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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.