"Its better to be bettor than a caller because.."

[punter11235]

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Let's put $100 in a pot, and both pick a number out of a hat from 1-10. The higher number gets the pot, with some conditions.

You pick 6. Great for you, it's above average! Would you bet your number is higher than mine? Don't do anything yet, just hold that thought.

Now I pick my number. I offer a sidebet of $10 that my number is higher than yours, if you don't take it, you lose claim to the $100. You'll probably call, because you don't want to be bluffed out of the $100, but how are you feeling about your 6 now?

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:-) I was hoping for such an argument.
If for example we play limit , the pot is 100$ and the bet is 50$ betting your 6 is major mistake. If the bet is small, like 10$ its correct to bet, if the bet is 100$ betting is pathetically bad. Its all depends...

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but that's not relevant in a theoretical discussion such as the OP.

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Do you realize that in that game (number poker) for every bet size there is a number where its correct to check-call rather than bet ?
Do you realize that in pot-limit (when you have to bet the pot) version of that game you are correct to bet about 10% of your good hands ? (with raising and check-raising allowed ). Do you know how small the bet must be to make betting a 6 theoretically correct ?
Even in games when Villain may only call the bet need to be small to make betting a 6 correct ( I cant remember exact size now but its not the point)