Maximum 3-Betting Ranges

We now know enough math and theory to figure out what 3-betting ranges make sense based on which position opened.

In order to accomplish a quick estimate, we’ll assume players are using the same 3-betting frequencies from all possible remaining positions.
This assumption is dropped in the final hand chart at the end of this section, but will be useful now for giving us a starting point for figuring out what sort of 3-betting ranges are possible.
We should also note that simply dividing 30 percent by the number of players left to act will give us an accurate estimate for the maximum amount each player can 3-bet, but it will not get us the exact correct answer.

That’s because the estimate does not take into account the fact that two or more players can have a hand which will 3-bet the same open.

Therefore, we should instead figure out how often each player must not 3-bet in order for the open to be 3-bet less than 30 percent total.
Here’s an example. Since there are five players left to act when the UTG player opens, we must multiply the odds each player does not 3-bet the open together to get the correct answer.