From the hero's (bb) point of view, the villain can have a decently wide range (most aces, broadways, good suited connectors, and pairs) from the cutoff, but probably isn't on just a steal because it's pre ante. His check back on the flop always seems like some sort of value hand because he would likely c-bet all his air. I'm thinking its a medium value hand like a weak jack, or 7. A 4 isn't much showdown value with two streets to come so I would expect him to bet one on the flop. It could also be a monster like top set. He would be more likely to bet middle/bottom set because there are more combos of top pair for the hero to have, but he could check and then be aggressive with it on later streets since the hero is short stacked, and the money will probably get in by the river anyway if the hero has some sort of decent value hand. When he just calls your turn lead his range basically stays the same (monsters, and medium value hands). When he jams over your river bet those medium value hands go out the window and the villain is polarized to monsters and air. However, I don't see much air being in the villains range because I expect him to bet most flops when he misses, especially on a dryer board like this. I think you are actually beat here and should fold.

*When I say the villain is polarized to monsters and air, his monsters don't have to just be sets. KJ, aj, and qq+ are basically the same thing as a set on this board by the river because the hero should never have aj or any over pair themselves. If the hero flopped a set, then they are just going to get pair off, even though they should never be set mining with their stack size. However, I think most people are likely to bet kj+ and qq+ on the flop and check back a set because a set just looks so much stronger in absolute strength even though in this situation the relative strength of aa and jj are basically the same. So, I would expect the hero's shove range on river to be mostly sets, than a good jack or an overpair even though they are all “monsters”. 

bennymacca said:

Cutoff's shove in the river looks bluffy as hell to me, tbh you rep a missed draw so if that means you are actually strong then well played. Maybe a hand like 88 or 99 that you are turning into a bluff and trying to get the other guy off a queen

What missed draw is he repping besides missed diamonds? He won't check behind with 56 on the flop. Missed diamonds are the only other thing, but I tend to still think that villain is betting this flop with almost all of his air, and backdoor diamonds would be decent to double barrel if another diamond hits. The river just seems like a terrible spot to shove as a bluff because you can't think that a standard player is going to fold a jack or better. The hero shouldn't have a hand like 77-1010 because he would shove those in preflop with his stack size, so he is either bluffing, or has a jack or better that he wont fold.

An adjustment you could make to playing this hand would be to start cbetting your air on the flop. Unless you hit an Ace or a King its your best chance at winning this pot. Once he calls flop we can usually put him on a pair and play turn and river accordingly. This means either checking back turn to see another card or barrell a turn card that connects with the board. Being that this board is super dry there are not many threatening turn cards to barrell except for overcards. If we are not cbetting the flop we need to just fold to the hero's lead on the turn. I'm just curious…what exactly do you think you were representing?