In the first example of the section, you had A♥ A♠ on a Q♦ 7♦ 2♣ 4♠ board, the pot was $100, you and your holdem opponent each had $400 behind, and your holdem opponent was on a diamond flush draw. Our conclusion was that you should have bet at least $40 because he was 3.9-to-l to make his draw, so you should have offered him no better than 3.5-to-l pot odds.

Let’s reconsider the same example, except now you hold Q♥ Q♠. You have top set instead of an overpair, and the 4♦ and 2♦ make your holdem opponent’s flush, but give you a full house. Your opponent now has seven outs instead of nine, so he’s 5.3-to-l to beat you (7/44). By our earlier reasoning, you should offer no better than 5-to-1 pot odds, so you should bet at least $25 (offering $125-to-$25).

But our earlier reasoning doesn’t hold anymore! Why not? Because if the 4♦ or 2♦ comes, not only do you not lose, but you stand to win your holdem opponent’s remaining $400 on the river. Let’s compare two expectations: one where you make a big bet, forcing your holdem opponent to fold, and another where you check, allowing him to draw for free.

If you bet a lot, forcing your holdem opponent to fold, you’ll win the $100 pot every time. So your expectation is $100.

If you check, then you win $100 whenever no diamond comes (35/44), win nothing when a non-pairing diamond comes (7/44), and win $500 ($100 plus $400) when the 44 or 24 comes (2/44). Your expectation if you check is $102.28.

$102.28 = (35/44)($100) + (7/44)($0) + (2/44)($500)

Because your Texas Holdem opponent will occasionally make a second-best hand and get stacked, you’d prefer that he draw for free than that he fold. The lower bound of your betting range isn’t $25 — it’s $0.

Obviously, you’d rather bet and have your holdem opponent call than check. But you should bet an amount that you’re fairly sure your poker opponent will call, even if that’s less than $25 (although in this case it wouldn’t be)

If your opponent could catch his draw, but still be second-best, tend to bet an amount you’re fairly sure he’ll call. Don’t miss a chance to stack him by blowing him out too early.

Also recommended:

1. When Your Opponent Could Have One of Several Draws
2. Expectation and Multiple Possible Hands
3. An Example of the Play (Bluff on the Turn and River)