Breaking a made flush
| Hold | Expected value | Verdict |
|---|---|---|
| Ah Kh Qh Jh | 18.4255 coins | Correct play |
| Ah Kh Qh Jh 3h | 6.0000 coins | 12.4255 coins worse |
| Ah Kh Qh 3h | 1.2128 coins | 17.2128 coins worse |
The pat flush is a certainty worth exactly six coins. The four-card royal is a gamble worth 18.4255, because one card in the remaining forty-seven turns it into 800.
The royal completes only 2.13% of the time. It is worth chasing anyway, because 800 multiplied by a small probability still outweighs a guaranteed six, and because the draw also produces flushes, straights and pairs along the way.
Breaking a made straight
| Hold | Expected value | Verdict |
|---|---|---|
| Ah Kh Qh Jh | 18.4681 coins | Correct play |
| Ah Kh Qh Jh 10c | 4.0000 coins | 14.4681 coins worse |
| Kh Qh Jh 10c | 0.7872 coins | 17.6809 coins worse |
The same decision with less to give up. A straight pays four, and the four-card royal is worth 18.4681.
What the draw actually returns
Holding four to a royal does not only win when the royal lands. Enumerating every draw from A-K-Q-J of one suit:
- Royal flush: 2.13% of draws
- Flush: 17.02%
- Straight: 6.38%
- Paying pair: 25.53%
- Nothing: 48.94%
More than half the draws still pay something. That is what makes the play comfortable as well as correct.
The one thing to remember
Hold four to a royal over anything except a made royal. Over a flush, over a straight, over two pair, over a paying pair. It is the highest-value rule in video poker and it is the one most players will not do.
Always bet the maximum coins. The 800-per-coin royal payout usually applies only at five coins; at fewer it drops to 250, which removes most of the reason this play is correct at all. Our pay table page covers what else to check on the screen.
Frequently Asked Questions
- Should I really break a flush for four to a royal?
- Yes. The four-card royal is worth 18.43 coins against exactly 6.00 for the flush.
- How often does the royal complete?
- One card in forty-seven, or 2.13%. The hold is still correct because the payout is 800 for one coin at maximum bet.
- What if I am not betting maximum coins?
- Then the royal usually pays 250 per coin rather than 800, and much of the reason for this play disappears. Always bet maximum coins.
- Do I break a royal for a royal?
- No. A dealt royal flush is held whole, every time.
Hold values and hand frequencies on this page are computed by full enumeration: every one of the 2,598,960 five-card deals, and every possible draw from the 47 remaining cards. The evaluator is checked against published hand counts before any page is generated. Full-game return percentages such as 99.54% come from published optimal-play analyses and are attributed rather than derived here, because deriving them requires evaluating every hold for every deal. Pay tables vary by machine, so read the screen.