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Breaking up suited Ace-10 is best Double Double play

Breaking up suited Ace-10 is best Double Double play

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Reader reports on unusual casino happenings include a set of "woulda, coulda, shoulda" tales.

"If only I'd made this move or not made that one, I woulda, coulda, shoulda won big."

The latest comes from Giorgi, a video poker player who had second thoughts about a play he made on a quarter 9-6 Double Double Bonus Poker machine.

"I had an Ace of clubs, 10 of clubs, Jack of diamonds, 8 of hearts and 7 of clubs," he wrote via email. "Since it was Double Double Bonus, I'm always pushing for four Aces and hope the kicker comes, too. So I held the Ace and discarded the other four cards.

"On the draw, the first three cards were Jack, King and Queen, all in clubs, then a Queen of spades. So I got a five-coin payoff for the pair of Queens, but the first three cards of that draw sure would have been nice next to Ace and 10 of clubs.

"A royal flush for $1,000 would have made my day. Two Queens for $1.25 just gave me enough for another hand.

"So tell me, did I make a bad mistake?"

I told Giorgi to relax on a couple of fronts. First, there's no guarantee he would have drawn the other three high clubs had he held both Ace and 10. It's more likely his draw would have been completely different. The random number generator keeps shuffling right up until you hit the draw button, and Giorgi's timing would have been different had he reached to hold a second card.

Besides, the play he made was the one that yields he highest average return.

If you hold just the Ace and discard the rest, the average return per five coins wagered is 2.26 coins. Giorgi's proposed alternative, holding suited Ace-10, averages only a 1.96-coin return.

An Ace-10 hold ranks only fifth in potential draws. After the lone Ace, the next best holds are Ace-Jack (2.20-coin average), the lone Jack (2.12) and the inside-straight draw Jack-10-8-7 (2.02).

Here's the way it works.

If you hold the Ace by itself, there are 178,365 possible four-card draws. Of those, 121,051 are losing hands. Of the winners, 43,389 will be pairs of Jacks or better, 8,874 two pairs, 4,102 three of a kinds, 399 straights, 209 flushes, 288 full houses, five four of a kinds with 5s through Kings, 32 four Aces without a low-card kicker, three hands with four 2s, 3s or 4s with an Ace, 2, 3 or 4 as a kicker, 12 four Aces with a 2, 3 or 4 kicker, and one straight flush.

Take all the payoffs on all those winning hands and average them, and you get the 2.26-coin average payback.

Hold Ace-10 instead, and there are 16,125 possible three-card draws, with 12,189 bringing no return. Of the winners, there are 2,847 high pairs, 711 two pairs, 281 three of a kinds, 47 straights, 119 flushes, 18 full houses, one four of a kind 5s through Kings, one with four Aces, and one royal flush.

The average of the returns on all those winners is 1.96 coins.

If you hold Ace-10, a long-shot draw for a royal is possible, but the only four-Ace hand will include a 10, so the 2,000-coin pay for four Aces and a kicker is impossible. You can't draw four 2s, 3s or 4s with a kicker because the 10 is in the way.

A higher percentage of draws to Ace-10 bring straights or flushes, but a lower percentage bring full houses.

On balance, the better play is the hold the Ace. Giorgi got it right.

Look for John Grochowski on Facebook and Twitter (@GrochowskiJ).

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