Hold three to a royal or four to a flush?
Hold the three to a royal and throw away the fourth flush card.
Average return per coin on Jacks or Better 9/6: Hold three to a royal 1.4829 · Hold four to a flush 1.3404.
Open this hand in the analyzerJacks or Better 9/6 strategy chart
The hand
%20scale(0.6)'%20fill='%23D40F1B'%3e%3cpath%20d='M50%2095C21%2072%203%2055%203%2032C3%2015%2015%204%2029%204C39%204%2046%2010%2050%2019C54%2010%2061%204%2071%204C85%204%2097%2015%2097%2032C97%2055%2079%2072%2050%2095Z'/%3e%3c/g%3e%3cg%20transform='translate(106%20196)%20scale(1.26)'%20fill='%23D40F1B'%3e%3cpath%20d='M50%2095C21%2072%203%2055%203%2032C3%2015%2015%204%2029%204C39%204%2046%2010%2050%2019C54%2010%2061%204%2071%204C85%204%2097%2015%2097%2032C97%2055%2079%2072%2050%2095Z'/%3e%3c/g%3e%3c/svg%3e)
%20scale(0.6)'%20fill='%23111317'%3e%3ccircle%20cx='50'%20cy='27'%20r='21.5'/%3e%3ccircle%20cx='25.5'%20cy='57'%20r='21.5'/%3e%3ccircle%20cx='74.5'%20cy='57'%20r='21.5'/%3e%3cpath%20d='M45.5%2052C45.5%2076%2041%2089%2029%2098h42C59%2089%2054.5%2076%2054.5%2052Z'/%3e%3c/g%3e%3cg%20transform='translate(106%20196)%20scale(1.26)'%20fill='%23111317'%3e%3ccircle%20cx='50'%20cy='27'%20r='21.5'/%3e%3ccircle%20cx='25.5'%20cy='57'%20r='21.5'/%3e%3ccircle%20cx='74.5'%20cy='57'%20r='21.5'/%3e%3cpath%20d='M45.5%2052C45.5%2076%2041%2089%2029%2098h42C59%2089%2054.5%2076%2054.5%2052Z'/%3e%3c/g%3e%3c/svg%3e)
| Play | Cards held | Return per coin |
|---|---|---|
| Hold three to a royalBest | K♥ Q♥ J♥ | 1.4829 |
| Hold four to a flush | K♥ Q♥ J♥ 5♥ | 1.3404 |
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
Both holds can still make a flush, but only the three-card royal can make a royal, a straight flush or a straight, and drawing two cards to three high cards also pairs them more often. On Double Bonus 10/7 the flush pays seven for one, and that tips the play the other way.
Does the paytable change the answer?
The answer changes on Double Bonus Poker 10/7, highlighted below.
| Paytable | Hold three to a royal | Hold four to a flush |
|---|---|---|
| Jacks or Better 9/6 | 1.4829 | 1.3404 |
| Jacks or Better 8/5 | 1.4514 | 1.1489 |
| Bonus Poker 8/5 | 1.4514 | 1.1489 |
| Bonus Poker Deluxe 9/6 | 1.4579 | 1.3404 |
| Double Bonus Poker 10/7 | 1.5171 | 1.5319 |
| Double Double Bonus Poker 9/6 | 1.4579 | 1.3404 |
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.