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I of course do the expected and re-raise to $800
That's not the expected if this means you still had chips in front of you after that raise.
Instead of just calling in the hopes of getting like an extra 1/7th pot, you can bluff here with the ace of clubs literally every single time. If your reaction is "well then they call", then you're wrong in one of the two because they can't both call your bluffs and fold to the nuts.
I don't advice bluffing much in live games, but if you have a problem of getting called and people are actually making laydowns against you, start bluffing them until they adjust. Especially if you have cards in your hand that makes it impossible or hard for them to have the nuts, like in this instance. If you had AcKd they never call when you shove right? That's $600 in profit right there without ever seeing a showdown.
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I’m wondering if it wasn’t an opportunity for an unconventional move or thinking “outside the box.”
It's actually so inside the box that you can't see the boundaries of the box within reach. You're solving a problem that shouldn't exist.