I would like Cindy to min bet here.

that definitely looks like a weird checkback..

Just my analysis, it's sometimes wrong but w/e.

linuslove probably only ever bets for value Ax+ on turn, it's possible an occasional pp bets, but that's rare. So it's like this: on the river you have multiple options in cindys spot: if you make it so you only want two options: check back, or jam, then you should check back Ax probably. Nothing worse will ever call if that's your size. solver seems to agree and checks back Ax half the time.

I went back and resolved it with four river sizes for cindy's river decision: $121, $404, $1010, or river jam. It likes betting 1/4 pot size the most and will do it with Ax around 80% of the time.

I checked out the $121 bet, and it is always called by King high, however, range explorer says villian will have quads 3.3% of the time on the river, and king high 10%. Pio does check quads on river a small % of the time. The math shows that you make about $12 in value from king high every time you bet $121, but when you get checkjammed all in, and call everytime, then you lose about $100 to quads every time you bet. It is negative ev to vbet tiny, even if you get called with king high all the time the money lost vs quads outweighs it. Also they never have AA because betting turn with AA is terrible.

I checked out the $1010 bet, and you called by king high there as well, so there's very little difference between the flatting range from the $121 bet and the $1010 bet. Solver is basically split between checking Ax and betting around $1010. It's very close. Betting $121 is terrible.

This solvery stuff can all be a bit unrealistic, it's unlikely that linuslove mixes checking/betting quads on river like it does, and he prob swings more in one direction between checking/betting. Depending on what he actually does with 6x here, for cindy it's either a very easy check with Ax or an easy bet. The decision only becomes hard for cindy if Linus bets quads about 80% of the time and checks about 20% of the time, or near those percentages.

but yeah, I think adopting a simplified strategy and betting basically a range of hands that are Qhigh and lower and Ax+ around 20-25% pot size in cindy's spot is the correct play to make. you basically bet that size because it's less than the % of hands that are kinghigh and lower on the turn in linuslove's spot. (according to range explorer, king high and lower is about 35% of hands that barrel turn). So you basically make money with that sizing if linuslove does not make king-high hero calls on the river.

I dont understand why you say that is the correct sizing because its less than the % of hands he is going to fold

https://gyazo.com/d188a2b115a62f4dee1768b266f5bda7

https://gyazo.com/f93fb77bef036419352400f89edb2116

https://gyazo.com/557aa3de294fdf1264c29ff3e31ebde2

My numbers were a little off; You should run the sim to check it yourself.

last picture is solvers checking range on river in the BB. You can see that he has nothing 50% of time. It barrels turn with AK, trips, and all the flush draws lower than King high flush.

In the button, if you bet $1,000 to win $4,000, and they call with king high but fold Queen high and below, it's pretty +ev. Since BB has queen high and worse 50% of the time you would be risking be winning $4,000 half the time you bet $1,000 with a bluff. so your ev with that bet would be about +$1,000.

It's a little more complicated than that, as you have to take balance and the ev of other options into account, but i'm going to stop rambling here.

And then there's something obvious but i mention it anyway, you should jam all the 6x instead of betting $1,000 with them.