3rd Nut Kicker on Paired Board (UTH)
I looked a little deeper into the case of calling (1x bet) on the river with 3rd nut kicker against a paired board. Basic strategy (i.e., no other info known) says to call this hand. However, by taking into account how much the other players have “hit” the board, you can improve this decision. Similar to the 2nd nut kicker on an unpaired board analysis, the decision comes down to how many total “good” cards the players hold, relative to the table size. The table below provides an advanced strategy of when to call with 3rd nut kicker given easily obtained table info. A “good” player card is anything that hits the board, or 2nd nut kicker or better.
| players | total player board hits & kickers | notes | ||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | ||
| 6 | -25% | -15% | -5% | +5% | +20% | +30% | +45% | fold if ≤ 3 good player cards |
| 5 | -12% | -5% | +6% | +17% | +28% | +42% | +54% | fold if ≤ 2 good player cards |
| 4 | -4% | +5% | +17% | +27% | +38% | +49% | fold if ≤ 1 good player cards | |
| 3 | +5% | +15% | +25% | +35% | +45% | always call | ||
| 2 | +13% | +23% | +33% | always call | ||||
| 1 | +22% | always call | ||||||
Practically, this advanced strategy is very intuitive, and you’ll find it agrees with your experience. When no one hits the board, or even has a playable kicker, your chances of winning with a minimum kicker go down considerably. However, when everyone hits the board, sometimes multiply (e.g., full house), your chances increase considerably. The table above quantifies this effect, and shows you the relative strength of your hand for the range of scenarios.
Overall, you’ll find the 3rd nut kicker on a paired board decision comes up about 2.5% of the time. While it’s not really frequent, it’s a decision that most players mull over. Knowing the advanced strategy will help you make your final decision quicker, and with more confidence.
Discount Gambling 
Just got back from Harrah’s. Did pretty good over all. Had a bad start on UTH but recovered a little later. Took $100 to Mississiipi about 2030 and ended up with a grand winners by 1000.