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Should you break a flush to go for a royal?

Yes. Throw away the fifth card and draw one to the royal.

Average return per coin on Jacks or Better 9/6: Hold four to the royal 18.4255 · Keep the flush 6.0000.

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

The hand

PlayCards heldReturn per coin
Hold four to the royalBestA♠ K♠ Q♠ J♠18.4255
Keep the flushA♠ K♠ Q♠ J♠ 3♠6.0000

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

One card in 47 makes the royal, which pays 4,000 coins on a five-coin bet. Seven more spades still give you the flush, and the missing ten of another suit makes a straight; a pair of jacks or better comes up often too. On a 9/6 machine that is worth about three times what the made flush pays.

Does the paytable change the answer?

The answer is the same on all 6 paytables below.

PaytableHold four to the royalKeep the flush
Jacks or Better 9/618.42556.0000
Jacks or Better 8/518.27665.0000
Bonus Poker 8/518.27665.0000
Bonus Poker Deluxe 9/618.42556.0000
Double Bonus Poker 10/718.63837.0000
Double Double Bonus Poker 9/618.42556.0000

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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