Extras muddle the picture
By John Grochowski
Evaluating a video poker machine is usually pretty straightforward. A 9-6 Jacks or Better machine where full houses pay 9-for-1 and flushes 6-for-1, will return more to players than an 8-5 machine. A 10-7-5 Double Bonus Poker game, where full houses pay 10-for-1, flushes 7-for-1 and straights 5-for-1, is a much better gamble than a 9-6-4 version of the same game.
Your mileage may vary in any one session, of course. Losing streaks happen on the best of games, and a big hand or two can make you a winner on a coin gobbler. But over a long time, the odds of the games will lead those with better pay tables to return more money to players.
It gets trickier when extra elements are added, such as progressive jackpots and sequential royals. Can a game that’s lower-paying on its surface become the better bet if a progressive jackpot gets large enough?
Of course it can. Let’s take a simple example, a 9-6 Double Double Bonus Poker machine with no progressive jackpot vs. a 9-5 DDB machine with a progressive pay on royal flushes. At the starting value of a 4,000-coin jackpot for a five-coin wager, the 9-6 machine returns 98.98 percent with expert play, while the 9-5 machine pays 97.87 percent.
To get to a 98.98 percent return, the progressive royal on the 9-5 DDB machine needs to reach 6,026 coins. That’s pretty normal. A reasonable rule of thumb for Jacks or Better-based video poker games is that every 2,000-coin increase in a royal flush progressive raises the overall payback percentage by about one percent. At that point, long-term returns on 9-6 and 9-5 DDB are about the same, though the 9-5 game will be a more volatile experience with more of its return in the top jackpot and less in the more common full houses.
That’s simple enough, but the situation gets muddier when extra elements are added. A reader emailed to ask about a couple of Double Double Bonus games he’d seen in the same casino.
“I play dollar Double Double Bonus Poker at a casino that has it two pretty interesting ways,” he wrote. “It has 9-6 DDB with three progressives, on the royal, aces with kicker, and aces without kicker. It also has 9-5 DDB with just one progressive on the royal, but it has a $50,000 jackpot for a sequential royal. Is it worth giving up a unit on the flush and the ace progressives to get the sequential royal?”
With that many extras in play, there are a number of things to be weighed. How far above the rollover values of 4,000 coins on the royals are the two progressives? Are the other jackpots on the 9-6 game far above the usual 800 coins on four aces and 2,000 on four aces plus a 2, 3 or 4 as the fifth card? And what about that sequential royal, anyway?
The one with the smallest effect is the sequential royal, with the big payoff if the cards in a royal flush are on the screen in order of rank. There are 120 ways to arrange the five cards in a royal flush, and only one of them is the 10-Jack-Queen-King-Ace sequence. You know how rare royal flushes are. With expert play in 9-5 Double Double Bonus Poker at the 4,000-coin royal level, they come up an average of once per 40,065 hands.
With an average of one of every 120 royals sequential, you may or may not see one in the proper order in your lifetime.
How much does the sequential royal add to the overall payback percentage? Only about two-tenths of a percent, nowhere near making up the 1.1 percent difference between 9-6 and 9-5 Double Double Bonus.
Unless there is a great disparity between the progressive jackpots, with the 9-5 game’s royal progressive on the high side and the three progressives down near the starting point on the 9-6 game, then the 9-6 DDB game is going to be the higher-paying game.
With that three-way progressive, the Double Double Bonus machine has a chance of reaching the break-even point fairly often. If the three progressive jackpots are high enough, the payback percentage can reach or exceed 100 percent, heady territory for video poker players.
Calculating a break-even point is trickier than with a single progressive. If the only progressive was on royal flushes, 9-6 Double Double Bonus would become a 100-percent game with the royal payoff at 5,846 credits. If the only progressive was on four aces with a 2, 3 or 4, the break-even point is a 2,760-credit return. If a progressive only on four 2s-4s with an ace, 2, 3, or 4, the magic number is 1,152.
But with three progressive levels, all contribute to raising the payback percentage. One way to get to 100 percent is 5,500 coins on the royal, 2,100 on the aces plus kicker and 822 on the four aces, no kicker. Another way is jackpot levels of 4,800, 2,249 and 883 credits.
Understand that four aces, no kicker, occurs more frequently than the bigger-paying hands, so if the game is a 100-percenter based in part on the four-ace return, it probably won’t stay that way for very long. Someone will draw the aces and reset the pay to 800 coins.
When all this was explained by return email, the same reader wrote to ask about a special case in strategy.
“In 9-6 Double Double Bonus Poker with a three-way progressive on the royal, four aces with kicker and four aces, no kicker, I was dealt ace-2-3-4 of clubs and the ace of diamonds. I know the play is the four-card straight flush in a non-progressive game, but if the ace progressives get big enough, would you ever just hold the aces?”
There are turning points where holding the aces becomes better play, but it’s an interaction of the two ace jackpots. That’s very difficult to evaluate.
If the only progressive taken into account was the jackpot on four aces plus kicker, the turning point is a jackpot of 6,280 coins instead of the starting point of 2,000. At that level, the average return per five coins wagered is 11.9149 coins regardless of whether you hold ace-2-3-4 or the two aces plus one of the low kicker cards. You’re not likely ever to see a progressive that large, but if you do, the proper play is to hold a kicker along with the aces from that turning point onward.
If the aces-plus-kicker pot was constant at 2,000 coins, but there was a progressive on four aces, no kicker, starting at the rollover of an 800-coin payout, the turning point is 1,923 coins. When four aces, no kicker, pay that amount, the average return for holding A-A is 11.9160 coins, nudging past holding ace-2-3-4, at 11.9149.
But both jackpots increase simultaneously. Let’s say four aces, no kicker, pays 1,200 coins, a 50 percent increase from the usual 800-coin pay. How big does the aces plus kicker pay have to be for a strategy change? The turning point is 4,890 coins. If four aces pays 1,200 coins and four aces with a kicker pays 4,890, the average return per five coins play is 11.9149 coins regardless of whether you hold suited ace-2-3-4 or A-A.
If four aces are worth less than 1,200, it will take a bigger aces-kicker jackpot to bring a turning point, and if the aces alone are worth more, a somewhat smaller aces-kicker prize will turn the strategy around. But one or both jackpots will have to be at a level much higher than you usually see in the casino.
As a practical matter, holding the four parts of a straight flush is almost always the way to go, just as in a practical sort of way, 9-6 Double Double Bonus with a three-way progressive is almost always a higher payer than 9-5 DDB with a single progressive and a sequential royal.