Dealt Quads in Quick Quads - Video Poker Strategy

I've played a lot of Quick Quads. It quickly becomes obvious that you get a lot more dealt quads in this game than you do in regular video poker. I decided to figure out how frequently this happens,Bob Dancer is one of the world's foremost video poker experts.  He is a regular columnist for Casino Player, Strictly Slots, and the Las Vegas Review-Journa land has written an autobiography and a novel about gambling.   He provides advice for tens of thousands of casino enthusiasts looking to play video poker.  Bob's website is www.bobdancer.com  and to use this as an excuse to review the math of how to figure these things out. Most video poker math is fairly simple once it's explained, but many players have no idea of how to attack the problem.

In the attached chart we're examining how many quads we get for each rank. In Quick Quads, you probably know, if we have trips and the ranks of the other two cards add up to the rank of the trips, we get paid the same as if we had a regular quad. That is, 44422 and 4443A both count as four 4s. (You pay an extra coin per line to compensate for the extra quads.)

In regular video poker there are 48 dealt quads of each rank. That is, you can have four aces with the 2c, four aces with the 2d, four aces with the 2h, etc. Since there are 52 cards in the deck and 48 of them are not aces, you can obviously combine the four aces with each one of the other 48 cards. You can't get Quick Quad aces, jacks, queens, or kings, so for these four ranks, you're stuck with the "normal" 48 quads each.

If we're counting up how many Quick Quads we get with the ranks between 2-T, we find it matters if the other cards are paired or not. That is, you have more ways to get 88862 than you do to get 88844. Let's see why.

Notation-wise, I call the 62 an "unmatched QQ duo" and 44 a "matched QQ duo" when we're talking about quad 8s. In strategies I create for this game, you'll see these terms.

To get 88862, there are four ways to get the eights (i.e. 8c8d8h, 8c8d8s, 8c8h8s, 8d8h8s). For each of these, there are 16 ways to get the unmatched QQ duo (i.e. four ways to get the 6 and four ways to get the 2). This multiplies out to 64 (i.e. 4 * 4 * 4 = 64). For every unmatched QQ duo, we'll get 64 Quick Quads.

To get 88844, there are still four ways to get the eights but only ways to get the pair of 4s (4c4d, 4c4h, 4c4s, 4d4h, 4d4s, 4h4s). This multiplies out to 24 (i.e. 4 * 6 = 24). For every matched QQ duo, we'll get 24 Quick Quads.

To add these up, we need to see how many unmatched QQ duos and how many matched QQ duos are present for each rank. The chart lists these. It should be obvious that we only have matched QQ duos with the even-numbered ranks, and we only have one of these per rank. As we increase in the size of the rank, there are always more Quick Quads available.

Rank Combinations to Make
the uQuick Quad Number of
New Quads Natural Quads Total Quads
A None 0 48 48
2 AA 6 48 72
3 A2 16 48 112
4 A3, 22 22 48 136
5 A4, 32 32 48 176
6 A5, 24, 33 38 48 200
7 A6, 25, 34 48 48 240
8 A7, 26, 35, 44 54 48 264
9 A8, 27, 36, 45 64 48 304
T A9, 28, 37, 46, 55 70 48 328
J None 0 48 48
Q None 0 48 48
K None 0 48 48
    
 Totals  624 2024

Since there are 2,598,960 unique dealt hands, we end up getting a dealt natural quad once every 4,165 hands (i.e. 2,598,960 / 624 = 4,165). In Quick Quads, we get quads every 1,284 hands (i.e. 2,598,960 / 2,024 = 1,284.071), which is more than three times as often.

Assuming you're playing about 600 base hands per hour (which is moving pretty good on a Triple Play, Five Play, or Ten Play machine), this comes out to a dealt quad every two hours or so. I've had as many as four in one hour (I won big that day), and have gone as long as eight hours between dealt quads (I lost a mint). If you play this game you'll have both kinds of experiences.