Hold a low pair or four to a flush?

Break the low pair and hold the four to a flush.

Average return per coin on Jacks or Better 9/6: Hold four to a flush 1.2128 · Hold the pair 0.8237.

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

The hand

Play	Cards held	Return per coin
Hold four to a flushBest	5♥ 9♥ K♥ 2♥	1.2128
Hold the pair	5♥ 5♣	0.8237

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

Nine cards of the suit are left among the 47 you can draw, so the flush comes in about one time in five, and it pays six times the bet on a 9/6 machine. A pair of fives pays nothing until it improves to two pair or better. The high card in the flush draw adds a little more: catching a king pairs it for a paying hand.

Does the paytable change the answer?

The answer is the same on all 6 paytables below.

Paytable	Hold four to a flush	Hold the pair
Jacks or Better 9/6	1.2128	0.8237
Jacks or Better 8/5	1.0213	0.8135
Bonus Poker 8/5	1.0213	0.8135
Bonus Poker Deluxe 9/6	1.2128	0.8165
Double Bonus Poker 10/7	1.4043	0.7434
Double Double Bonus Poker 9/6	1.2128	0.7332

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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The hand

Why

Does the paytable change the answer?

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