This week, I received a question from a reader who wanted to know how high a progressive jackpot must go before playing a suited Ace-10 over a single Ace in Jacks or Better. It is such a simple question, yet it helps to illustrate so many critical points in learning how to play Expert Strategy for video poker.
The first point is for a basic Jacks or Better machine, a suited Ace-10 is not playable. While a 2-card Royal is hardly the most powerful hand, it is a fairly frequently occurring one. When a player has 3 High Cards, with 2 of them of the same suit, he discards the third High Card and plays the two suited ones.
While hitting the Royal is very rare, the hefty payout of 800 makes it worth dropping the third High Card. The one exception to this is the suited Ace-10. Because the 10 is not a High Card and hitting a Straight from a 2-Card Triple Inside Straight is so rare, holding the single Ace actually produces a slightly higher expected value.
In a full-pay Jacks or Better, the difference is quite minimal. The single Ace has an expected value of 0.4640 while the suited A-10 has an expected value of 0.4606.
If we move this to a Progressive at initial reset, then the Royal is still at 800, but the Full House goes down to 8 and the Flush to 5. This makes the expected value of the single A equal to 0.4606. The suited Ace-10 has an expected value of 0.4493.
The gap has widened a bit but, as the Progressive meter increases, only the suited Ace-10 will benefit. Yes, it is possible to draw a Royal from a single Ace, but not if you’ve discarded the 10 of the same suit. So, if you hold both the Ace and 10, you have one chance in 16,215 of getting the Royal Flush. At 800 units, the Royal will contribute nearly 0.05 of the 0.4493 expected value.
As the meter goes up, the expected value of the suited Ace-10 will increase as well. At 900 units it will be 0.4555. Much closer to the single Ace, but still below it. At 1,000 units, it will be 0.4617 which now makes it the play of choice.
In fact, at 983 is where the expected value of the suited Ace-10 exceeds that of the single Ace. So, on a quarter machine, the meter would have to hit $1,228.75 to make it worth going for the Royal.
This number is not actually an exact amount, but a close approximation. The expected value of these hands is not absolute, as it depends slightly on the other 3 cards. I would say it is fair enough to use that amount mentioned as a good place to change your strategy.
This brings to light the second critical point. Strategy changes as the pay table changes. It does not matter if it is the Royal Flush or the Flush that changes its payout. Every change in the pay table makes changes to the expected values of numerous hands which can cause a shift in the order of the strategy table. This shift can impact how we play hands.
These changes in expected value will not usually be very big. As you can see in the example above, we start with two hands whose expected values differ by only about 0.01. But, as the Royal goes from 800 to about 1000 units, the expected value of the suited A-10 moves up by a mere 0.01+ which is just enough to push it to be higher than that of the single Ace.
Frequently, a payout change will make a difference to many hands so the impact may be even smaller. But, in this case, the change to the Royal payout impacts only 1 of the 2 possible ways to play the hand.
It should be no surprise changes in payouts to Two Pair, Trips, Full House and Quads will most heavily impact a hand like a Low Pair, where as a change in payout to a Straight or Flush will impact non-Pair hands such as partial Straights and Flushes.
This is why we see so many changes in the strategy as we move to Bonus Poker and further into Double Double Bonus Poker. In that case, the huge payout for Aces can make us even discard a Two Pair (Aces + something else) in order to retain a chance to get Quad Aces.
The overall lesson is that you can’t assume that the strategy for one pay table will inherently carry over to another. While you may not destroy your bankroll by playing Jacks or Better strategy on a Progressive (not matter the size of the jackpot), you will still be reducing your real payback below that of the theoretical one, which is not something I recommend.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].