Odds on the river

Question

What are the odds of somebody getting 4 of a kind on the river to beat your already achieved full house.

Also if it can be calculated, what would the odds be for losing a winning hand on the river

A one-outer is 1/44 probability, or 43 to 1 odds, 2.27%. – Lee Daniel Crocker Sep 17 '21 at 23:26 — Lee Daniel Crocker, Sep 17 '21 at 23:26

score 1 · Answer 1 · answered Sep 16 '21 at 15:50

The odds of drawing the card that you need to turn a three of kind into quads are 2.1 percent.

This article has a great explanation and more. https://www.oddsshark.com/poker/four-kind-odds

From the site:

2%: Percent chance to hit quads by the river with a pocket pair (1 in 122)

0.2%: Percent chance to hit quads on the flop with a pocket pair (1 in 407)

0.001%: Percent chance to flop quads without a pocket pair (1 in 1000)

0.0001%: Percent chance that quads get beaten (1 in 100,000)

score 1 · Answer 2 · answered Sep 16 '21 at 16:41

Assuming quads is the only hand that beats you, there's only 1 card on the deck that makes you lose, while the remaining 43 make you win.

Since the river is just one card, the chance of your hand getting beaten is 1/44, or about 2.2%. You win the remaining 43/44 (about 97.8% of the time)

Odds on the river

2 Answers2