Poker Math That Matters

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We’re starting to get a glimpse at how tricky it can be to
properly size our value bets. It’s takes a very good grasp of our
opponent’s strategy to do this well at the table. That requires
hard work and experience, but the rewards show up with a much
improved win rate.
As a general rule, when you're value-betting, you want your
opponent calling with more than 50% worse hands than better
hands. To demonstrate this, we can imagine we bet $1. We'll let
x equal the percent villain calls with a worse hand. So 1-x will
be the percentage he calls with a better hand.
x($1) + (1-x)(-$1) > 0
1x -1 + 1x > 0
2x = 1
x = 0.5
Given this, sometimes we have assumptions that do not allow us
to bet. For example, let's say we're on the river with T♠T♣. The
board has come down 2♥3♦8♥J♦A♥. Our opponent is a
conservative, timid player. We've bet half-pot on both the flop
and turn. Our opponent has called both our bets. Once he called
the turn, we gave him the assumed range of 99, 89 or a flush
draw. The A♥ on the river removes a lot of the flush draw
combinations we had given him. We feel he'll play mostly
connected, suited hands with perhaps a few 1-gappers in his
range. So, we'll give him about 10 combinations of made
flushes. There are 18 combinations we beat, and 10 have us
beat. We have the best hand the vast majority of the time at
64%. However, this doesn't mean we should bet. Since our
opponent is conservative and timid, the A♥ is likely to have
scared our opponent. It would be a reasonable to assume that he
will no longer call a bet with either his 99 or 89. That leaves