The thing I like the least here is your river bet size. I can understand firing the third barrel here, but half pot just doesn’t make a lot of sense in a situation where your three-barrel range is polarized enough that there’s some ambiguity as to whether you can even get called by that many worse hands when betting AK (which there is – if you think villain is decent then you shouldn’t be expecting them to pay off a random Ax that often on this river).

If the river was a random blank – like a Tc or something – then I could understand going relatively small, since that’s a card where you can have some thinner three-barrels for value, and there’s less likelihood of villain having a check-raising range. However, this card does two things:

1. It means you now lose in the event that villain does have 7dXd, 7x6x, 7x4x, or a rivered boat, meaning you can’t value-bet as thinly (another reason AK is not a guaranteed value bet).

2. It puts some hands in villain’s check-raising for value range, which theoretically puts some hands in their check-raise bluffing range, which further incentivizes you to avoid thin value-betting unless you’re confident they’re actually check-raise bluffing too much.

The harder it gets for you to three-barrel thinner for value on any given runout, the bigger your third barrel should be, because you’re getting closer to the point where all your value-bets always win when called (because your value-betting threshold gets higher) and all your bluffs lose when called (because they’re bluffs anyway) – as your range polarizes, you have fewer and fewer hands that sometimes win and sometimes lose, and you have fewer hands that play ambiguously versus a raise.

A half-pot third barrel here suggests you’re trying to barrel not only AK, but some hands worse than that for value – if you’re unclear about villain’s check-raising tendencies, this is going to be problematic. I would recommend sizing up a little to begin with – in the region of 16-18bb even if you’re going to keep betting AK – but in reality I think a preferable strategy here is to simply polarize your third-barrel range so that nothing in it plays ambiguously versus a raise, and size up to something like 25-30bb with that range.

Of course, if villain is check-raise bluffing this spot too much, then you should just three-barrel every hand that beats their bluffs and never fold the river, but it’s unlikely that’s the case. River spots where villains have too many check-raise bluffs are few and far between.