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Going for Fours
Introduction
I encountered a variant of video poker called Going for Fours at the Treasure Island casino on November 28, 2005. This game functions like traditional video poker, with the distinction that if a player achieves three of a kind with a maximum bet, they may opt to pay a fee for a chance at a second draw. This second draw is taken from the remaining deck. I'm uncertain whether players are allowed to take a second draw if they have already discarded a card needed to complete four of a kind. The subsequent tables illustrate potential results for both Jacks or Better and Double Bonus games.
The pay table below pertains to Jacks or Better. In this game, charging for the second draw amounts to 6 coins, equivalent to 1.2 betting units.
Going for Fours - Jacks or Better
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal Flush | 800 | 854450366112 | 0.000025 | 0.019914 |
| Straight Flush | 50 | 3698647500240 | 0.000108 | 0.005388 |
| Four of a Kind on First Draw | 25 | 81080481069000 | 0.002362 | 0.059053 |
| Four of a Kind on Second Draw | 23.8 | 115194836612808 | 0.003356 | 0.079873 |
| Full House on First Draw | 7 | 395111752769160 | 0.011511 | 0.080576 |
| Full House on Second Draw | 5.8 | 154496278010556 | 0.004501 | 0.026106 |
| Flush | 5 | 374257867491648 | 0.010903 | 0.054517 |
| Straight | 4 | 387241695432144 | 0.011282 | 0.045126 |
| Three of a Kind on First Draw | 3 | 9619262643312 | 0.00028 | 0.000841 |
| Three of a Kind on Second Draw | 2 | 4436668586378950 | 0.129255 | 0.258509 |
| Two Pair | 1.8 | 2275558356349910 | 0.066294 | 0.11933 |
| Jacks or Better | 1 | 7383064971540380 | 0.215093 | 0.215093 |
| Non-Paying Hand | 0 | 18708175764454200 | 0.54503 | 0 |
| Total | 34325022950618400 | 1 | 0.964326 |
The next pay table represents Double Bonus. Here, the charge for a second draw is 12 coins when holding three 5s through Kings, 19 coins for three 2s through 4s, and 37 coins when holding three Aces.
Going for Fours - Double Bonus
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal Flush | 800 | 836527838328 | 0.000024 | 0.019497 |
| Straight Flush, Four 5-K on First Draw | 50 | 59359808748744 | 0.001729 | 0.086467 |
| Four Aces on First Draw | 160 | 7757967060144 | 0.000226 | 0.036162 |
| Four Aces on Second Draw | 152.6 | 12213720388512 | 0.000356 | 0.054299 |
| Four 2-4 on First Draw | 80 | 18011747848248 | 0.000525 | 0.041979 |
| Four 2-4 on Second Draw | 76.2 | 24064749980352 | 0.000701 | 0.053423 |
| Four 5-K on Second Draw | 47.6 | 78590905415928 | 0.00229 | 0.108985 |
| Full House on First Draw | 9 | 369850749110136 | 0.010775 | 0.096975 |
| Full House on Second Draw (37 coin fee) | 1.6 | 16339725648756 | 0.000476 | 0.000762 |
| Full House on Second Draw (19 coin fee) | 5.2 | 32333643819936 | 0.000942 | 0.004898 |
| Full House on Second Draw (12 coin fee) | 6.6 | 105422247614700 | 0.003071 | 0.020271 |
| Flush | 6 | 380604008079792 | 0.011088 | 0.066529 |
| Straight | 5 | 530205892037136 | 0.015447 | 0.077233 |
| Three of a Kind on First Draw | 3 | 8920593585792 | 0.00026 | 0.00078 |
| Achieving Three of a Kind on a Second Draw (with a fee of 37 coins) | -4.4 | 240296462393220 | 0.007001 | -0.030803 |
| Achieving Three of a Kind on a Second Draw (with a fee of 19 coins) | -0.8 | 476073716409864 | 0.01387 | -0.011096 |
| Achieving Three of a Kind on a Second Draw (with a fee of 12 coins) | 0.6 | 1552708415863400 | 0.045235 | 0.027141 |
| Two Pair, Jacks or Better | 1 | 11347312314013700 | 0.330584 | 0.330584 |
| Non-Paying Hand | 0 | 19064119754761700 | 0.5554 | 0 |
| Total | 34325022950618400 | 1 | 0.984087 |
The lower right cells indicate a return rate of 96.43% for Jacks or Better and 98.41% for Double Bonus.
Strategy
This is how the screen appears when you secure three of a kind on the initial draw. I experienced this with three kings in Double Bonus, which incurs a 12 coin fee for a second draw.
Players should consider paying for a second draw provided that the possibility of achieving four of a kind remains. I'm not aware if the machine allows the second draw if the card needed for a four of a kind has already been discarded, but I suspect it does not.
Methodology
Analyzing this game proved to be quite challenging within a limited timeframe. Despite employing various shortcuts, it still required around three days of processing time. The figures in the combinations row are only accurate to 15 significant digits. I hope that in my next existence (or wherever I may go), Excel can manage an unlimited number of digits.