Not Quite Perfect

            This week, I received an e-mail from a reader looking for the strategy for Triple Double Bonus Poker.  My home grown programs do not handle the 'kicker' situation for games like Double Double or Triple Double Bonus Poker, so I could not provide it to him.  If he insists on playing it without the totally correct strategy, his best bet would be to use Double Double Bonus strategy for the most similar paytable as the Triple Double Bonus.  Don't get me wrong, I don't recommend just using whatever is the next best paytable.  Sometimes, the impact may be slight, but other times it might be far more significant.


            I would not suggest someone take basic jacks or better strategy and use it on a Triple Double game.  If you look at the progression from jacks or better to Bonus to Double Bonus to Double Double Bonus to Triple Double Bonus, you'll see slow shifts in the strategy corresponding to the changes in the payouts of each game.  Jacks or better is 4 steps away from Triple Double while Double Double is just one step away.  Also, looking at the most significant paytable differences, I estimated that the strategy impact of the greater payout on the quads with kickers would have a minimal impact to the strategy. 


            Like with all video poker games, there are countless paytables.  My reader did not provide me with the one he was most interested in.  The top 3 paying patyables are very similar with the only difference coming in the Flush payout.  Other than that, it pays 4,2,1 and 1 for Straight down to Jacks or Better and 9 for Full House.  There is a version of Double Double that pays 1, 1, 3, 4, 6, 9 which is the closest you'll find.  The big difference is the payout of 2 vs 3 for the Trips, which will make a decent sized impact to our strategy.  


            As I said earlier, I don't have the programs to figure out kicker payouts, so what I will present here is a rough idea of the impact.  In Double Double, one of the strategy changes compared to its counterparts is that we hold a Pair of Aces instead of Two Pair (where one is Aces).   This will be one of the most scrambled hands in Triple Double.  Playing the Pair gives us opportunities for Trips and Quads.  The payout on the Quads is increased and the payout on the Trips is lowered (considerably).  The Two Pair and Full House payouts are unchanged, so the question is how much has the EV of the Pair of Aces been impacted by the payout changes.  Fortunately, taking a single hand and determining the impact is not too hard even when having to account for the kickers.  Assuming that the 2nd Pair and the 5th card were not a 2, 3 or 4, there are 12 ways for the Player to get Four Aces plus the kicker.  The payout of this hand goes from 400 to 800 for a net positive impact of 4800 units.  There are 1852 possible Three of a Kinds with a negative impact of 1852 for a net of about 3000 units.  Thus, the expected value goes up by about 0.2.  Even if the 2nd Pair AND the 5th card were 2, 3 and 4's, the expected value would still go up by a smidge, leaving the strategy of splitting the Two Pair as the correct one.


            So, now we know that the impact on a Pair of Aces is that the expected value goes up on the Pair while stays the same on the Two Pair, we have to wonder what happens to our Low Pair strategy?   A Low Pair in Double Double has an expected value of only 0.9.  Despite the high payout on Quads, the fact that if the hand does not improve it is a losing hand keeps the expected value below 1.  With Two Pair at 1.7, it is fairly obvious that there is NO way that the strategy here will change.  Stick with the Two Pair even if one is 2's - 4's.   The expected value will from 0.88 to about 0.96 depending on how many of the desirable kickers are discarded as part of the draw. 


            Looking at the strategy table for Double Double you'll note that there is nothing even around the expected value of the Low Pair.  As it moves from 0.88 to 0.96, it will not jump over anything.  As such, we learn from this that this part of the strategy table is not impacted by the move from Double Double to Triple Double.


            Since the biggest impacts to payouts are on Trips and Quads, we only need to be concerned with hands that can turn into these.  Thus 4-Card Straights are of no concern.  Likewise with 4-Card Flushes.  We do have to be somewhat concerned with 3-Card Straight Flushes (3-Card Straights and 3-Card Flushes are not playable), but these can only become Trips and not Quads.  These expected values will decrease slightly.  2-Card Royals are also impacted by the payout drop in Trips.  They cannot become Quads with kickers so they cannot be impacted there.  Last but not least, holding a single High Card will have its expected value impacted as well by both the payout changes in Trips and Quads. 


            Ideally, my reader goes about to find a full strategy for Triple Double Poker.  It does exist.  One of these days, I will updated my video poker software to account for those kickers.  Until now, my father's strategies have provided the strategies I've needed for kicker games.  In the meantime, using the Double Double strategy will have to do and you'll have to realize that you might be costing yourself a few coins.