# 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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