Odds to improve your Hold'em hand by the river
First things first. Two weeks ago, this column provided a Hold'em odds chart for taking your hand on the flop and improving it right on the very next card (fourth board card). That's valuable information, since you can sometimes correctly call the smaller bet on the flop to try to improve, but if that misses, you should not call the bigger bet on the turn.
Regrettably, I included a silly error in the last entry of the chart. That entry was intended to provide your odds against making a flush on the next card with a suited hand, when the flop contains two cards of your suit.
Problem was, I depicted all three cards in the flop as being the same suit! That of course, would already be a flush! The flop should've contained only two clubs (while you held two clubs in your hand). I apologize for my careless oversight, especially to those of you who read it and said, "Whaa?"
While we're on that subject, this would be a good time to supply your odds of improving certain hands if you played them all the way to the river. That takes a far greater investment than just paying to see the turn card.
In a $5/$10 limit Hold'em game, for example, the bet on the flop is $5, but the bet on the turn is $10. So on the flop, it'll cost you five bucks to see the turn card, but $15 to go all the way to the river. Same thing if the stakes were $20/$40 -- the flop bet costs $20 and the bet on the turn is an additional $40.
With that being true, only hands with greater potential and more likely odds-to-fill can afford to take that kind of heat. Here are most of those hands with their associated odds against improving by the time you get to the river.
Your hole cards: J/10
Flop is: K-Q-2
Make a straight: 2-to-1
Your hole cards: club/club
Flop is: club/club/spade
Make a flush: 2-to-1
Your hole cards: 6/6
Flop is: Ad/Jd/6d (show suit symbols)
Make full house: 2-to-1
Those first three hands are classic "go-all-the-way" situations. Even when you flop at "set" and are convinced you're up against a made flush (as in example 3), you'll still fill up often enough to go to the river.
Now these next two hand situations are much more in question. If your hand looks like it's currently beaten, you usually need the pot to be pretty big to make playing all the way worthwhile.
Your hole cards: Q/J
Flop is: Qd-Jd-10d (show suit symbols)
Make full house: 5-to-1
Your hole cards: 9/10
Flop is: A-6-7
Make straight: 5-to-1
Finally, here are some "pie-in-the-sky" draws that might tempt you to go all the way to the river, but are virtually never worth the cost. When you flop one of these, just get rid of it!
Your hole cards: 6c/7c (show suit symbols)
Flop is: Ac-Kh-2d: (show suit symbols)
Make a flush: 23-to-1
Your hole cards: 7/8
Flop is: 9-3-2
Make a straight: 22-to-1
Your hole cards: 9/9
Flop is: A-K-10
Make trips: 11-to-1
As always, you need to compare the expected final size of the pot (excluding your own future bets) with the odds against making your hand. These last three longshots will seldom, if ever, pay you back enough money when you hit to cover all the times you miss.