Mother Knows Best

18 December 2022

By John Grochowski

QUESTION: I just started playing video poker, though I've played slots for a long time. My mom's a video poker player and I started playing a little so I could sit next to her.

She loves Double Double Bonus Poker, so I've been trying to follow along. One play she makes doesn't really make sense to me. If she's dealt two pairs, she holds both of them even if there's a high pair.

It seems to me that since a high pair pays the same 1-for-1 as two pairs, you might as well hold the high pair and discard three cards to have more chances at four of a kind.

ANSWER: Mother knows best. It's a lot easier to complete a full house with a one-card draw than it is to draw the right two cards for four of a kind even with a three-card draw.

There is an exception in DDB if the high pair consists of Aces. Then it's best to hold the Ace pair and draw three cards.

Let's run some numbers. Assume you're dealt a hand such as Jack-Jack-10-10-6 of mixed suits. If you hold both pairs, 43 of 47 draws will leave you at two pairs. The other four draws will bring full houses.

If you hold only the Jacks, there are 16,250 possible three-card draws. The result is a high pair on 11,520 draws while 2,629 bring a second pair, 1,852 are three of a kind, 169 are full houses are 45 are four of a kind.

You have only a 0.28 percent chance of drawing four of a kind. Hold both pairs, and you draw a full house 8.51 percent of the time. Hold only one pair, and you draw a full house or better only 1.32 percent of hands.

If you're playing 9-6 Double Double Bonus, where full houses pay 9-for-1, your average return for holding both pairs is 8.40 coins per five wagered, better than the 7.24 when holding only one pair.

Reducing the full house pay narrows the gap, but doesn't eliminate it. At 8-for-1 on full houses, the margin is 7.98 vs. 7.19; at 7-for-1 it's 7.55 vs. 7.13; and at 6-for-1 it's 7.13 vs. 7.08.

If the high pair is Ace-Ace, the best play changes. Four Aces pay 160-for-1 instead of the 50 on four 5s through Jacks or 800 on four 2s, 3s or 4s. If accompanied by a 2, 3 or 4 as the fifth card, the four-Ace pay zooms to 400-for-1, or a 2,000-coin bonanza for a five-coin bet.

At all pay tables, it's a better play to go for the Aces. In the 9-6 game, average returns on Ace-Ace-10-10-6 are 9.50 coins on Ace-Ace and 7.13 on Ace-Ace-10-10. The gap increases as full house payoffs decline. Go for the Aces.

QUESTION: I get why you say there are 36 dice combinations in craps -- 6 times 6 is 36. But isn't there are lot of repetition? I count only three 7s with 6-1, 5-2 and 4-3, not six.

ANSWER: Four on the first die and three on the second is a different combo than three on the first and four on the second. They add up to the same total, but the difference matters in the odds of the game.

If you lump 4-3 and 3-4 together along with 5-2 and 2-5 and 6-1 and 1-6, you could come to the conclusion seven occurs only three times as often as 12, produced only when both dice land on 6. In reality, the seven occurs six times as often as 12. That's built into the odds and payouts.