No Risk Double Up

Introduction

I had my first experience with No Risk Double Up on its launch day, February 1, 2013, at Red Rock. It’s one of the offerings on the WMS My Poker machines. The concept of the game revolves around the potential to play a bonus round after a winning hand, allowing the player to increase their winnings up to four times, potentially reaching a multiplier of 16. The appeal lies in its 'no risk' aspect, where the least a player can receive in the bonus is the original payout for their hand. However, they do incur a non-refundable charge equivalent to their initial wager in video poker to access this bonus feature.⁴When a player places a 10-coin bet, half goes towards the standard video poker hand, while the other half activates the No Risk Double Up feature.

Rules

1. The player conducts their play according to the usual rules of video poker.
2. If the player attains any winning hand during the draw, they are granted a specific chance to engage in the Double Up opportunity.
3. This likelihood varies based on the poker hand achieved.
4. In the Double Up feature, the player initially selects one from five face-down cards, four of which are aces and one is a joker. The aim is to uncover an ace. If the joker is selected instead, the multiplier will remain at 1x; if an ace is revealed, the next level of the game is accessed.
5. In the subsequent round, three aces and two jokers await. Choosing a joker results in a multiplier of 2x; otherwise, the rules state to refer to the next guide.
6. Moving to the next phase, players face two aces and three jokers. Here, a choice of a joker leads to a multiplier of 4x. Still, seeing an ace leads to the consideration of the following instructions.
7. In the final level, with just one ace and four jokers, selecting a joker gives a multiplier of 8x, while finding the ace results in a multiplier of 16x.
8. The player receives their payout based on their poker hand in addition to any multiplier they have acquired.
9. Presented here is a visual representation of the bonus game.

My first draw resulted in a four of a kind. The chance of engaging in the bonus round with a four of a kind is 100%, as indicated in the table next to the pay table.

Following this, I was dealt five cards, and my task was to select one of the four aces.

The image does not clarify which card I selected, but I successfully picked one of the aces.

In the next step, I had to choose one of the three aces from a new set of five cards.

Unfortunately, it seems I may have picked one of the jokers, which concluded the bonus and awarded me a 2x multiplier.

Subsequent tables illustrate the probabilities and expected returns for the pay tables I observed at Red Rock. The 'bonus prob.' column indicates the chance of triggering the bonus feature with that particular hand, while the 'adjusted pay' column reflects the average payout for that hand, accounting for the probability of entering the bonus and the average multiplier.

Odds

The forthcoming table displays the probabilities related to the Double Up feature for some of the aforementioned games, based on optimal strategies.

Lastly, for those seeking more than just average returns per hand, I've provided the 55-9-5 Jacks or Better table, segmented by hand and its corresponding multiplier. This allows a clear assessment that shows the standard deviation rests at 12.09.

I found this game relatively straightforward to analyze, and here’s the methodology I used.

Analysis

Calculating the average multiplier, assuming a win in the Double Up feature, involves basic mathematics to determine that the probability for a 1x multiplier is (1/5), for a 2x it stands at (4/5) × (2/5), for a 4x it's (4/5) × (3/5) × (3/5), while for an 8x it's (4/5) × (3/5) × (2/5) × (4/5), and for a 16x, it's (4/5) × (3/5) × (2/5) × (1/5). The last cell in the table presents the average multiplier earned, which is calculated to be 3.8352.

1. Next, assess the 'adjusted pay' for each hand to understand what the player might expect to win on average for each draw, relative to their total wager. This is calculated as w × (p × 3.8352 + (1-p) × 1)/2 = w × (p × 2.8352 + 1)/2, where w signifies the base win for that hand and p represents the probability of accessing the bonus feature. The division by 2 is necessary because the player has to double their initial stake to activate the Double Up.
   

   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. For instance, in a 9-5 Jacks or Better game, the base payout for a flush is 5 coins, with the bonus feature's probability at 1/3. Consequently, the anticipated total payout for a flush turns out to be 5 × ((1/3) × 2.8352 + 1)/2 = 4.8627.
   
   Here, I entered the adjusted payouts into the prize column. Please note, the calculator does not support decimals in that section, so I multiplied the adjusted payouts by 100 and rounded the results to the nearest whole number.
   
3. Use my video poker return analyzer With the resulting combinations, determine the probability for each hand and construct a comprehensive return table.
   
4. Should you encounter a pay table not listed on this page for this particular game, you can apply this calculation method to ascertain the return independently. This adjusted win calculation method can also create strategic insights for any game utilizing my

standard deviation for n-play video poker video poker strategy calculator .

Rule Screens

Written by: Michael Shackleford