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Going for Fours

Last update: January 6, 2006

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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