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Triple Trouble
Introduction
I came across a video poker variant called Triple Trouble at the Red Rock Casino back in May 2007. It was also depicted during a peyote-fueled vision experienced by Tony Soprano in a Las Vegas episode. The fundamental gameplay mirrors traditional video poker. Additionally, three devil icons may activate either after the initial deal or the draw. If all three are illuminated post-draw, the player earns three times their wager, coupled with three free spins where all winnings are tripled. Landing three devils during a free spin results in a payout of nine times the original bet, though no extra free spins are granted.
I've been informed that the likelihood of triggering free spins is 1.6%. During my experience, I had to make 186 attempts before activating my first feature. Here’s the frequency at which I encountered each number of devils:
3 devils: 1
2 devils: 24
1 devil: 62
0 devils: 99
Total: 186
I believe my extended wait was due to sheer bad luck. The chance of landing exactly one devil within 186 attempts is calculated at 15.06%.
Below is the return table for the game available at the Red Rock, not taking into account the bonus feature.
Triple Trouble-Red Rock Pay Table
| Hand | Payoff | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 800 | 543603228 | 0.000027 | 0.021817 |
| Straight flush | 50 | 2344607496 | 0.000118 | 0.005881 |
| Four A | 200 | 4515410220 | 0.000227 | 0.045305 |
| Four 2-4 | 40 | 10456785924 | 0.000525 | 0.020984 |
| Four 5-K | 25 | 31918369380 | 0.001601 | 0.040032 |
| Full house | 7 | 213391202292 | 0.010705 | 0.074937 |
| Flush | 5 | 222687455196 | 0.011172 | 0.055858 |
| Straight | 4 | 291874249212 | 0.014643 | 0.058570 |
| Three of a kind | 2 | 1466496448776 | 0.073570 | 0.147141 |
| Two pair | 1 | 2405076093936 | 0.120657 | 0.120657 |
| Pair | 1 | 4244026406472 | 0.212912 | 0.212912 |
| Nonpaying hand | 0 | 11039899885068 | 0.553844 | 0.000000 |
| Total | 19933230517200 | 1.000000 | 0.804094 |
The average win from a bonus feature in video poker is calculated as 3 + 3 × 3 × 0.804094 = 10.236846. For three devils received during a free spin, the average win totals 3 × 9 × 0.016 = 0.432. Therefore, the overall average win per feature is 10.236846 + 0.432 = 10.668846. The return generated from the feature is 10.668846 × 0.016 = 0.170702. Consequently, the overall return rate of the game stands at 0.804094 + 0.170702 = 0.974796.
In January 2018, I observed this payout table at the Seaport Casino located in Aruba.
Triple Trouble-Red Rock Pay Table
| Hand | Payoff | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 800 | 45,525,632 | 0.000027 | 0.021926 |
| Straight flush | 50 | 195,901,205 | 0.000118 | 0.005897 |
| Four A | 200 | 375,619,835 | 0.000226 | 0.045225 |
| Four 2-4 | 40 | 870,780,444 | 0.000524 | 0.020969 |
| Four 5-K | 25 | 2,648,746,035 | 0.001595 | 0.039864 |
| Full house | 6 | 17,739,917,574 | 0.010680 | 0.064078 |
| Flush | 5 | 18,595,092,458 | 0.011194 | 0.055972 |
| Straight | 4 | 24,414,725,751 | 0.014698 | 0.058792 |
| Three of a kind | 2 | 121,747,145,510 | 0.073293 | 0.146586 |
| Two pair | 1 | 199,858,785,822 | 0.120317 | 0.120317 |
| Pair | 1 | 355,107,019,965 | 0.213778 | 0.213778 |
| Nonpaying hand | 0 | 919,503,282,869 | 0.553550 | 0.000000 |
| Total | 1,661,102,543,100 | 1.000000 | 0.793403 |
The value assigned to the bonus feature is 0.169162, contributing to a total return of 0.962565.