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Two-pair strategy changes minus Aces

Two-pair strategy changes minus Aces

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A shuffle through the Gaming mailbag:

Q. I play 9-6 Double Double Bonus Poker. It’s the one game with a full pay table at casinos near me.

I have a strategy question. I know that if I have two pairs including Aces, I should hold the Aces and discard the other pair to go for the big four-Ace hands. What if I have a high pair and low pair, like Jack-Jack-2-2 along with junk card, like a 7? Should I hold the high pair? Should I hold the low pair because if I get four of a kind with a kicker I can get 800? Should I hold both pairs?

A. Assume you’re betting five coins in 9-6 Double Double Bonus. Given Jack-Jack-2-2-7, 43 possible draws will leave you with two pairs for a five-coin return. The other four — the two Jacks and two 2s — complete full houses for 45-coin returns. The average return is 8.40 coins.

If you hold the Jacks and discard the rest, you could draw the other two Jacks for 250 coins, you could improve to three of a kind or full houses, but the average return dips to 7.24 coins.

Holding just the 2s eliminates the guaranteed return for a high pair. Even though four 2s pays 400 coins and four 2s with a kicker pays 800, the loss of the guarantee drives the average return down to 4.40 coins.

Unless your two pairs include Aces, hold both pairs.

Q. Please help a newbie! How can you say there are 36 possible combinations of two dice? That seems like way too many.

Just to look at 7, you say there are six ways to make 7. I count only three. There’s 6-1, 5-2 and 4-3.

I’m sorry if I’m missing something obvious that experienced players know, and I’m sorry if you’ve explained this before, but I just started playing and I don’t know who else to ask.

A. No need to apologize. New players are constantly picking things up on the fly, so sometimes I need to circle back on old discussions to bring newcomers up to speed.

In addition to 6-1, 5-2 and 4-3, you can make 7 with 1-6, 2-5 and 3-4. Six on the first die and 1 on the second is a different roll than 1 on the first die and 6 on the second.

Imagine you’re playing with one red die and one green die. The colors make it obvious that green 6 and red 1 is a different roll than green 1 and red 6.

That’s important in calculating the odds of the game. If you looked at the ways to make 6 as 5-1, 4-2 and 3-3, and 7 and 6-1, 5-2 and 4-3, you could fool yourself into thinking you had the same chance of making 6 as 7.

But using the different colored dice example, you’d see 6 could be made with green 5-red 1, green 4-red-2, green and red both 3, red 4-green 2 and red 5-green 1.

That’s five ways to make six, and we’ve already seen the six ways to make 7. You don’t have the same chance of making 6 as 7. Seven will come up more often.

There’s only one way to make 12 because red and green must both be 6, but two ways to make 11 because 6-5 is different than 5-6.

You could do this exercise with every possible combination, but to cut straight to the final tally, there are 36 possible combinations of two six-sided dice. Odds and payoffs in the game grow from that fact.


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