Should You Break a Flush to Go for a Royal Flush?

Dealt: K♥ Q♥ J♥ 10♥ 3♥
Best play: Hold K♥ Q♥ J♥ 10♥.

Jacks or Better hand K♥ Q♥ J♥ 10♥ 3♥, with the best hold marked

It feels wrong to throw away a paying flush, but four to a royal is worth over three times as much. The 800-for-1 royal dominates, and several draws (the 9 for a straight flush, any other suited card) still pay.

Every hold that matters, exactly

Expected return per coin bet on 9/6 Jacks or Better, averaged over every possible draw. A return of 1.000 gets your bet back on average.

Hold Return Cost
K♥ Q♥ J♥ 10♥ 19.5532 best
K♥ Q♥ J♥ 10♥ 3♥ 6.0000 13.5532
K♥ Q♥ J♥ 3♥ 1.2128 18.3404
K♥ Q♥ 10♥ 3♥ 1.1489 18.4043
K♥ J♥ 10♥ 3♥ 1.1489 18.4043
Q♥ J♥ 10♥ 3♥ 1.1489 18.4043

Getting this hand wrong costs 13.5532 coins per coin bet, or 1355.3% of your wager on this hand. Over thousands of hands, mistakes like this are what separate a 99.5% game from a 97% one.

Practise the hands that trip people up

Casino Trainer deals you real video poker hands, solves every one of the 32 possible holds, and shows exactly what each mistake cost. It's the same calculation as on this page.

More hands: Every Jacks or Better hold decision · Video poker strategy · The 9/6 paytable

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