Video Poker Math: RTP, Volatility, and Budgeting

Understand video poker RTP, volatility, and bankroll math in Canada. See exact hourly odds, swings, and CAD budgeting benchmarks.

A video poker session can be described by the return of the pay table, the hit rate, the swing of a single hand and the size of your stake. Here each of those is defined, the best-known games are compared, exact odds show how far a 720-hand hour can drift from the average, the royal flush and the gap between a typical hour and the average are examined, and a closing section turns coin values into budgets.

Reading RTP and House Edge Correctly

RTP stands for return to player: over a very long run, the part of every dollar staked that is paid back when each hand is played perfectly. Whatever is left is the house edge. For 9/6 Jacks or Better that is 99.54% returned and 0.46% kept, an expected cost of C$4.56 on each C$1,000 wagered.

The return of video poker can be calculated exactly. Each of the 2,598,960 starting hands has a best hold, and averaging over every outcome gives a constant for any pay table. So when a full house and a flush shrink from 9 and 6 to 8 and 5, the expected cost climbs from C$4.56 to C$27.02 per C$1,000. In that sense a return is a property of the table and not a promise about your next hour.

Read every return with three caveats. It presumes flawless holds, so errors pull it down, and the guide that prices each hold mistake puts numbers on that. It presumes a five-coin bet wherever the royal flush pays extra on the fifth coin. And it is a long-run average that no individual session comes anywhere near.

The Three Dials: Return, Hit Rate, and Swing

Hit rate is the share of hands that pay something, even if only the bet back. Swing, the standard deviation, measures how widely one hand’s payout varies, expressed in bets; the wider it is, the more the payout depends on rare big hands. The table below puts all three side by side for popular games, together with the expected result of a 720-hand hour at C$1 a hand, which is C$720 wagered.

Two points. First, swing and return are separate things: Triple Double Bonus 9/7 posts 99.58% with a swing of 9.9, nearly the 99.54% return of 9/6 Jacks or Better, whose swing is only 4.4. More swing changes the shape of the payout, not its average. Second, games over 100% display a gain in the final column, but that is an average across a vast number of hours, not the result of a typical one. The next section explains why.

What One Hour Can Look Like at 720 Hands

Ontario’s Standard 2.18 requires at least 2.5 seconds between the start of a game and the next game cycle. At that floor an hour holds at most 1,440 game cycles, so the 720-hand pace in our examples is half of the ceiling. Each row below comes from the exact distribution of results over 720 hands at C$1 a hand. In a poor hour, one hour in 20 does worse. A middle hour is the median, which half of all hours beat, and in a good hour only one hour in 20 does better.

Take 9/6 Jacks or Better. Its expected result for an hour is a loss of C$3.28, but the middle hour loses C$19 and only 35.9% of hours end ahead. Rare big hands pull the average upward without lifting most hours, which leaves the typical hour below it. Triple Double Bonus 9/7 expects almost the same loss, yet its middle hour loses C$96 and one hour in 20 loses more than C$225.

How does the picture change over longer sessions? The next table tracks the chance of ending ahead as the hand count grows, still at 720 hands an hour.

Follow 9/6 Jacks or Better across its row. The chance of ending ahead shrinks as the sample grows, from 39.2% after 100 hands to 29.3% after 3,000, because the cost accumulates steadily and the typical outcome slides below zero. Triple Double Bonus 9/7 moves the other way, climbing from 23.2% to 41.0%, since extra hands give its rare big prizes more chances to appear. Even so, the median result after 3,000 hands remains a loss of C$136, which shows that better odds of finishing ahead are not the same as good odds.

The Royal Flush Share of the Return

The royal flush supplies only 1.98 percentage points of the 99.54% that 9/6 Jacks or Better returns. Take it away and the figure drops to 97.56%. Expect a royal roughly once per 40,391 hands, about 56 hours at 720 hands an hour. The table converts that into odds for several amounts of play:

In practice most sessions are played without ever seeing the royal, so the rest of the return has to arrive in smaller lumps. Even a flawless player has a 70% chance of going 20 hours without one. That is simply how this game behaves, and it means no short session can pass judgment on a pay table.

How Long Until a Return Becomes Visible

The average of N hands wobbles less than a single hand does. The swing of one 9/6 hand is 4.42 bets, and the average return over N hands wobbles by that figure divided by the square root of N. The table expresses the wobble in percentage points of the money wagered.

The edge of the game is 0.46 points, and the gap between 9/6 and 8/5 is about 2.2 points, so both sit far inside the spread of a normal session. Shrinking the spread to 1 point takes about 195,000 hands, roughly 270 hours at this pace. No sample of play that size separates a 9/6 table from an 8/5 one; the table on the screen does, which is what our guide to reading pay tables teaches.

Choosing a Coin Size That Fits Your Budget

Choose the budget first and the coin size second. If the budget covers only the average cost, an ordinary bad hour will break it, so compare your stake with the poor hour from the earlier table: 98 bets on 9/6 Jacks or Better and 225 bets on Triple Double Bonus 9/7. Multiplying by the cost of a hand at each coin value gives the figures below, always at five coins a hand.

Working backwards: if an hour should cost no more than C$100, a poor 9/6 Jacks or Better hour fits the C$0.20 coin, at C$98, and does not fit the C$1 coin, at C$490. Even a poor hour is not the worst one, because one hour in 20 does worse, so stake only money you can afford to lose entirely, and give yourself a time limit next to the money limit, since speed multiplies cost.

Related Reading on Video Poker

The series has seven other guides, running from the first deal to the provincial rules. Pick one below or return to the video poker hub:

• the starter guide to video poker: what a hand costs, why the fifth coin matters and where regulated play is available.
• video poker hands and pay tables: how likely each hand is, what it adds to the return and what a 9/6 label tells you.
• the Jacks or Better variants guide: return, hit frequency and swing for the best-known pay tables.
• how wild cards reshape video poker: what happens to the lowest paying hand and which holds turn upside down.
• multi-hand video poker and Ultimate X: extra lines and carried multipliers, and what each does to cost and swing.
• common video poker mistakes: short pay tables, fewer than five coins, broken flushes and more.
• video poker rules and safety in Canada: provincial models, Ontario’s standards and the tools licensed sites provide.

Averages Describe the Crowd, Not Your Hour

Each figure above summarizes a crowd of hands, and your session is a single draw from it. Video poker is entertainment you pay for: the pay table bakes in the expected cost, the swings decide how a given hour feels, and no return, table or strategy guarantees a profit. Settle on a budget and a time limit before dealing, and use the spending caps, breaks and self-exclusion options explained on our responsible gambling page.

Author:

Lucas Portela

Owner, BoldGambler • Avanhandava/SP

Oddsmaker, affiliate and content creator in the iGaming industry.

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