This is, of course, nonsense.
To be precise, it only holds in one specific case:
- your opponent has a made hand
- you have nothing (well, a draw)
- if you do not improve, you lose the hand
- if you do improve, you are guaranteed to win
At this point I looked at my odds in PokerOffice. I was not happy about the situation, but the combined odds of making trips and making my straight (1.6:1) were slightly better than the pot odds I was being offered (1.8:1), so I called.
My opponent flipped over 9-8 offsuit for a total bluff. I had not even considered that I might be ahead... I should have though, it was (somewhat) reasonable that he might have AK or something, and figured he had showdown value.
In general of course, deciding whether or not to call should be based on much more than just comparing two numbers (pot odds and your odds to improve).
- Your opponent may improve. More generally, you might improve but still lose. For example, in the case above, he might have had an Ace, so that a 3 on the turn or river would give me trips but still kill me.
- You may have implied odds. When you are on a flush draw, you can call against the odds (up to a point!) in the hope that your opponent will put in more money after you make your flush.
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