I certainly misunderstood the rules there. Please have another look.

At first glance, I thought the strategy would be similar to Multi-Strike, but your comment rings true - strategy would also depend on previous wins as well. Kind of like Multi-Strike in reverse with as many different strategies as Ultimate X! I have faith that you and JB can devise a single strategy that is close enough to optimal... (hint, hint!) lol Thanks for the summary!

Good write-up; I'm a medium-knowledge player and I found it easy to follow. The little intuitive math-itch in my head says 4x unit bet plus the hand bet for a streak bet (I'm assuming you lose all 5 units when the hand craps out, no matter what you may win, if anything) seems like a huge house edge for VP, but I don't have the skills to prove it, and I don't know how often a streak bet pays beyond, say, a 2x hit. You said it took you a long time to get a streak of 5 to demo the full movement of the streak cards. And they do say a free ride occurs 19 in 2000 losing hands, so slightly less than 1% of the time, so that's not exactly a safety net (not sure why you're saying 1 in 500 on this in the bullet points, when the help screen shows 19 in 2000, but you did say it varied with the game).

I guess you'd have to play optimum strategy for an 8-5 JOB and hope a streak happened often enough to justify the huge overbet. But then again, you have odds x odds in a streak, so that could get nice with a big hand in front. I'm a sucker for stuff like this added to a game, so I'd try it, but probably couldn't afford it for long.

Quote: beachbumbabs

not sure why you're saying 1 in 500 on this in the bullet points, when the help screen shows 19 in 2000, but you did say it varied with the game)

Oops. I don't know where I got that 1 in 500. When I make a mistake, it is usually on simple arithmetic.

Quote: camapl

At first glance, I thought the strategy would be similar to Multi-Strike, but your comment rings true - strategy would also depend on previous wins as well. Kind of like Multi-Strike in reverse with as many different strategies as Ultimate X! I have faith that you and JB can devise a single strategy that is close enough to optimal... (hint, hint!) lol Thanks for the summary!

Much like Ultimate X, I think a single strategy could get pretty close to optimal. At every stage of the game there is a huge incentive to just stay in the game. Since the Streak bet is four units I think it would be reasonable to just add four to every pay and run it through JB's strategy calculator.

I wrote a simulator some time ago for Jacks or Better Winning Streak Poker. I dusted it off and plugged in the 19/2000 free streak probability, and the 9/5 Jacks or Better strategy when using the "add 4 units to each payoff" method. After 5 billion trials the return was 97.19%, which is 1.58% lower than the optimal strategy calculated by WMS. For comparison, 5 billion trials with standard 9/5 Jacks or Better strategy returned 94.21%.

Quote: JB

I wrote a simulator some time ago for Jacks or Better Winning Streak Poker. I dusted it off and plugged in the 19/2000 free streak probability, and the 9/5 Jacks or Better strategy when using the "add 4 units to each payoff" method. After 5 billion trials the return was 97.19%, which is 1.58% lower than the optimal strategy calculated by WMS. For comparison, 5 billion trials with standard 9/5 Jacks or Better strategy returned 94.21%.

Dang. I guess that shoots down my theory. I wonder how it would go if you tweaked the constant added to each win. Also, the 19/2000 is not the same for every game. My next visit to the Red Rock I'll note some specific examples.

Quote: JB

For comparison, 5 billion trials with standard 9/5 Jacks or Better strategy returned 94.21%.

This paytable should be 98.45%. I'm guessing you had a better return than 94.21% (or something else is missing here), because that would indicate that you got closer to theoretical with the Winning Streak poker.

Quote: CrystalMath

This paytable should be 98.45%. I'm guessing you had a better return than 94.21% (or something else is missing here), because that would indicate that you got closer to theoretical with the Winning Streak poker.

D'oh. I see what you were saying now. Please ignore my previous comments.

Quote: CrystalMath

This paytable should be 98.45%. I'm guessing you had a better return than 94.21% (or something else is missing here), because that would indicate that you got closer to theoretical with the Winning Streak poker.

I think the point is that applying standard strategy to WSP results in a 94.21% RTP, while building a strategy based on adding 4 units (the streak bet) results in an RTP of 97.19%. So, using a custom strategy based on adding 4 units is better than playing standard 9/5 JoB strategy, but is still sub-optimal.

Based on my own experience applying near-perfect DW play to WSP machines, the optimal WSP strategy must be pretty deviant from standard play - these machines eat me alive, but they're fun!

Quote: rdw4potus

I think the point is that applying standard strategy to WSP results in a 94.21% RTP, while building a strategy based on adding 4 units (the streak bet) results in an RTP of 97.19%. So, using a custom strategy based on adding 4 units is better than playing standard 9/5 JoB strategy, but is still sub-optimal.

Based on my own experience applying near-perfect DW play to WSP machines, the optimal WSP strategy must be pretty deviant from standard play - these machines eat me alive, but they're fun!

Yes, at first, I completely missed the point. I didn't realize what he meant until I made my post.

Curious why folks would use 9-5 JOB strategy when the illustrated machine is set for 8-5; you would look for a 9-5 machine, or the strategy translates over, or I'm just missing something? Thanks!

Quote: beachbumbabs

Curious why folks would use 9-5 JOB strategy when the illustrated machine is set for 8-5; you would look for a 9-5 machine, or the strategy translates over, or I'm just missing something? Thanks!

That's a good question. I think we keyed in on the 9/5 paytable because that's the one we hope to be able to play, though there are probably minor strategy changes for the 8/5 and 8/6 paytables which will likely be more common on these machines.

I think JB picked 9-5 arbitrarily, or felt that was the best return one could realistically find, plus it is a little easier working with a game with as few types of winnings hands as possible. WMS says they should have the Free Streak probabilities for me shortly. I'm hoping today.

Some nitpicks:

14. If the fifth hand advances, ...

16. When the player eventually loses any hand on level one will be paid at a 1x multiplier, on level two at a 2x multiplier, on level three at a 5x multiplier, and on level four at a 10x multiplier.

Level 4: The flush pair pays 5 at a 10x multiplier for 10×5 = 50 credits.

The last sentence has an extraneous space before the period.

Paytable list: Write 800 for all games where the Royal is 250. Currently 250-9-6 JoB has a higher payback than 500-9-6 JoB.

Quote: Wizard

I'm open to paying for the analysis, as well as giving full credit. Just imagine the fame and glory. The women will be very impressed *ahem*.

I got a good chuckle out of the last two bits.

Quote: JB

I wrote a simulator some time ago for Jacks or Better Winning Streak Poker. I dusted it off and plugged in the 19/2000 free streak probability, and the 9/5 Jacks or Better strategy when using the "add 4 units to each payoff" method. After 5 billion trials the return was 97.19%, which is 1.58% lower than the optimal strategy calculated by WMS. For comparison, 5 billion trials with standard 9/5 Jacks or Better strategy returned 94.21%.

Interesting results. A 4.24% loss isn't too bad if you change nothing I guess. I wonder how similar that number is to playing standard VP strategy for Ultimate X. Also I would be interested to know what return you'd get if you played Multistrike Strategy "in reverse" if it isn't too much of a PITA. I wonder if that would be better than a 1.58% loss compared to optimal.

Quote: Wizard

I'm open to paying for the analysis, as well as giving full credit. Just imagine the fame and glory. The women will be very impressed *ahem*.

Wiz;

I'm already impressed and a fan, though recent, so it's working. I'm also aware you're happily married so suppressing the urge. :) But I got a thing for a math brain bigger than mine, which is not inconsiderable. Keep up the good work - it's fascinating stuff.

Quote: tringlomane

Some nitpicks...

Thanks for all those corrections. I just made those fixes.

Quote: beachbumbabs

I'm already impressed and a fan...

Thanks! Welcome to the forum. We could certainly use more women around here.

Quote: Wizard

Dang. I guess that shoots down my theory.

Actually, I think that is the best solution for now, unless/until a better one is found. It's a significant improvement over using the standard single-hand strategy, which is probably what most recreational players will be using. Considering the complexity of the game, I don't even know if it's possible for a single strategy to get much closer to optimal than the "add 4 units" strategy. It's also possible that the free streak probability for 9/5 Jacks is higher than 19/2000, which would bring the return of the "add 4 units" strategy closer to the 98.77% that WMS calculated.

Quote: beachbumbabs

Curious why folks would use 9-5 JOB strategy when the illustrated machine is set for 8-5; you would look for a 9-5 machine, or the strategy translates over, or I'm just missing something? Thanks!

I chose 9/5 because it was the best Jacks or Better paytable on the list where the Royal Flush wasn't shorted.

I just heard from WMS.

First, they corrected me about the Free Streaks happening before you see the cards, like in Multi-Strike. If there is one, it is made known to the player AFTER the hand. So, this will depress the odds a bit. My apologies for the previous misstatement.

Second, they gave me the Free Streak probabilities, which are now on my Free Streak page. For 9-5 Jacks it is 0.95%.

Wait - the Free Streak is a random chance conditional upon a losing hand? If so, that eliminates the possibility for both a winning hand and a simultaneous Free Streak, so the overall probability of continuing should actually improve.

Quote: MathExtremist

Wait - the Free Streak is a random chance conditional upon a losing hand? If so, that eliminates the possibility for both a winning hand and a simultaneous Free Streak, so the overall probability of continuing should actually improve.

The absence of wasted Free Streaks would improve the probability over the situation that we had previously assumed, but it would also create the absence of hands that you would play using optimal strategy under normal circumstances, as you wouldn't have prior knowledge of the freebie hands. Every hand would be played aggressively towards any win, sacrificing the return of the current had for the opportunity to play the next.

This makes for an interesting question. Let's look at an example.

x = 25% = probability of any winning hand under conventional strategy to maximize the EV of one hand only.
y = 30% = probability of any winning hand under conservative Winning Streak strategy.
z = 1% = probability of Free Streak.

If the Free Streak were revealed up front, as in Multi-Strike, then the probability of advancing would be 0.01*1 + 0.99*0.30 = 0.3070

If the Free Streak is determined and revealed after a losing hand, the the probability of advancing would be 0.30*1 + 0.70*0.01 = 0.3070.

The same either way. However, if the Free Streak is revealed early, the player has the benefit of using optimal strategy 1% of the time to maximize the EV of that hand. Under the wait and see rule the player has to always play the EV wasting conservative strategy. It also seems logical that the sooner you can get information, the better. Then again, I've been fooled by paradoxes before.

Perhaps one could argue that there would be two different conservative strategies, depending on the hope of getting a Free Streak. That will certainly muddy the waters. I'll wait to see if anyone raises that point.

I just uploaded a video I took of Winning Streak to YouTube. Note the Free Streak around the 4:10 point.

Thanks for the video. I wish you could have got as excited as the women near you that fill the audio. ;)

All these plays you are ahead in the single play game, but I'm unsure if these are correct overall and I mentally questioned on my first viewing. All but the first one has less than an 0.05 EV advantage in 1-line play.

0:58 you hold 2KQ suited (hold 2 only on bottom level): 2KQ suited is 0.082965 units higher
1:02 you hold 256 suited (hold 2 on bottom level; possibly 256K suited): 256 suited is 0.024842 units higher vs. 2 only and 0.061979 higher vs. 256K suited
1:26 you hold 256 suited (4 of a kind on level 1; hold 2567 instead): 256 suited is 0.042553 units higher vs. 2567 unsuited
2:37 you hold 2 only (go for 4 to a flush with holding one duece with trips at 1X, quads at 2X, straight at 5X, quads at 10X): 2 only is 0.041471 units higher than 2385 suited
3:51 you hold 279 suited (possibly go for 2789 unsuited on bottom level): 279 suited is 0.042553 units higher vs. 2789
5:56 you hold JT suited (possibly go for KJT9 straight on bottom level): JT is 0.03361 units higher than KJT9
6:07 you hold A2T suited (possibly go for deuce only on bottom level) A2T suited is 0.011437 units higher than deuce only [If Wild Royal paid 25 for 1, I would think A2T suited is clearly correct]

You chose the highest EV hand in single play in all of these, but they were all within 0.05 betting units in single-line video poker except the first one. So not surprisingly, I am questioning some of these plays due to their probability of "advancing".

Using the "4 units for every winning hand rule", all the hands I suggest are better except at 2:37 where you made the right play, according to this suggested strategy. Although the one at 1:02 is an exception to basic strategy, and deuce only is best given the exceptions. At 5:56 my suggestion is also bad, throw them all away is suggested. Also with the "add 4 strategy" deuce only is better than A2T with a 20/12/10/4/4/3 paytable as well as a 25/15/9/4/4/3 paytable.

I think this video is a good example why this game will be a huge pain for any player that wishes to play near optimally.

Quote: Wizard

If the Free Streak were revealed up front, as in Multi-Strike, then the probability of advancing would be 0.01*1 + 0.99*0.30 = 0.3070

If the Free Streak is determined and revealed after a losing hand, the the probability of advancing would be 0.30*1 + 0.70*0.01 = 0.3070.

The same either way.

When I saw you mention that the Free Streak was revealed immediately, I also questioned it, since the help screen says the opposite. I made a post asking about it, but then flagged it to get rid of it after quickly realizing that regardless of whether the Free Streak is announced before or after the hand is played, the hand will advance.

If I were to guess, they probably did it this way to somewhat simplify the already-complex analysis, so that they didn't have to mix normal strategy with the strategy for the current situation.

Quote: JB

Considering the complexity of the game, I don't even know if it's possible for a single strategy to get much closer to optimal than the "add 4 units" strategy.

JB, did you try adding different values other than 4 in your simulation? I would be curious to see results for different (larger) figures. I am assuming that "add 4 units" was suggested because that is the added cost to play. It isn't a bad suggestion; however, it seems like a larger number would be in order, as there seems to be no limit to the number of hands in a streak. Playing even more conservatively (by adding a larger number to any win) would increase the number of hands paid at 10X, as opposed to Multi-Strike where there is at most one hand paid at the top multiplier.

(Added:) I doubt a number higher than 10 would be useful, as you will have the three hands at less than 10X, so the average multiplier over all hands would never be 10 or higher.

Quote: tringlomane

You chose the highest EV hand in single play in all of these, but they were all within 0.05 betting units in single-line video poker except the first one. So not surprisingly, I am questioning some of these plays due to their probability of "advancing".

I'm sure lots of my plays were wrong. I made that video long before I thought of the "add four" strategy. The reason I posted it so late was that I forgot I made it and didn't notice it until I downloaded another movie from the memory card.

So, as per the name, this game is extremely streaky? It seems like you'll just bleed a ton of money until you're able to get a straight+ to the 10x multiplier. Even then, your payments per game are 1/5th of what they would be without the winning streak component, leading to a quick deterioration of a bank roll. Am I missing something?

Quote: ahiromu

So, as per the name, this game is extremely streaky? It seems like you'll just bleed a ton of money until you're able to get a straight+ to the 10x multiplier. Even then, your payments per game are 1/5th of what they would be without the winning streak component, leading to a quick deterioration of a bank roll. Am I missing something?

That's right. Much like multi-strike, but with no cap on the number of hands in a winning sequence.

Quote: camapl

JB, did you try adding different values other than 4 in your simulation? I would be curious to see results for different (larger) figures. I am assuming that "add 4 units" was suggested because that is the added cost to play. It isn't a bad suggestion; however, it seems like a larger number would be in order, as there seems to be no limit to the number of hands in a streak. Playing even more conservatively (by adding a larger number to any win) would increase the number of hands paid at 10X, as opposed to Multi-Strike where there is at most one hand paid at the top multiplier.

(Added:) I doubt a number higher than 10 would be useful, as you will have the three hands at less than 10X, so the average multiplier over all hands would never be 10 or higher.

...bump...