spoonitnow's 5000th Post: Game Theory and Poker

Originally Posted by daviddem

This kinda translates into "I need at least 50% equity against villain calling range to make a v-bet", doesn't it?

Exactly.

Some interesting things about EV calc's:
1) All EV calc's start positive (nut hands are winners), and
2) always have a slope less than or equal to 0 (good hands win more than, or at least as much as, bad hands),
3) whether Hero bets, calls, checks or folds (no line will make a worse hand have more EV than a better hand when both are played correctly).

For the mathematically literate:
Given that EV is a function of hand x and betting line L (where L includes all prior actions and the current action), then:
All EV(x|L) are monotonically decreasing functions.

conclusions, taking into account that a fold is always 0EV:
If the EV of a call falls below 0 for any value, then a fold is less -EV than a call for all greater values. (If it's -EV to call with hand x, then it is -EV to call with any hand that can't beat x.)

If the EV of any bet is below 0 for any value, then Hero can not bluff for exploitation. (When Villain calls too much, Hero exploits by not bluffing.)