No Risk Double Up

Introduction

 

I first played No Risk Double Up on the day it premiered, Feb. 1, 2013, at the Red Rock. It is one of various games available on the WMS My Poker machines. The thrust of the game is that sometimes on a winning hand the player plays a bonus game in which the player may double his win up to four times, or to a multiplier of 2⁴=16. There is "no risk," because the worst that can happen in the bonus is the player gets paid the base amount for his hand. However, the player pays for the bonus feature via a non-refundable fee equal to his video poker wager.

Rules

 

1. Player makes a 10-coin bet. Five coins pay for the standard video poker hand and 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.
4. This probability depends on the poker hand.
5. In the Double Up feature, the player will first pick one of five face-down cards. Four are aces and one is a joker, and the goal is to pick an ace. If the player picks the joker, then his multiplier is 1x. Otherwise, see rule 6.
6. In the next stage, there are three aces and two jokers. If the player picks a joker, his multiplier is 2x. Otherwise, see rule 7.
7. In the next stage, there are two aces and three jokers. If the player picks the joker, then his multiplier is 4x. Otherwise see rule 8.
8. In the next stage, there is one ace and four jokers. If the player picks a joker, then his multiplier is 8x. If the player picks the ace, his multiplier is 16x.
9. Player is paid according to his poker hand and any multiplier earned.

 

Here is an example, in pictures, 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 seen in the table 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 ended the bonus, giving me a multiplier of 2x.

Odds

 

The following tables show the probability and return for the pay tables I noticed at the Red Rock. The "bonus prob." column refers to the probability of playing the bonus feature with that hand. The "adjusted pay" column refers to the average win for that hand, considering the probability of playing the bonus and the average bonus multiplier.

The next table shows the Double Up feature probability for some of the above games, assuming optimal strategy.

Finally, for those for whom an average return per hand won't do, here is the 55-9-5 Jacks or Better table broken down by hand and multiplier. This table allows us to see that the standard deviation is 12.09.

Analysis

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

1. 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.
    

   Multiplier Table

   Multiplier	Combinations	Probability	Expected Multiplier
   1	125	0.2000	0.2000
   2	200	0.3200	0.6400
   4	180	0.2880	1.1520
   8	96	0.1536	1.2288
   16	24	0.0384	0.6144
   Total	625	1.0000	3.8352

2. Determine the "adjusted pay" for each hand. This is how much the player can expect to win, on average, 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.
    
3. 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.
    
4. 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.

Rule Screens

Written by: Michael Shackleford