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Going for Fours
Introduction
Going for Fours is a video poker variation I noticed at the Treasure Island casino on November 28, 2005. The game plays like regular video poker except if the player has a three of a kind, and made a max bet, he may pay a fee for a second draw. The second draw is from the remaining cards in the deck. I don't know if the game lets the player take a second draw with a three of a kind if the fourth card to the four of a kind was already discarded. The following tables show the possible outcomes for the Jacks or Better and Double Bonus games.
The following pay table is for Jacks or Better. In this game the fee for the second draw is 6 coins, or 1.2 bet 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 is for Double Bonus. In this game the fee for the second draw is 12 coins with three 5-K, 19 coins with three 2-4, and 37 coins with 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 |
| Three of a Kind on Second Draw (37 coin fee) | -4.4 | 240296462393220 | 0.007001 | -0.030803 |
| Three of a Kind on Second Draw (19 coin fee) | -0.8 | 476073716409864 | 0.01387 | -0.011096 |
| Three of a Kind on Second Draw (12 coin fee) | 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 show a return of 96.43% for Jacks or Better and 98.41% for Double Bonus.
Strategy
Here is what the screen looks like when you get a three of a kind on the first draw. This was when I got three kings in double bonus, for which the fee for the second draw is 12 coins.
The player should indeed pay for the second draw as long as a four of a kind is possible. I do not know whether the machine even lets the player take the second draw if the fourth card to the four of a kind was already discarded, but I tend to think it wouldn't.
Methodology
This game was a difficult one to analyze in a reasonable period of time. Even with all my short cuts it still look about 3 days of computer time. The numbers in the combinations row are only to 15 significant digits. I hope in heaven (or wherever I end up) Excel can handle any number of digits.
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