Two Pair Overload

            How come it seems that you get an overabundance of Two Pairs when you are playing Double Double Bonus Poker.  For those not familiar with this game, it is a variant of video poker that pays only 1 for Two Pair.  This is because it pays some serious payouts for having certain Four of a Kinds with a particular set of Kickers.  Thus, four Aces with a 2/3/4 pays 400 for 1.  This is half of the payout of a Royal which can definitely make for a good night. 

            I'm sure that in the long run, I get just as many Two Pairs when I play Bonus Poker as when I play Double Double Bonus Poker.  It's just that a string of them in Bonus Poker results in a nice winning streak and a run of them in Double Double lead to a nice streak of pushes.  When you get a Two Pair in Bonus Poker on the deal, you have a roughly 1 in 12 chance of getting a Full House and if you don't you still have a winning hand.  In Double Double, you have a roughly 11 in 12 chance of winding up with a push and a 1 in 12 chance of the Full House.

            If you are a regular player of Double Double, there is little doubt that every time you are dealt a Two Pair that you give some thought to throwing one of them back, giving you a chance to earn Quads.  The thought process being that Two Pair is no more valuable than a High Pair and you open up new opportunities to get Trips, a Full House still and Quads. 

            Now, if you're dealt two Low Pairs, I doubt you think about this option very long.  If you discard one of the Pairs, you don't have a guaranteed winner.  As the most likely outcome is that you'll wind up with just this Pair, giving up a sure winner is probably not what you want to do.  A Two Pair has an expected value of 1.7.  As a guaranteed winner it certainly leaves something to be desired, but it still beats a Low Pair by a large margin.  A pair of 5's - 10's has an expected value of only 0.7+.  This is the worst case scenario as these Quads are worth the least and have no opportunity for the kicker bump up.  A Pair of 2's, 3's or 4's has an expected value of 0.9.  Much improved over the other Low Pairs, but still well short of the Two Pairs 1.7.

            So, we've now clearly covered the notion of discarding one Pair when you have Two Low Pair.  What about when at least one of the Pair is a High Pair?  A High Pair is also a guarantee winner.  So, do the odds of hitting a Full House with a 1 card draw outweigh the potential of other Two Pairs, Trips, Full Houses and Quads with a 3-card draw?  Ironically, a High Pair is more valuable as a Pair than a Pair of 2's thru 4's than it is as Quads.  Quad J's is in the lowest paying category of Quads.  As a result, the High Pair (excluding Aces) has an expected value of about 1.4, which is still below that of our Two Pair. 

            That leaves a Pair of Aces.  This is the win-win situation.  A Pair of Aces is a guaranteed winner and the HIGHEST paying of all the Quads.  It should then be no surprise that the expected value of a Pair of Aces is 1.9 which exceeds that of our Two Pair.  As such, it is the ONLY time you should discard Two Pair to keep only one Pair.  While this expected value is somewhat impaired if the other Pair is Low (2's - 4's) it still pays to keep just the Aces.  For it to be worthwhile in the long run, however, you will need to hit your Quad Aces from time to time with some of them being with the kicker.  Keep in mind that 1 in 366 (roughly) draws will result in Quads with about a quarter of them with the kicker.  This means you may go a LOT of Pairs of Aces without hitting the Quads.  A hot streak on these will result in a significant increase in your bankroll.  Conversely, a cold streak will take its toll on your bankroll and potentially your psyche.  As always, the important part is to stick to your strategy and keep only the Pair of Aces.

            Lastly, in case you are wondering, the strategy does not hold for other Bonus games.  In the other common games, the strategy is to keep the Two Pair.