Hold percentage is the share of the coins put into a machine that the machine keeps. Add up the coins in, subtract the coins paid out, and divide by the coins in. If 500,000 coins go in and 497,700 come out, the machine has held 2,300 of them: 2,300 ÷ 500,000 = 0.46%. The return is whatever is left over, here 99.54%.
Those are the numbers for a 9/6 Jacks or Better paytable played correctly, which is why the example looks tidy. A real machine's hold rarely does. It is a different kind of number from the return printed in a paytable guide, and mixing the two up leads to some confident and wrong conclusions.
A calculation and a measurement
The return of a paytable is worked out from the table and from the best possible strategy. Nobody has to play a hand to produce it. The hold is counted from hands that were actually dealt, to actual players, in an actual period. The two agree only when three things line up: enough hands, players who hold the right cards, and bets of the size the paytable assumes. Each one can fail.
| Machine | Return | Long-run hold |
|---|---|---|
| 9/6 | 99.54% | 0.46% |
| 9/5 | 98.45% | 1.55% |
| 8/6 | 98.39% | 1.61% |
| 8/5 | 97.30% | 2.70% |
| 7/5 | 96.15% | 3.85% |
| 6/5 | 95.00% | 5.00% |
Too few hands
A single hand of 9/6 Jacks or Better has a standard deviation of 4.42 bets, as the variance post works out. Averaging over more hands shrinks the spread, but only with the square root: after n hands, the measured return is typically within 4.42 ÷ √n of the true one, as a fraction of the coins in.
Take 100,000 hands at five coins, which is 500,000 coins in. The expected hold is 0.46%, about 2,300 coins. One standard deviation of the machine's net result is 4.42 × √100,000 × 5, about 6,990 coins, which is 1.4 points of the coins in. The expected hold sits only a third of a standard deviation above zero, so roughly one stretch of that length in three would show the machine paying out more than it took. Treat the one-in-three as a rough figure: only about 2.5 royals are expected in 100,000 hands (100,000 ÷ 40,400), and a distribution that depends on so few of them is lumpy.
The practical consequence is that a hold figure from one machine over a month says almost nothing about its paytable. It takes about a million hands before the typical swing, 0.44 points, falls to the size of the 0.46-point edge (the swing equals the edge at a little over 900,000 hands).
The wrong players
The return in the table assumes correct play on every hand. Every mistake, such as breaking a made flush for a straight draw or keeping a kicker with a pair, costs something and adds to the machine's hold. No player can push the long-run hold below the correct-play figure, so errors can only move it in one direction, upwards.
That makes a measured hold ambiguous. A hold of 2.70% might be an 8/5 machine with flawless players, or a 9/6 machine whose players give away 2.24 points between them (2.70 − 0.46). The number alone cannot say which. Nor does it say anything about your own play, which is the one part you control. The Jacks or Better hold order is the cheapest way to move your personal figure towards the paytable's.
The wrong bet
The table's returns also assume the maximum bet of five coins. The royal flush pays 800 per coin at five coins but only 250 per coin at one, a difference of 550 per coin on a hand that arrives about once in 40,400. That is 550 ÷ 40,400 = 1.36 points of return, or about 1.4. The same 9/6 glass, played at one coin, holds roughly 1.8% instead of 0.46%.
Hold depends on the paytable, on the players and on the bet, and only the first of those is printed on the machine. A low hold figure is not evidence of a good paytable, and a high one is not evidence of a bad one.
What to read instead
Everything the player controls is visible before the first hand. Read the full-house and flush rows, since they identify the machine (the full-pay ladder prices each cut), bet the maximum coins, and hold the cards the strategy says to. Video Poker: Jacks or Better keeps a paytable for every variant on screen and has strategy hints you can turn on, so the paytable is always in front of you to check against.
Hold also leaves out how violently a machine pays, which is a separate property. Two paytables can return the same amount and feel very different over a session, because the spread comes from how much of the return sits in rare hands. That is covered in the variance post, and what it means for a stack in bankroll and session length.
Hold is a useful figure for the people running a bank of machines, who see millions of hands. For one player in one sitting, the paytable's return is the number worth knowing, and the hold is mostly noise.
Video Poker: Jacks or Better has real casino paytables for Jacks or Better, Deuces Wild, Bonus Poker and Double Bonus, with a full paytable for every variant always on screen. It works offline, with no ads and no real money, so the chips have no cash value.