Three Card Poker

A line's worth is simply how often that hand is dealt. Raise the flush from 3 to 4 to 1 and the bet returns 4.96% more of every stake; raise the straight flush by five whole units and it returns barely one point more, because the hand almost never comes. The small lines at the top of a schedule are advertising; the two at the bottom are the price.

Every combination of the figures a Pair Plus circle commonly prints below a 40 to 1 straight flush, from the best to the worst. For a table paying 35 to 1 on the straight flush add 0.22% for each of the five units; for 45 or 50 to 1 subtract it. The flush line splits the table in two: every schedule in the lower half carries a 3-to-1 flush and costs 4.96% more than its twin above.

The first table is all the arithmetic there is. A Pair Plus bet returns the sum of each line's payout times that line's worth, and loses the stake on every high-card hand, which is 74.39% of deals. The 40/30/6/4/1 table therefore gives up 2.32%; drop its flush to 3 and it gives up 7.28%, the difference being exactly the flush line's worth.

The key number: The flush line is worth 4.96% of the stake per unit of payout, the largest lever on the circle after the pair itself, which is why a 3-to-1 flush never belongs to a cheap schedule, whatever it prints at the top.

The same logic runs the other way. A schedule generous enough at the top can turn the bet in the player's favour: pay the straight flush 50 and three of a kind 33, with 6, 4 and 1 beneath, and the house edge becomes -0.56%, a negative figure, which is the arithmetic reason such a table is not printed anywhere a casino intends to keep.

Each row is a complete solve of every player hand against every dealer hand, with the dealer qualifying on queen high. The bonus is paid on a raised hand whatever the dealer holds, so its lines are worth exactly what the Pair Plus lines are: one unit on three of a kind moves the ante by 0.24%, one unit on the straight flush by 0.22%. The last column is the one that does not move: the raising border stays at queen-six-four on every row.

A player who puts one unit on the ante and one on Pair Plus every hand is making a two-unit bet whose price is the average of the two. With the usual ante bonus and a Pair Plus circle printing 40/30/6/4/1, the two units together cost 2.84%, less per unit than the ante alone; with the 3-to-1 flush version of that circle they cost 5.32%, more than a glance at the top of the schedule would suggest.

The rule: Whether adding Pair Plus makes a session cheaper or dearer per unit is decided by the Pair Plus schedule alone: below the ante's own price it lowers the blend, above it it raises it, and the ante bonus has no say in that comparison.

What the second bet certainly does is change the shape of a session. Pair Plus settles on the deal, before any decision, and loses on three hands in four; the ante is decided later and more evenly. A player who wants the quieter game plays the ante alone, whatever the schedule.

Every figure on this page is a lookup once a table's two schedules are known, and both are printed on the felt or a tap away in the rules. On the Pair Plus circle, read the flush line first and the three-of-a-kind line second; the straight flush figure, however large, moves the price least. On the ante bonus, read the three-of-a-kind line, which is where tables differ most, and confirm that the dealer qualifies on queen high rather than something else.

The tables listed below run on play credits and show their schedules in full, so a reader can open one, find its two lines in the grids above, and know what the game costs before a single real chip is staked. A title whose schedule is not in the grids is priced from the first table in a few seconds of arithmetic.