Two Pair or not Two Pair

18 March 2004

By Elliot Frome

One of the most confusing hands in Video Poker has got to be the Two Pair. It wasn't always this way. Back in the days of just Jacks or Better, I think most people quickly recognized the benefits of keeping the two pair even when one of the pair was a pair of Jacks or Better. When the math gurus came along, this was quickly confirmed with Two Pairs having an Expected Value (EV) of 2.60, while a High Pair has an EV of only 1.54. The Two Pairs paying 2, and the Four of a Kinds paying 'only' 25, made this not much to think about.

Along came the Deuces Wild Version of Video Poker. Two Pairs isn't even a winning hand! The strategy was quickly developed that made it proper play to dump one of the two pairs (it doesn't matter which). The Single Pair has an EV of .56. If you chose to hold the Two Pair, your EV would drop to .50. A bit closer than our earlier example, but again, not much to think about.

Of course, this was true of Full-Pay Deuces. Next came Double Pay Deuces, which paid 4 on the Full House and reduced the Quads and Quints. This alteration made the Two Pairs a playable hand again. Double Pay Deuces was originally intended to be a less generous form of Full Pay Deuces, but the attempt backfired. Most of the games were quickly pulled, but you can supposedly still find some at Sam's Town in Las Vegas.

Next up was Triple-Pay Deuces. This managed to 'cool-down' the Deuces game, but still pays 100% on the nose. Because the Full House was set back at '3', the reduction in Quints payback is not enough to make playing Two Pair a worthy play. So, back to holding only a Single Pair we went.

Just to keep the player guessing, the next major version was NSUD (Not so ugly Deuces/Ducks). This version once again paid 4 on Full House while paying 4 as well on Four of a Kind and 16 on Quints. The Pair is no match for the EV of .68 that the Two Pairs takes on when it pays 4.

The good news is that at least this leaves us with some basic guidelines for Deuces Wild. If the Full House pays 4, then it's almost certainly the right play to keep Two Pairs. If it pays only 3, then the right play is the Pair. I say 'almost certain' because you never know what version is coming out tomorrow. To be certain, you should always check the strategy table for the specific game.

Of course, our story doesn't end there. To muddle the picture even further, along came the Bonus Games. Because Two Pairs is a paying hand in Bonus Poker, trying to create a rule of thumb becomes very difficult. When you hold Two Pairs, you are relying on the payback of Two Pairs and Full Houses. When you hold a single Pair, you are relying on the payback of Pairs, Two Pairs, Trips, Full Houses and Quads.

Let's at least review some of the more popular versions of Bonus Poker. Of course, first came regular Bonus Poker. The added payouts on Quads was offset by the reduction in the

payout of Full Houses. The net result was almost no change to the decision being made. Two Pairs has a significantly higher EV (2.51) to even that of a Pair of Aces (1.68).

The next entry was, of course, Double Bonus Poker. The increase of the Four of a Kinds even higher and the reduction of the Two Pairs down to 1, makes the equation much closer. A Pair of Aces has an EV of 1.761, while Two Pairs has an EV of 1.766. Two Pairs still wins.

Double Double Bonus Poker is next on our list. Here the Pair of Aces finally beats out the Two Pair. A Pair of Aces is at about 1.92 while the Two Pairs is at 1.68. Enough of a difference to make a Pair of Aces a clear favorite. All other combinations of Two Pair continue to be played as such.

There are, of course, many other variations of Bonus Poker out there. Unfortunately, there is no clear pattern that I could come up with. This is why, in order to achieve Expert Play, it is advised to learn one game and learn it well before moving on to other games.

Below is a table that shows the EV of 2 Pair vs. a High Pair for a variety of Full-Pay machines.

Game	Two Pairs	Pair of A's	High Pair
Jacks or Better	2.60	1.54	1.54
Deuces Wild	0.50	0.56	0.56
Double Pay Deuces	0.68	0.54	0.54
Triple Pay Deuces	0.50	0.52	0.52
NSUD	0.68	0.55	0.55
Bonus Poker	2.51	1.68	1.53
Double Bonus Poker	1.766	1.761	1.46
Double Double Bonus	1.68	1.92	1.45
Double Joker Wild	1.49	0.76	0.76