Put one coin in and the paytable column for one coin is lit. Put five in and the column for five is lit. Read across the rows and almost everything is simple multiplication: four of a kind pays 25 per coin, so it pays 25, 50, 75, 100 or 125 for one to five coins. The royal flush is the exception. It pays 250 per coin for one, two, three or four coins, then 800 per coin at five. This post is about what that one row does to the return, and why it makes the fifth coin the best coin you stake.
The jump in numbers
At four coins a royal flush pays 4 × 250 = 1,000. Add a fifth coin and the same hand pays 5 × 800 = 4,000. One extra coin staked, 3,000 extra on the top prize. Without the bonus the fifth coin would only have taken the royal to 1,250, so the bonus is worth 2,750 on its own. Per coin, 800 is 3.2 times 250.
What it does to the return
Under correct play a royal arrives about once in 40,400 hands, which is 0.0000248 of hands. The royal's share of the return is that frequency times the payout per coin:
- At 800 per coin: 800 × 0.0000248 ≈ 0.0198, or 1.98 points of return.
- At 250 per coin: 250 × 0.0000248 ≈ 0.0062, or 0.62 points.
The difference is 1.36 points. Every other row is proportional to the bet, so the full-pay 9/6 table returns 99.54% at five coins and 99.54 − 1.36 = 98.18% at one to four, if you hold the same cards. You can do slightly better at fewer coins by re-optimising your holds for the smaller prize, which brings the figure to about 98.4%. I quote that second number from the standard published analysis rather than from the subtraction, so treat it as approximate.
The fifth coin returns more than it costs
Take the figures at face value. Four coins bet at about 98.4% return about 3.94 coins on average. Five coins bet at 99.54% return about 4.98. The fifth coin therefore adds roughly 1.04 coins to the expected return for a cost of one coin. It is the only coin in the whole table that on average comes back with more than you put in, and the royal row is the reason.
Compare the expected loss per hand, using the same figures:
- Four coins: 4 × (1 − 0.984) ≈ 0.064 coins per hand.
- Five coins: 5 × (1 − 0.9954) ≈ 0.023 coins per hand.
Betting more per hand costs less per hand, which looks backwards until you remember that the extra coin is the one that carries the 4,000. Any amount of time spent at one to four coins is time spent on a weaker version of the same game. The standard rule follows: if you cannot afford five coins a hand at the denomination in front of you, move to a smaller one.
The catch
All of this is an average over a very long run, and the long run is very long. Five coins × 40,400 hands is 202,000 coins staked for each royal, on average. Over 10,000 hands the chance of seeing at least one is about 22%, so most sessions never reach the row that earns the extra return. What you feel at the machine is the 97.6% game underneath, with the bonus held back for a hand that mostly does not come. That is why max coin is the right choice for the maths, and why it can still feel like a lot of staking for little visible reward.
Fewer coins, a slightly different strategy
When the royal is worth less, drawing for it is worth less. Take the case from the four-to-a-royal decision: you hold A♠K♠Q♠J♠ and a fifth spade, a made flush paying 6 per coin. Break it and keep the four high spades, and 47 cards remain. One is the T♠, seven are other spades that make a flush at 6, three are tens of other suits that make a straight at 4, and twelve pair one of your high cards for 1.
- At 800 per coin: (800 + 42 + 12 + 12) ÷ 47 ≈ 18.4 per coin.
- At 250 per coin: (250 + 42 + 12 + 12) ÷ 47 ≈ 6.7 per coin.
Both beat the made flush's 6, so the hold is right either way, but at four coins or fewer it wins by a sliver rather than by a factor of three. A correct chart is written for one pay column, which is another reason to stay on five coins: the strategy you learned is the strategy you use. The paytable guide covers how to read the rest of the table.
What to check before you play
- Look at the royal flush row first. 800 in the five-coin column means the bonus is there; a smaller number means the machine is weaker than its other rows suggest.
- Read the full house and flush rows, 9 and 6 for the full-pay game, next.
- Bet five coins every hand, or change the denomination so that you can.
Video Poker: Jacks or Better offers Jacks or Better, Deuces Wild, Bonus Poker and Double Bonus, each with its full paytable always on screen, so the royal row is the first thing to check. Strategy hints can point at the correct hold while you practise. It plays offline, and the chips are free and have no cash value.