The measurement
| Bet | Top prize | Pays | Its share of the return |
|---|---|---|---|
| Ultimate Texas Hold'em, Trips | Royal flush | 50 to 1 | 0.20% |
| Let It Ride | Royal flush | 1,000 to 1 | 0.68% |
| Three Card Poker, 6 Card Bonus | Royal flush | 1,000 to 1 | 1.10% |
| Keno, 8 spot | Catch all eight | 25,000 to 1 | 14.94% |
Read the first row. The Trips bet advertises a royal flush at 50 to 1. Of everything that bet returns to players, the royal flush supplies 0.20%. Take the royal off the pay table entirely and the bet would cost a fifth of a percentage point more, which is less than the difference between two blackjack tables.
What is actually carrying each bet
| Bet | The line doing the work | Pays | Its share |
|---|---|---|---|
| Ultimate Texas Hold'em, Trips | Flush | 7 to 1 | 26.07% |
| Let It Ride | Two pair | 2 to 1 | 42.08% |
| Three Card Poker, 6 Card Bonus | Three of a kind | 7 to 1 | 29.91% |
| Keno, 8 spot | 7 hits | 1,500 to 1 | 33.10% |
Two of these are the lowest-paying line on their own table. Three of a kind at 7 to 1 supplies more of the 6 Card Bonus than every other outcome combined, and it is the smallest number printed. The pattern is not an accident of these four schedules; it follows from how the arithmetic works. A prize a thousand times the stake occurring once in a hundred thousand hands returns a hundredth of what a prize seven times the stake occurring once in fourteen does.
Why the tables are built this way
A pay table has to do two jobs at once. It has to return a specific fraction of what is staked, which is arithmetic, and it has to make someone want to place the bet, which is not. The top line does the second job almost exclusively.
That is not deception. Every figure is printed, nothing is hidden, and a player who computes it can see what we just computed. But it does mean the number the eye lands on is the number carrying the least information about what the bet costs, and it is a reliable enough relationship to use as a habit.
The habit this suggests
When you look at a new pay table, read the bottom lines first: the small payouts on common hands. They decide what the bet costs and they are where casinos differ from each other. The top line is where they all look the same, because it costs almost nothing to be generous about something that almost never happens.
This is the same conclusion keno reaches from the other direction, where the board advertises 25,000 and the seven hit line quietly supplies twice as much of the return. And it is why the Pair Plus flush line matters more than any jackpot: moving that one payout from 4 to 3 takes the bet from 2.32% to 7.28%, which is a bigger change than deleting a royal flush from any table here.
How this was computed
Each bet's return is the sum, over every outcome, of that outcome's probability times its payout. The share attributed to a line is that line's own contribution divided by the total. Nothing here is estimated and no pay table is invented: the frequencies come from complete enumerations of 2,598,960, 20,358,520 and 133,784,560 card hands, and from keno's exact hypergeometric probabilities.
Figures are produced at build time by
five_card_math.py, six_card_math.py,
seven_card_math.py and side_games_math.py. Each
checks its own category counts before anything is written; the six-card
engine checks two of them against closed-form formulas rather than
against a remembered table, after an earlier version of that check was
itself wrong in two places while the engine was right. Every figure is in
the open dataset under CC-BY. Last computed
September 2026.