The jackpot line pays for the sign, not the player

The measurement

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 0.17%. Make the royal a losing hand and the bet would cost 0.16 of a percentage point more; pay it as an ordinary straight flush and the difference is 0.03 points. Either is less than the difference between two blackjack tables.

What is actually carrying each bet

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 any other single line (31.46%), and it is the smallest number printed. On Let It Ride the pair of tens or better line supplies more than every other line combined (51.82%). 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 pays a fiftieth as much in winnings as a prize seven times the stake occurring once in fourteen.

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 what it pays back. The share attributed to a line is that line's own contribution divided by the total. Every line is counted with the stake it returns: a hand paid 7 to 1 gives back 8 units, which is how keno prints its pays ("9 for 1" gives back 9). The Let It Ride row is the third bet, the one that cannot be pulled back. 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.

Corrected on 18 October 2026: the Let It Ride row left out its commonest paying line, a pair of tens or better at 1 to 1, which inflated every share: the royal flush supplies 0.40% of the return, not 0.68%, and the line doing the work is the pair, not two pair.

Corrected on 19 October 2026: the card games were counted on their winnings ("to 1") and keno on what it returns ("for 1"), two different totals under one heading. Every row now counts what the bet returns, stake included, so the top lines read 0.17% (Trips, was 0.20%), 0.25% (Let It Ride, was 0.40%) and 1.01% (6 Card Bonus, was 1.10%); keno is unchanged. Two sentences were also wrong: three of a kind supplies more of the 6 Card Bonus than any other single line, not more than all the others combined, and the thousand-to-one prize pays a fiftieth as much in winnings as the seven-to-one one, not a hundredth.

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 house edge is in the open dataset under CC-BY. Last computed October 2026.