Why does a straight beat a flush in 3-card poker?
Because with three cards a straight is rarer than a flush. Hands rank by how hard they are to get, and three of a kind is rarer still, which is why it beats a straight.
Of the 22,100 three-card hands, 720 are straights and 1,096 are flushes; 52 are three of a kind.
Every three-card hand
| Hand | Hands | Chance | Pair plus pays |
|---|---|---|---|
| Straight flush | 48 | 0.22% | 40:1 |
| Three of a kind | 52 | 0.24% | 30:1 |
| Straight | 720 | 3.26% | 6:1 |
| Flush | 1,096 | 4.96% | 3:1 |
| Pair | 3,744 | 16.94% | 1:1 |
| High card | 16,440 | 74.39% | — |
Why
In five-card poker a flush is the rarer hand, so it ranks above a straight. With three cards the counts flip: there are only twelve rank sequences for a straight, while any three cards of one suit make a flush. The paytables follow the same order, paying more for a straight than for a flush.