2nd Nut Kicker on Unpaired Board (UTH)
A lot of times when playing Ultimate Texas Hold’em, you’ll be faced with a 1x river call with a bare minimum kicker. It probably occurs to you that the strength of your call depends on how much of the board the other players have hit. For example, say you’re looking at 1x calling an unpaired board with 2nd nut kicker. Basic strategy says to call if it’s not a scare board, nor gutshot board, and there’s no possible flush on board, or if both your kickers play. (This situation occurs 1.3% of the time if you play basic strategy, and more frequently if you play less aggressively than basic strategy.) Your odds are better if the players at the table connected with the board (made a lot of pairs) than if everyone missed. I ran some simulations to quantify this effect, to show how you can use table information to improve this call.
| total players |
total pairs | notes | ||||
|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | ||
| 2 | +1.3% | +11% | +17% | always call | ||
| 3 | -3.4% | +5.3% | +12% | +21% | +33% | fold if no pairs |
| 4 | -5.3% | -0.0% | +7.8% | +16% | +26% | fold if < 2 pairs |
| 5 | -16% | -5.8% | -1.4% | +11% | +21% | fold if < 3 pairs |
| 6 | -28% | -16% | -4.7% | +4.9% | +14% | fold if < 3 pairs |
So, for example, say you have Jh 2s and the board is Ah Ks Th 9d 3s. With no more information, the odds are that you should call (+19.1%). However, if you’re at a full table (6 players), and all the other players only made 2 pairs with the board, then you should fold. The percentages of the table don’t exactly apply to this specific case, but are averages over 20 million hands, and all cases where basic strategy said to call with 2nd nut kicker.
Discount Gambling 
Is there a reason you are not taking into account 1st nut kickers in other players’ hands?
I wanted to keep the fold criteria as simple as possible, and figured the 2D table above was as much as people would remember. Knowledge of outstanding nut (and 2nd nut) kickers is helpful, but not of the same value as board hits. That’s because if the dealer pairs, you lose all your bets, whereas if the dealer only has a better kicker, you’ll keep your Ante. I leave it up to the player to synthesize in knowledge of nut and 2nd nut kickers among fellow players.
For preflop marginal Kx hands like K5o, are the number of aces in other players’ hands important or negligible?
The number of over cards in the player’s hands is indeed significant for your borderline 4x raise hands. I haven’t looked at it in a while, but the number of high cards in the player’s hands make a difference. But it’s too much information for most people, and too complicated a strategy to specify.
What is a “nut kicker”? Sorry, I am new to poker, and I cant find this definition anywhere.