No Risk Double Up Poker

As mentioned in the thread WMS video poker debut at the Red Rock, two major new video poker games debuted at the Red Rock today, not to mention lots of new pay tables to standard video poker.

This thread shall focus on the new game No Risk Double Up Poker. Here are the rules.

1. Player makes a 10-coin bet. Five coins pays for the standard video poker hand, and the other five enable the No Risk Double Up feature.
2. The player plays his hand according to standard video poker rules.
3. If the player gets any paying hand on the draw then he will have a specified chance of playing the Double Up feature. This probability depends on the poker hand.
4. In the Double Up feature the player will first pick from face down five cards. Four are aces and one is a joker. If the player picks the joker his multiplier is 1x. Otherwise go onto rule 5.
5. In the next stage there are three aces and two jokers. If the player picks the joker his multiplier is 2x. Otherwise go onto rule 6.
6. In the next stage there are two aces and three jokers. If the player picks the joker his multiplier is 4x. Otherwise go onto rule 7.
7. In the next stage there is one ace and four jokers. If the player picks a joker his multiplier is 8x. Otherwise, if the player picks the ace, his multiplier is 16x.
8. Player is paid according to his poker hand and any multiplier earned.

I show the expected multiplier in the Double Up feature is 3.8352, or 2397/625.

The following table shows my analysis of 55-9-5 Jacks or Better. There are lots of other pay tables, but I'll just run this one up the flag pole for now.

Hand	Pays	Feature Probability	Adjusted pay	Combinations	Probability	Return
Royal flush	800	1	1534.08	50,841,598	0.000031	0.046954
Straight flush	55	1	105.47	214,210,910	0.000129	0.013601
Four of a kind	25	1	47.94	3,914,082,611	0.002356	0.112962
Full house	9	1	17.26	19,051,457,919	0.011469	0.197939
Flush	5	0.333333333	4.86	19,370,987,397	0.011662	0.056706
Straight	4	0.333333333	3.89	20,771,970,996	0.012505	0.048646
Three of a kind	3	0.2	2.35	122,823,581,699	0.073941	0.173803
Two pair	2	0.166666667	1.47	212,898,461,571	0.128167	0.188730
Jacks or better	1	0.166666667	0.74	334,272,435,996	0.201235	0.148163
Loser	0	0	0.00	927,734,512,403	0.558505	0.000000
Total				1,661,102,543,100	1.000000	0.987504

Any questions or comments?

Spot on, as always.

Quote: Wizard

Any questions or comments?

Is there a progressive jackpot?

I'm guessing you mean 55-9-5 Jacks or better (not 99-9-5)?

Were the double up probabilities given in the rule screens?

And this looks like this is really going to jack up the variance. Worse than Triple Double Bonus if I did the math right. Partially because 1.5% of the game's return comes from a Royal with an 8X multiplier...haha I got 145.54 betting units per hand for the variance. As a comparison, Triple Double Bonus is only 98.28 bets per hand. These swings aren't worth the extra 0.25% on the return for me and adds a lot of "risk", imo. :)

Quote: tringlomane

I'm guessing you mean 55-9-5 Jacks or better (not 99-9-5)?

Yes, that was a typo.

Quote:

Were the double up probabilities given in the rule screens?

Right there on the main screens. It shows a something like a ruler for each hand, and which sections lead to the bonus.

Quote:

And this looks like this is really going to jack up the variance. Worse than Triple Double Bonus if I did the math right. Partially because 1.5% of the game's return comes from a Royal with an 8X multiplier...haha I got 145.54 betting units per hand for the variance. As a comparison, Triple Double Bonus is only 98.28 bets per hand. These swings aren't worth the extra 0.25% on the return for me and adds a lot of "risk", imo. :)

I haven't calculated it, but I roughly estimate the standard deviation to be about 15.

I essentially agree with tringlomane on the volatility (I calculated 146.13, which gives a standard deviation of 12.09). It's outrageous and not worth it.

What is the overall chance of playing the double feature?

Quote: CrystalMath

I essentially agree with tringlomane on the volatility (I calculated 146.13, which gives a standard deviation of 12.09). It's outrageous and not worth it.

I made some small errors in the copying/pasting phase. :( I forgot the 1X data (makes little difference in the final result...lol) and copied losing hand variance data for each level instead of just 1X...blah. I still didn't get your number though, ugh. Now I have 146.38. It's obviously ~146.

Quote: MathExtremist

What is the overall chance of playing the double feature?

1 every 10.90 hands on average.

Quote: MathExtremist

What is the overall chance of playing the double feature?

I get 9.1729%.

Here is a table showing the probability of every possible win, as opposed to using an average multiplier. I get a standard deviation of 12.09,

Hand	Bonus	Pays	Multiplier	Total win	Total Combinations	Probability	Return
Royal flush	Yes	800	16	6400	73,211,901,120	0.000001	0.007522
Straight flush	Yes	55	16	440	308,463,710,400	0.000005	0.002179
Four of a kind	Yes	25	16	200	5,636,278,959,840	0.000090	0.018097
Full house	Yes	9	16	72	27,434,099,403,360	0.000440	0.031710
Flush	Yes	5	16	40	9,298,073,950,560	0.000149	0.005971
Straight	Yes	4	16	32	9,970,546,078,080	0.000160	0.005122
Three of a kind	Yes	3	16	24	35,373,191,529,312	0.000568	0.013629
Two pair	Yes	2	16	16	51,095,630,777,040	0.000820	0.013124
Jacks or better	Yes	1	16	8	80,225,384,639,040	0.001288	0.010303
Royal flush	Yes	800	8	3200	292,847,604,480	0.000005	0.015044
Straight flush	Yes	55	8	220	1,233,854,841,600	0.000020	0.004358
Four of a kind	Yes	25	8	100	22,545,115,839,360	0.000362	0.036193
Full house	Yes	9	8	36	109,736,397,613,440	0.001762	0.063420
Flush	Yes	5	8	20	37,192,295,802,240	0.000597	0.011941
Straight	Yes	4	8	16	39,882,184,312,320	0.000640	0.010244
Three of a kind	Yes	3	8	12	141,492,766,117,248	0.002271	0.027258
Two pair	Yes	2	8	8	204,382,523,108,160	0.003281	0.026249
Jacks or better	Yes	1	8	4	320,901,538,556,160	0.005152	0.020606
Royal flush	Yes	800	4	1600	549,089,258,400	0.000009	0.014104
Straight flush	Yes	55	4	110	2,313,477,828,000	0.000037	0.004085
Four of a kind	Yes	25	4	50	42,272,092,198,800	0.000679	0.033931
Full house	Yes	9	4	18	205,755,745,525,200	0.003303	0.059456
Flush	Yes	5	4	10	69,735,554,629,200	0.001120	0.011195
Straight	Yes	4	4	8	74,779,095,585,600	0.001200	0.009604
Three of a kind	Yes	3	4	6	265,298,936,469,840	0.004259	0.025554
Two pair	Yes	2	4	4	383,217,230,827,800	0.006152	0.024608
Jacks or better	Yes	1	4	2	601,690,384,792,800	0.009659	0.019319
Royal flush	Yes	800	2	800	610,099,176,000	0.000010	0.007835
Straight flush	Yes	55	2	55	2,570,530,920,000	0.000041	0.002270
Four of a kind	Yes	25	2	25	46,968,991,332,000	0.000754	0.018851
Full house	Yes	9	2	9	228,617,495,028,000	0.003670	0.033031
Flush	Yes	5	2	5	77,483,949,588,000	0.001244	0.006219
Straight	Yes	4	2	4	83,087,883,984,000	0.001334	0.005335
Three of a kind	Yes	3	2	3	294,776,596,077,600	0.004732	0.014197
Two pair	Yes	2	2	2	425,796,923,142,000	0.006836	0.013671
Jacks or better	Yes	1	2	1	668,544,871,992,000	0.010733	0.010733
Royal flush	Yes	800	1	400	381,311,985,000	0.000006	0.002449
Straight flush	Yes	55	1	27.5	1,606,581,825,000	0.000026	0.000709
Four of a kind	Yes	25	1	12.5	29,355,619,582,500	0.000471	0.005891
Full house	Yes	9	1	4.5	142,885,934,392,500	0.002294	0.010322
Flush	Yes	5	1	2.5	48,427,468,492,500	0.000777	0.001944
Straight	Yes	4	1	2	51,929,927,490,000	0.000834	0.001667
Three of a kind	Yes	3	1	1.5	184,235,372,548,500	0.002958	0.004436
Two pair	Yes	2	1	1	266,123,076,963,750	0.004272	0.004272
Jacks or better	Yes	1	1	0.5	417,840,544,995,000	0.006708	0.003354
Royal flush	No	800	1	400	-	0.000000	0.000000
Straight flush	No	55	1	27.5	-	0.000000	0.000000
Four of a kind	No	25	1	12.5	-	0.000000	0.000000
Full house	No	9	1	4.5	-	0.000000	0.000000
Flush	No	5	1	2.5	484,274,684,925,000	0.007774	0.019436
Straight	No	4	1	2	519,299,274,900,000	0.008337	0.016673
Three of a kind	No	3	1	1.5	3,684,707,450,970,000	0.059153	0.088729
Two pair	No	2	1	1	6,653,076,924,093,750	0.106806	0.106806
Jacks or better	No	1	1	0.5	10,446,013,624,875,000	0.167696	0.083848
Loser	No	0	1	0	34,790,044,215,112,500	0.558505	0.000000
Total	0	0	0	0	62,291,345,366,250,000	1.000000	0.987504

Quote: Wizard

I get 9.1729%.

Here is a table showing the probability of every possible win, as opposed to using an average multiplier. I get a standard deviation of 12.09.

These numbers are correct. (I'm not surprised. :P) I also found my last dummy error on the SD/Variance; I thought of it while trying to fall asleep last night, and now I have the same result.

I just created a page for No Risk Double Up Poker. Please have a look. As always, I welcome all comments, corrections, and questions.

Quote: Wizard

Please have a look. As always, I welcome all comments, corrections, and questions.

"I first played No Risk Double up"
Somewhat pedantic, but 'up' should be capitalized like the rest.

"5. In the Double Up feature the player will first pick from face down five cards. Four are aces and one is a joker. If the player picks the joker his multiplier is 1x. Otherwise go onto rule 5."
This, and the next few rule counts are off. Should be 'onto rule 6.' etc.

Question/Clarification:
Are you only allowed to play the 'Double Up' part with a max bet, or is the surcharge an amount equal to your original bet? (That is, a 1 credit bet with double up enabled would charge 2 credits.)

Quote: Wizard

I just created a page for No Risk Double Up Poker. Please have a look. As always, I welcome all comments, corrections, and questions.

Quote:

5.In the Double Up feature the player will first pick from face down five cards. Four are aces and one is a joker. If the player picks the joker his multiplier is 1x. Otherwise go onto rule 5.

You should use a comma after the prepositional phrase, "In the Double Up feature, the player..."

Also, you wouldn't go, "Onto," rule 5, you would just, "go to," or you could, "go on to," rule 5...and you need a comma after, 'Otherwise.'

Actually, "Otherwise, see rule 5..." would be the best way to do it.

Quote:

NUMBERS 6 and 7

"If the player picks the joker his multiplier is 2x."---You need a comma after joker because you are not making an if-then statement, thus it is a preopsitional phrase. Alternatively, you could change the end of the sentence to, "...joker, then his" or "...joker then his"

Commas after, "Otherwise." Same thing about, "Onto," as above.

Quote:

NUMBERS 6-8

There should be a comma after, "In the next stage," which applies to all three of these items.

Quote:

Finally, for those for whom a average return per hand won't do,

It should be 'an,' instead of 'a,' the next word beginning with a vowel.

CONCLUSION

There were a few other small things, but they would have been nit-picky.

What is your personal opinion of the game, overall? I'm not really a big fan of Video Poker, in general, but the last thing I would ever want is for the EV distribution to become even more top-heavy.

Thanks for those corrections.

I think you need to bet five credits on the video poker bet to be able to enable the bonus feature, but will verify that my next visit to the Red Rock.

I added some more material to my page, if you would care to take another look.

Quote: Wizard

Thanks for those corrections.

Unfortunately, you didn't consistently correct these. Now you have some of them with commas and some of them without commas. This is actually worse than completely omitting the commas imo. I copied all the text and edited it the best I could; the pics and tables are omitted. The Double Up probability table is labeled as 17-7 Joker Wild though fyi. I promise that I am a decent grammar/usage nit, so feel free to use this as needed.

Rules

1. The player makes a 10-coin bet. Five coins pays for the standard video poker hand, and the other five enable the No Risk Double Up feature.
2. The player plays his hand according to standard video poker rules.
3. If the player gets any paying hand on the draw, then he will have a specified chance of playing the Double Up feature. The exact probability depends on the winning poker hand's strength.
4. In the Double Up feature, the player will pick one card from five cards face down. There are four aces and one joker. If the player picks the joker, his bonus ends with a multiplier of 1x. Otherwise, see rule 5.
5. In the next stage, there are three aces and two jokers. If the player picks the joker, his bonus ends with a multiplier of 2x. Otherwise, see rule 6.
6. In the next stage, there are two aces and three jokers. If the player picks the joker, his bonus ends with a multiplier of 4x. Otherwise, see rule 7.
7. In the last stage, there is one ace and four jokers. If the player picks a joker, his bonus ends with a multiplier of 8x. If the player picks the ace, his bonus ends with a multiplier of 16x.
8. The player is paid according to his poker hand and any multiplier earned.

Here is an example of the bonus game.

First, I got a four of a kind on the draw. The probability of the bonus feature with a four of a kind is 100% as displayed to the right of the pay table.


Then, I was given five cards and challenged to pick one of the four aces.


It isn't clear which card I chose from the picture, but I did pick one of the aces.


Next, I was asked to picked one of three aces in the next set of five cards.


I must have picked one of the jokers, which gave me a multiplier of 2x and ended the bonus.

The next table shows the Double Up feature probability for each game, assuming optimal strategy.


Finally, here is the 55-9-5 Jacks or Better table broken down by hand and multiplier. This table allows us to calculate that the standard deviation for this variant is 12.09.

Analysis

This game was pretty easy to analyze. Here is how I did it.

Determine the average multiplier, assuming the Double Up feature was won. It requires simple math to see the probability of a 1x multiplier is (1/5), 2x is (4/5)×(2/5), 4x is (4/5)×(3/5)×(3/5), 8x is (4/5)×(3/5)×(2/5)×(4/5), and 16x is (4/5)×(3/5)×(2/5)×(1/5). The following table shows the probability of each multiplier. The lower right cell shows the average multiplier earned is 3.8352.


Determine the "adjusted pay" for each hand. This is how much on average the player can expect to win for each hand on the draw, relative to his total wager. This is defined as w*(p*3.8352 + (1-p)*1)/2 = w*(p*2.8352 + 1)/2, where w = base win for the hand, and p=probability of bonus feature. The reason for dividing by 2 is the player must double his bet to enable the Double Up feature.

For example, in 9-5 Jacks or Better, the base win for a flush is 5, and the probability of the feature is 1/3. So the expected final win for a flush is 5×((1/3)×2.8352 + 1)/2 = 4.8627.

Use my video poker return analyzer, putting the adjusted pays in the prize column. Note that the calculator doesn't accept decimals in that column. What I did was multiply the adjusted awards by 100 and rounded that product to the nearest integer.

Use the resulting combinations to get the probability of each hand and create a return table.
If you encounter a pay table not on this page for this game, you can use this method to find the return yourself. This method of calculating the adjusted win can also be used to create strategies for any game using my video poker strategy calculator.

And another thing, am I the only one who noticed playing 55-9-6 DDB is a significantly worse game than regular 9/6 DDB? For shame, WMS.

I was also appalled at the Triple Triple Bonus paytable you listed. Pathetic for Red Rock to even offer that game for that low of a return.