TexasHoldEm > Underbetting Is A Bigger Sin Than Overbetting

Making the right-sized bet is hard. Mathematically, you want to make your opponents make unprofitable bets. But, psychologically, they may not always be doing the math. That's when this concept becomes a good one to keep in the back of your head:

No matter what your goal is with the hand, overbetting is always safer than underbetting

This seems counterintuitive, especially since it's so tempting to get focused on preserving one's stack, but that's a dangerous way to think. Better is to concentrate on the possible outcomes when betting on a hand. If you bet too much:

  1. Your opponent may fold (mathematically, you win the pot, $P)
  2. Your opponent may call you or bet into you with a weaker hand, increasing the amount of money you win (you win at least $P + 2$O, your overbet and your opponent's call)
  3. Your opponent may call or bet into you with a stronger hand, increasing the amount of money you lose (You lose $O -- remember, none of the money in the pot already was yours, once it was bet)

But if you underbet:

  1. Your opponent may fold (you win $P)
  2. Your opponent may call you or bet into you with a weaker hand, increasing the amount of money you win (you win at least $P + 2$U)
  3. Your opponent may call or bet into you with a stronger hand (You lose $U)
  4. Your opponent may call you or bet into you with a weaker hand, but make a better hand on the draw, beating you (you lose at least $U)

So let's work this out mathematically. Assuming all scenarios are equally likely, then:

Value(Overbet) = ($P + $P + 2$O - $O)/3 = (2$P + $O)/3

Value(Underbet) = ($P + $P + 2$U - $U - $U)/4 = (2$P)/4 = 0.5$P

So, if you overbet the pot, you increase the expected value of the pot by 1/6$P + 1/3$O, or one-sixth of the total pot size plus one-third of your bet size, versus what you'd make by underbetting the pot.

If you increase your odds of winning the pot, regardless of your bet, by playing tight, aggressive poker, you just improve your expected value from overbetting, because you decrease the likelihood of the negative terms in the above equation coming true -- but you've still got two -$Us in the underbet equation, versus one -$O in the overbet equation. So long as $O < 1.5$U, or your overbet isn't more than one-and-a-half times the underbet you were considering, you're making a profit in the long term by betting big rather than small when you can't decide or need to play the psych-out tactic.


This page last modified on November 12, 2005, at 10:54 PM

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