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Hold an ace alone or ace-king offsuit?

On Jacks or Better, hold both high cards: ace and king together beat the ace alone.

Average return per coin on Jacks or Better 9/6: Hold ace and king 0.4783 · Hold the king alone 0.4649 · Hold the ace alone 0.4566.

Open this hand in the analyzerJacks or Better 9/6 strategy chart

The hand

PlayCards heldReturn per coin
Hold ace and kingBestA♥ K♦0.4783
Hold the king aloneK♦0.4649
Hold the ace aloneA♥0.4566

Average coins back per coin bet on a five-coin bet, where a royal pays 4,000, counting every possible draw from the 47 cards left. Above 1.0000 the hold wins money on average.

Why

Two high cards give you two ways to make a paying pair, and they can still make a straight. In Double Double Bonus four aces pay 160 for one, and 400 with a deuce, three or four, so the extra draw to the lone ace is worth more there.

Does the paytable change the answer?

The answer changes on Double Double Bonus Poker 9/6, highlighted below.

PaytableHold ace and kingHold the ace aloneHold the king alone
Jacks or Better 9/60.47830.45660.4649
Jacks or Better 8/50.47720.45320.4605
Bonus Poker 8/50.48050.46680.4606
Bonus Poker Deluxe 9/60.44120.42290.4312
Double Bonus Poker 10/70.44930.44680.4295
Double Double Bonus Poker 9/60.44430.45540.4226

Average coins back per coin bet on a five-coin bet, where a royal pays 4,000, counting every possible draw from the 47 cards left. Above 1.0000 the hold wins money on average.

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