This is all extremely rough, based on a lot of estimations, and doesn't even begin to cover a lot of possibilities in the hand like getting raised on an earlier street or formulating a river 3 betting strategy. But I wasn't particularly happy with how I played a hand yesterday, so thought I'd put in some time building a rough idea of what a good betting range would look like on this board, and thought I'd share to see if anyone had any thoughts on where it could be improved or adjusted.

Let's assume V is a GTO bot and we are 300bb deep effective.

We open UTG+2, V calls bttn, and blinds fold.

Flop AA5r,

On a board this dry, I imagine our CB sizing would want to be on the smaller side (1/2 to 1/3), and we'll be Cbetting at least once at a reasonably high frequency. We will CB the top of our range AK, A5s, and 55 100% of the time and our check call range would consist of a mixture of pocket pairs, and some aces with maybe a quarter of AQ's and a progressively higher percentage of AJ's ATs's, A9s's and any other random AXs's we decide to open. The rest of the Ax and pocket pairs will be Cbet along with a wide range of random bluffs. Our x/f range will consist mainly of mid suited connectors with no bdfd, and we will have no x/r range.

Turn 8x

As our continuing range will now be stronger, we can increase our CB size to 60-70% pot. We will continue to cb the top of our range at 100% which as well as all combos of AK/A5s and 55, now includes some combos of 88 if we decided to CB it on the flop, and the occasional A8s if we decided to open pre, and then cb. Our choice to CB over x/c will now become completely linear based, and we will never be check-calling a hand better than a hand that we would cb for value. We will CB something like 50% of the AQ's we cb flop with, and a quarter of AJ's, choosing to check call the rest, and the rest of our aces along with a small percentage of KK/ QQ/ JJ. I would argue that this is a spot where there is no need to have any bluffs due to the fact we'd be bluffing with no equity. The only bluff that would really make much sense would be 56s/ 57s if we decided to open it, and for this to be profitable we would probably need a split river sizing in which we'd bet something like 80-120% of pot which we'd balance with some combos from the top of our range. We will again have no x/r range.

River Jx

The river is clearly the most difficult and complex to play. This is also where it becomes more difficult to keep assuming V as a GTO bot, as in play it is rare for players to have many hands they're turning into bluffs here. As mentioned in the turn play, if we do have a bluffing range here, then I think there is a strong argument to have a split sized betting range, but we'll continue without a bluffing range for now. So now assuming we have CB the turn, we have something like 15% of all possible AJ combos, a small % of possible 88 and A8s combos and all possible combos of 55 and A5s which we will again bet 100% of the time. We also have all combos of AK, which we may decide to bet ~50% of the time and check call the other half of the time. Again as our cbetting range gets stronger we can go slightly bigger towards a 75% sizing. We have around a third of AQ combos (which has now become the bottom of our range) that we will never bet, and check call around 25% of the time and check fold the rest of the time facing say a 70-80% pot bet size. We would be check calling 100% of AQ's and a small percentage of ATs's if we had decided to check call these on the turn, check folding anything worse. If we CB 75% pot, and are raised 2.7x our bet, then we will need to defend around the top 54% of our range to remain unexploitable. The top 54% of our range that I laid out for betting the river here would be 1 combo of AJ, 1/2 combo of A8s, 1.5 of A5s, 1 of 88 and half of the 3 combos of 55, folding the other 50% of 55 combos, and all 3 combos of AK. The river is also the first time that we will need to incorporate a check raising range, as we now have some combos of AJ and JJ that we check/ called turn with and will most likely want to x/r river with now. We will also have some 88 and A8s, that we have check called flop and turn with and will now want to check raise. To balance this I imagine we will x/r a hand like A9/7s, as KK/QQ/ATs/AQ all block hands that V is likely to have in his bet/ fold range.