Hands versus Money

6 October 2019

By John Grochowski

Winning the most hands and winning the most money at video poker are goals that sometimes conflict. When they do, they expert play is to use the strategy that wins the most money.

That’s the case in a 9-6 Double Double Bonus Poker question raised by Jody, who has asked me via email to unravel several knotty strategy problems this year.

The issue is a hand that includes a pair of Aces – a strong start in DDB – as well as a chance at a straight flush.

“I find this to be a tricky one,” Jody wrote. “What would you hold if you were dealt Aces of spades and hearts along with 2, 3 and 4 of hearts, if you were playing Double Double Bonus video poker?”

There are two viable plays. Holding the pair of Aces gives you a sure winner for the high pair, and also gives you chances at two pairs, three of a kind, full houses and four of a kind, including the 2,000-coin bonanza for four Aces with a low-card kicker.

Alternatively, you could hold Ace-2-3-4 of hearts. The big prize is a straight flush and a 250-coin pay if you draw the 5 of hearts, with flushes, straights and low pairs also possible.

You’ll win the most hands by holding the pair of Aces. But you’ll win the most money if you hold suited Ace-2-3-4.

Here’s the breakdown, first for holding Ace-Ace – a sure winner with a 5-coin pay for a five-coin bet.

There are 16,125 possible draws. Of those, 11,559 will leave you with the pair of Aces for the 5-coin return, and 2,592 will bring a second pair, also a 5-coin return. So 14,151 draws leave you with 5-coin pays.

You improve to three of a kind for 15 coins on 1,854 draws, full house on 165, four Aces for 800 coins on 36 draws and four Aces with the kicker for 2,000 coins on nine draws.

In all, you settle for a 5-coin return that just gives you back your wager on 14,151 draws, or 87.8 percent of all draws. You improve the hand and get more than your money back on 12.2 percent of draws. And your average return is 9.42 coins per five coins wagered.

What if you hold Ace-2-3-4 of the same suit?

Then there are 47 possible draws, and 33 bring no payback. You win on only 29.8 percent of draws.

Of the 14 winners, one is a straight flush for 250 coins per five coins wagered. Eight are flushes for 30 coins, three are straights for 20 coins and two pair up the Ace to get your money back.

Note that only two of 47 hands are high pairs for a 5-coin return. You may win only 29.8 percent of the time, but 12 of the 14 winners, or 85.7 percent, will get more than your money back.

You have a 1 in 47 chance, or 2.13 percent, of drawing the straight flush. At 250 coins, it doesn’t pay as much as the four-Ace jackpots, with starting with two Aces, you get all four – with or without the kicker – only 0.28 percent of draws.

The average return for holding the suited Ace-2-3-4 is 11.91 coins, about two and a half coins more per draw than holding Ace-Ace.

There’s risk involved in throwing away a sure winner. More often than not, you’ll wind up with no payback if you break up the Aces. But the improved chances of a big winner make going for the straight flush the expert play.

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