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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.
![](/games/videopoker/images/going4fours-small.jpg)
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.
![](/games/videopoker/images/going4foursK-small.jpg)
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.