Practical Poker Math

25% chance of winning and a 75% chance of losing. Thus,
you need money odds of something considerably more than
3 : 1 to justify further participation in the hand.
On the other hand, if you consider your 25% chance of
making the draw to win the pot plus the 50% chance that
your opponents will fold to a bet or raise, your total odds
of winning the pot are approximately 60%. With a 60%
chance of winning, you can participate with money odds of
2 : 1 (or even slightly less) instead of the 4 : 1 that are
required if you only consider your 25% probability of
improving the hand.
While it is not always possible to accurately predict an opponent’s
hand or future actions, knowledge of basic odds and
player history will give you a strong indication.
If you only consider the odds of improvement, you can
expect to win only 25% of the time. But with knowledge of
your opponents (and even with some overlap of possibilities),
in this situation you can expect to win well over 50% of
the time with a bet or raise.
The positive application of this concept of Total Odds will
help you discover value plays with good positive expectation
that you might have otherwise missed.
While it is certainly harmful to your bottom line to play with
an underlay, it is equally harmful to your long-term success
to pass on value opportunities that offer significant positive
expectation.
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Total Odds & Real Expectation