The flop: bet 2x or check
Hidden pairs, two pair and good flush draws are 2x hands.
You checked before the flop, so your hand wasn't strong enough for 4x. Now three community cards are out and you know much more. Bet 2x when the flop gives you any of these. This is the middle raise of the Wizard of Odds strategy, whose flop rules are credited there to James Grosjean:
- Two pair or better that uses at least one of your cards. Examples: on , or on .
- A hidden pair: one of your cards pairs the board, or you hold a pocket pair. The one exception is pocket deuces. Example: on .
- Four to a flush, with a ten or better of that suit in your hand. Example: on .
Check everything else. That includes a pair that's only on the board, straight draws, and weak flush draws.
A hidden pair is the key idea. If the flop is , those kings belong to the dealer as much as to you, so "you have a pair of kings" means nothing. But a pair that uses your card, even a small one, puts you ahead of every dealer hand that missed.
| You | Flop | Bet 2x | Check | Best |
|---|---|---|---|---|
| +0.865 | +0.429 | 2x (hidden pair) | ||
| +0.641 | +0.267 | 2x (hidden pair) | ||
| −0.180 | −0.315 | 2x (even bottom pair) | ||
| +2.517 | +1.726 | 2x (two pair) | ||
| +0.349 | +0.318 | 2x (flush draw, ten in hand) | ||
| +0.174 | +0.261 | Check (flush draw, nine high) | ||
| −1.548 | −1.144 | Check (pair only on the board) |
Look at on . A pair of threes isn't pretty, and the hand loses money however you play it. But betting 2x loses less than checking, because the dealer misses this flop most of the time.
Show the math: How the flop EV is computed
For a flop decision the app goes through every turn and river pair (C(47, 2) = 1,081) and every dealer hand (C(45, 2) = 990): 1,070,190 showdowns.
- Bet 2x: EV = average over all showdowns of the settled result with Play = 2.
- Check: for each turn and river, take the better of "bet 1x" and "fold (−2)", then average.
on : EV(2x) = 154367/178365 ≈ 0.8655; EV(check) = 10203/23782 ≈ 0.4290.
Quiz
Board:
You checked preflop. What's the best flop play?
- Bet 2x
- Check
Show the answer
A: Bet 2x. Your 7 pairs the board: a hidden pair. Bet 2x.
Quiz
Board:
What's the best flop play?
- Bet 2x
- Check
Show the answer
B: Check. The pair of kings is on the board. The dealer has it too. Check.
Quiz
Board:
What's the best flop play?
- Bet 2x
- Check
Show the answer
A: Bet 2x. Four to a flush with a ten of hearts in your hand. Bet 2x.
Quiz
What's a "hidden pair"?
- A pair on the board
- A pair that uses at least one of your two cards
- Any pocket pair, including deuces
- A pair the dealer can't see
Show the answer
B: A pair that uses at least one of your two cards. One of your cards pairs the board, or you hold a pocket pair. On the flop, pocket deuces are the exception.