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what exactly is your definition of a terrible spot?

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a spot where a decision could be very profitable or very bad but lack of information harbous a tough choice.

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When we have a decision like this, what do you think of using game theory to randomize?

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well, I guess you can do this, but I am not sure what his range is, he may be the type to raise/call with JQ, but may also be the type to only raise and call with a set.

I guess we can start to put a range together. JT+. QQ+. 33 77 JJ. Maybe some more hands like TT etc.

Then we have to give probabilities to raise/calling each and folding on the turn or calling on the turn. If you think he is a person who has a huge raising range on this flop then in my opinion he probably calls them all which gives you a tough decision on the turn.

Lets say he folds all of them but sets and AA/KK then betting is profitable by a large margin I believe.