Holding the low-card kicker in Double Double Bonus Poker
By John Grochowski
It’s always tempting to go for the big jackpot, and often in video poker that’s just what we do. We’ll break up a ﬂush, straight or high pair for a one-card draw to a royal ﬂush, tossing away smaller payoﬀs for a chance at a bonanza.
Still, in Double Double Bonus Poker, the best play is to discard a low-card kicker when holding three Aces, a play that sometimes confuses fans of the game. Several readers have emailed me to say they understand drawing two cards instead of one would increase their chances of drawing the fourth Ace. Still, they wondered, would they be better oﬀ to keep a low-card kicker since drawing the fourth Ace then would bring them a 2,000-coin jackpot, while four Aces without a 2, 3 or 4 as the ﬁfth card pays only 800 coins?
One fellow who had been holding the kicker came up lucky twice in one day. He had been playing 9-6 Double Double Bonus on a 50-cent Triple Play Poker machine. After holding three Aces and a deuce, he had to settle for three of a kind on two hands, but pulled the fourth Ace on the third. That’s a 2,030-coin hit, the kind of hand that can make your day at the casino.
He didn’t stop there. About 20 minutes later, he was playing some more Double Double Bonus on a 25-cent Five Play game. Again, he held three Aces and a deuce, and again, he drew the fourth Ace on one hand. Bam! A 2,060-coin jackpot.
And he went a step further, to a strategic territory where few players venture. Dealt three deuces with an Ace, he held that kicker, too. Sure enough, on one hand he drew the fourth 2, for an 800- coin jackpot instead of the usual 400 for four 2s, while settling for three of a kind on the other two hands.
Naturally, that set him to wondering, and he emailed to ask if it’s really the best play to discard the kicker. Sure, you’re twice as likely to draw the fourth Ace with a two-card draw, but four Aces plus a low card pay 2.5 times as much as four Aces with a 5 or higher. And if you fail to draw the fourth Ace, doesn’t holding the kicker increase your chances of drawing a full house?
He applied the same reasoning to the deuces hand. You’re half as likely to draw the fourth 2 if you hold the Ace kicker, but if you succeed, the payoﬀ is twice as much.
The problem with that little analysis is that you don’t toss away all chances at the bigger bonanza discarding one 2, 3 or 4 with the Aces, or by discarding one Ace, 2, 3 or 4 with three 2s, 3s or 4s. When you hold just the three Aces, there are still 11 potential kickers among the 47 cards remaining in the deck. Same deal with low cards. When you discard one kicker to go with 2s, 3s or 4s, there are still 11 more in play.
To give the scenario with the lowest diﬀerence in average payback between holding or discarding the kicker, I’m going to assume that full houses pay 9-for-1. Some Double Double Bonus machines pay only 8-for-1 or even (ugh!) 7-for-1 on full houses, but those lower paybacks move the percentages farther in favor of holding just the three Aces.
Let’s take care of three low cards ﬁrst.
The hand described in the email was three 2s with an Ace, but it just as easily could have been three 4s with a 3, three 3s with a 2 or any other combination of three 2s, 3s or 4s with either an Ace, 2, 3 or 4 as a potential kicker.
In any case, if you hold three matched low cards and a kicker, you have 47 possible draws. Just one will give you the fourth low card to go with the kicker and the 800-coin jackpot. Three remaining cards match the kicker and would bring a full house. The other 43 cards are no help, and leave you with three of a kind. The average return in a Double Double Bonus game that pays 9-for-1 on full houses is 33.6 coins per ﬁve coins wagered.
What if you hold the 2s alone? Then there are 1,081 possible draws. The biggest share, 969, will leave you with three of a kind. Sixty-six bring full houses, and 46 bring four of a kind. Of those 46 quads, 11 also will have a kicker for the 800-coin payday. Average return: 37.3 coins, making it a stronger play to toss the kicker.
The key is that if you hold the kicker, only 2.1 percent of your draws will bring four of a kind. If you hold just the three 2s and take a two-card draw, then 4.3 percent of your draws bring the fourth. You draw quads twice as often.
Four Aces with the kicker brings a bigger bonanza. A 2,000-coin hit makes your day. But the arithmetic is similar.
Hold the three Aces plus the kicker, and there are 47 possible draws. Just one will give us four Aces plus the kicker for that 2,000- coin bonanza. Three will bring full houses for 45 coins and 43 will leave three of a kind for 15 coins. The average return per hand is 59.15 coins.
If you hold just the three Aces, there are 1,081 possible two-card draws. Eleven of them will give you four Aces plus a 2, 3 or 4 for 2,000 coins, another 35 will give you four Aces without the kicker for 800 coins, 66 will bring full houses for 45 coins and the remaining 969 will leave us with three of a kind for 15 coins. The average return per hand is 62.45 coins per hand.
A couple of things to note: Just as in the example with 2s, you draw Ace no. 4 twice as often with a two-card draw. If you hold the kicker, you draw the fourth Ace only once per 47 hands, but when drawing two cards, you get the fourth Ace once per 23.5 hands. And nearly a quarter of those will also include a low-card kicker, meaning there’s still a decent shot at the 2,000-coin jackpot.
Also, the diﬀerence in the probability of drawing full houses is much lower than you might think. When we hold the kicker, we’ll draw a full house once per 15.7 hands. When we hold just the three Aces, we pull a full house once per 16.4 hands.
Of course, it’s hard to argue with luck, and if I were in the player’s position, I’d be plenty happy with two 2,000-coin hits. Would he have done anywhere near as well if he’d made the “right” play?
Maybe. For certain, he still would have had four Aces for 800 coins at least once on each draw. Video poker cards are dealt serially, oﬀ the top of the electronic deck. Since the Ace was the next card oﬀ the top in two of his hands, it would have been the next card oﬀ the top even if he’d held the kicker. Beyond that, there’s no way to tell if he would have drawn a low-card kicker on either big win, or if he’d have pulled the fourth Ace on another hand or two.
Either way, it’s a nice hit. As for me, I’ll stick with the percentages and discard the kicker. Playing video poker is not a one-shot deal. I know I’ll be back for more, and with repeated casino visits, playing the percentages will help more often than it hurts.