Everything so far has been about the ante and the play, which is the cheap half of the table. This chapter is about the expensive half, and about the single digit that governs it.
Pair Plus is a bet on your own three cards. It has nothing to do with the dealer at all. You put up a wager, and if your hand is a pair or better it pays according to the sign; if it is not, it loses. The dealer’s cards are irrelevant, the qualification rule is irrelevant, and your play-or-fold decision is irrelevant.
So the whole of the bet is a distribution and a pay table, and here is the distribution, which does not vary anywhere on earth:
| Hand | Number of the 22,100 | Frequency |
|---|---|---|
| Straight flush | 48 | 0.2172% |
| Three of a kind | 52 | 0.2353% |
| Straight | 720 | 3.2579% |
| Flush | 1,096 | 4.9593% |
| Pair | 3,744 | 16.9412% |
| Nothing | 16,440 | 74.3891% |
Three quarters of the time this bet simply loses. That is not a criticism; it is the shape of the thing, and the pay table is built around it.
Now the four signs you will actually meet, in the order pair, flush, straight, three of a kind, straight flush:
| The sign | House edge |
|---|---|
| 1-4-6-30-40 | 2.317% |
| 1-4-5-30-40 | 5.575% |
| 1-3-6-30-40 | 7.276% |
| 1-3-6-25-40 | 8.453% |
Read the first and third rows together, because that is the whole chapter.
The best common sign and the commonest sign differ in one digit. A flush pays 4 instead of 3. Everything else on the two tables is identical. And that one digit is worth 4.959 percentage points, which is to say the worse table costs you more than three times as much.
Why is one digit worth so much? Because flushes arrive 4.9593% of the time, and one extra unit paid 4.9593% of the time is worth 4.959% of your wager. The arithmetic is that direct. It is the single most efficient thing to know in this book: two seconds of looking, five percentage points.
Set that against the base game. The ante and play, solved perfectly, costs 3.373%. The good Pair Plus sign costs 2.317%, which is better than the base game. The bad one costs 8.453%, which is nearly two and a half times worse.
So Pair Plus is not a good bet or a bad bet. It is entirely a question of the sign above it, and it is the only wager in the casino I know of that swings from better-than-the-main-game to substantially-worse on the strength of a single printed character.
One warning about the far end of the table. Players look at the 40 for a straight flush and the 30 for trips, because those are the big numbers, and rooms know it. A table that pays 50 on the straight flush and 3 on the flush is advertising with the number that arrives once in 460 hands while economising on the one that arrives once in twenty. Weight what you read by how often it happens. Almost all of the value of this bet lives in the pair and the flush, and almost all of the marketing lives at the other end.