Today we are focusing on a common point where you can not stand against a tough button opponent who opens his 3BB to 9BB with 3 bets in Cutoff.
Since your opponent has made a triple increase in the button relative to the opening slope of the Cutoff seat, their range should also be quite wide. The main difference between your domain and the button is that you are limited, because you raise the best hand like AA / KK / AK again, while their hand is uncontrollable. This gives the button a relatively noticeable nut advantage on most flops, even if their overall range is not more limited than yours.
As a general rule, given the overall nut nut advantage of most flops, as well as their positional advantage, you are going to the button that you have put your entire domain in the flop by default. This stack depth creates a situation where the advantage of the button nut is so great that it seems unlikely that you will have much control even within the control range. Your preference is to check / contact with most hands and have a much better range and / or significant blockers when rotating, mixing a few bursts of gain control in turns. When it comes to check / check, look for opportunities to navigate the river to attack the wide and limited range of buttons in such situations.
The biggest mistake you can make at Cutoff in this situation is to over-handle small bets on the flop. While the button retains an advantage of the bead, the stock value of both ranges is almost close on most flops, and even hands such as Ace or King high have a special value against the betting range of the continuation of the button. Even hands with multiple back door pulls can make sense when you combine their equity with future bluff opportunities.
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