I’m working on analyzing the new IGT game called Quick Quads. This is a Triple Play/Five Play game where you bet six coins per line. On quads (i.e. 4-of-a-kinds) between deuces and tens inclusive, you get credit if you have trips (i.e. 3-of-a-kinds) where the fourth and fifth cards add up to the quad rank. For example, 55532 and 66633 will both get paid at whatever rate you get for quads.

The first thing to look at is how many extra quads are generated by this. To start with let’s look at a simple pair in a game without wild cards. (There are no Quick Quads with wild cards.) Specifically we’ll look at 4h 4d Ks 9c 7d. Obviously we’ll hold the pair of fours.

In regular video poker, when we draw three cards in a 52-card deck, we have 16,215 possible draws. When we draw to a pair, the relevant numbers are 1854 trips, 165 full houses, and 45 quads. If you’re having trouble visualizing how we can end up with 45 quads, in our example we can get fours with the 2c, fours with the 2d, fours with the 2h, fours with the 2s, etc. There are 45 different “kickers” we can have with 4444.

In Quick Quads this changes in three ways. First of all, let’s look at the hand 444A3. Since we started with two red fours, the third four may be either one of the black ones. There are four possible aces in the deck, along with four possible threes. Since any of these may be matched up with any of the others, the appropriate mathematical operation here is multiplication and we have 2*4*4 = 32 different ways to end up with 444A3 when we start with the given hand. Each of these quick quads “used to be” trips, so the number of possible trips will need to be reduced by 32. We will call this kind of Quick Quad “unmatched,” because the ace and three are not the same rank.

A different type of hand to look at is 44422. There are two different black fours, and six ways to get 22 --- namely 2c2d, 2c2h, 2c2s, 2d2h, 2d2s, and 2h2s. That leaves us 2*6 = 12 quick quads of this type, all of which “used to be” full houses. We will call these Quick Quads “matched” because the two deuces are matched with each other.

There is a third type of eligible quick quad we can get from this starting position --- namely 44888. There are four ways to draw three eights --- namely 8c8d8h, 8c8d8s, 8c8h8s, and 8d8h8s. Each of these “used to be” full houses. We will call them “higher match” as the rank of the Quick Quad is twice as big as the original pair.

If we’re playing Jacks or Better, among a few others, the value of the higher match Quick Quad is identical in value to that of a quad in the original rank. But in many other games, including Double Bonus among others, the value of four eights is not as great as the value of four fours. For this reason, any list of Quick Quads must list them separately.

Quick Quad Rank	Combinations to make the Quick Quads	Number of New Quads	Number of Higher Quads	Total Quads
A	None	0	4	45+4
2	AA	12	4	57+4
3	A2	32	4	77+4
4	A3, 22	44	4	89+4
5	A4, 32	64	4	109
6	A5, 24, 33	76	0	121
7	A6, 25, 34	96	0	141
8	A7, 26, 35, 44	108	0	153
9	A8, 27, 36, 45	128	0	173
T	A9, 28, 37, 46, 55	140	0	185
J	None	0	0	45
Q	None	0	0	45
K	None	0	0	45

These numbers assume that none of the cards we originally discarded could have been used in the Quick Quad. Obviously this isn’t always the case. In a hand like 44238, of mixed suits, let’s assume for now that you hold the pair and toss the other three. The deuce reduces the number of 44422 quads from 12 to 6. The trey reduces the number of 444A3 quads from 32 to 24. The eight reduces the number of higher match quads from 4 to 1.

This background work has to be done before we can work out strategies. Different games have different returns for quads than others. In some Quick Quad games, unusual amounts for quads are assigned to make the math work out. We’ll visit these issues later.

Bob Dancer is America's best-known video poker writer and teacher. He has a variety of "how to play better video poker" products, including the software "Video Poker for Winners," Winner's Guides, strategy cards, his autobiography Million Dollar Video Poker, and his two novels, including Sex, Lies, and Video Poker. Dancer's products may be ordered at www.bobdancer.com or by telephone at 1-800-244-2224 M-F 9-5 Pacific Time.