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Last Updated: February 16, 2021

# Mystery Bonus

## Introduction

Mystery bonus is a video poker by Realtime Gaming. It is based on conventional video poker. The twist is that the game will add a "Mystery Bonus" to the win for a randomly chosen hand. Which hand gets the Mystery Bonus is determined at the time of the deal. The following table shows the usual win for each hand (based on the total bet amount), the Mystery Bonus for that hand, and the total win after the Mystery Bonus.

### Mystery Bonus Pay Table

Win Base
Pay
Mystery
Bonus
Win with
Bonus
Royal flush 800 400 1,200
Straight flush 45 35 80
Four of a kind 20 5 25
Full house 8 2 10
Flush 5 3 8
Straight 4 1 5
Three of a Kind 3 1 4
Two pair 2 1 3
Jacks or better 1 1 2

## Analysis

To analyze this game, it was necessary to know the probability of the Mystery Bonus being applied to each hand. It is not hard to see playing that the probabilities are not equal.

A reader wrote a bot to play the game and collect data on which hand received the Mystery Bonus on over 12,000 games. The game played was at iNetBet. Following are the results.

### Mystery Bonus Sampling

Win Count Probability
Royal flush 1572 12.42%
Straight flush 2201 17.39%
Four of a kind 1993 15.74%
Full house 1171 9.25%
Flush 2122 16.76%
Straight 2046 16.16%
Three of a Kind 945 7.47%
Two pair 392 3.10%
Jacks or better 216 1.71%
Total 12658 100.00%

The next return table shows the overall return of the game. It shows the probability of each hand getting the Mystery Bonus, the expected value with the bonus, and the product of those two columns. The lower right cell shows an overall return of 98.88%.

### Mystery Bonus Return Table

Mystery
Bonus
Probability
Bonus
Average
Return
Expected
Return
Royal flush 0.124190 0.971559 0.120658
Straight flush 0.173882 0.964482 0.167706
Four of a kind 0.157450 0.972452 0.153112
Full house 0.092511 0.983667 0.091000
Flush 0.167641 1.000601 0.167742
Straight 0.161637 0.973946 0.157426
Three of a Kind 0.074656 1.035140 0.077280
Two pair 0.030969 1.090072 0.033758
Jacks or better 0.017064 1.181382 0.020159
Total 1.000000 0.988841

## Acknowledgement

I would like to thank Gary Koehler for sharing with me his data and analysis of the Mystery Bonus.

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