Hold’em vs. Dealer › Questions
Should you bet 1x or fold on the river in Hold’em vs. Dealer?
Bet 1x with any pair that uses one of your cards. With nothing, count the dealer’s outs, the unseen cards that would beat you: bet with fewer than 21, fold with 21 or more.
Folding always costs 2 units, the ante and the blind. The 21-out rule gives the exact best river play on 98.2% of 5,000 random rivers.
River spots, bet or fold
| Your cards | Board | Dealer outs | Bet 1x | Best |
|---|---|---|---|---|
| A♣ 10♦ | K♥ K♠ 4♣ 4♦ 2♥ | 4 | +0.6535 | Bet 1x |
| A♣ 7♦ | K♥ 9♠ 4♣ 3♦ 2♥ | 15 | −1.6798 | Bet 1x |
| K♣ 7♦ | Q♥ 9♠ 4♣ 3♦ 2♥ | 19 | −1.9263 | Bet 1x |
| J♣ 7♦ | Q♥ 9♠ 5♣ 3♦ 2♥ | 23 | −2.1566 | Fold |
| 8♣ 7♦ | K♥ Q♠ J♣ 4♦ 2♥ | 27 | −2.2535 | Fold |
| 7♣ 2♦ | K♥ 9♠ 2♣ 5♦ 3♥ | 12 | −1.3333 | Bet 1x |
Fold is always −2.0000: you give up the ante and the blind. Average result per unit of ante (the blind equals the ante; trips not included), with the best play on every later street. Exact: every card that can still come and every dealer hand.
Why
Folding at the river costs the ante and the blind, two units. Betting 1x puts one more unit at risk to keep both in play, so you only need to win a modest share of the time for the bet to cost less than folding. A dealer “out” is a hole card that would beat you; with fewer than 21 of the 45 unseen cards doing that, enough dealer hands lose to you, or fail to qualify, that betting comes out ahead of folding.