10/20 river valuebet

The problem is I can't be bluffing in Futgsicht's eyes because there is an italian donkey with 400e behind me. What size of river bet do you prefer and why?
Futgsicht is a good high stakes reg at this site (25/20, wtsd 28 after 2.7K hands)


BossMedia Game #2318362112: Table Table 50BB TH 592 - €10.00/€20.00 - No Limit Hold'em - 21:13:36 - 2010/09/05
Seat 1: Hero (€4332.00)
Seat 5: Futgsicht (€6152.49)
Seat 3: pop-killer (€1211.50)
Seat 4: Filt€r (€3723.00)
Seat 2: da_Wööölii (€5780.50)
Futgsicht posts the big blind of €20.00
Filt€r posts the small blind of €10.00
pop-killer is the button
*** HOLE CARDS ***
Dealt to Hero
Hero raises €57.50
da_Wööölii calls €57.50
pop-killer calls €57.50
Filt€r folds
Futgsicht calls €57.50
*** FLOP ***
Futgsicht checks
Hero bets €140.00
da_Wööölii calls €140.00
pop-killer calls €140.00
Futgsicht calls €140.00
*** TURN ***
Futgsicht checks
Hero bets €600.00
da_Wööölii folds
pop-killer calls €600.00
Futgsicht calls €600.00
*** RIVER ***
Futgsicht checks
Hero ???
pop-killer

Edit: double post

Well bet of course. We're never beat and it doesn't seem like checking would be good unless we know the fish will just shove his remaining stack in 100% of the time

I like a small bet, maybe a bit more than the fish has left

im pretty confident the fish will call with any crappy K, so we are obv looking to get value from futgischt. If hes a good reg his range by the time he calls turn should be 2p or some sort of good draw. the only type of draw we can look to get value from is Kxdd, and since there is a very small chance we are bluffing and also a very small chance he bluffraises us we should be looking to bet the maximum amount that gets a call from 2p...I'm thinking something like 940 is optimal, because it makes our hand look like thin value with 2p or even possibly AA/AK.

There is obv no sense in checking and villians range should be fairly polarized to missed draws like 78dd/89dd or some KXdd that I dont think he calls a bet with anyways so Id just bet around 1450 and hope to get called by a 2p/set type hand however unlikely those are because anything else just folds, but in all probability hes prolly just gonna fold most of the time, nothing u can do about that.

I heard some ways to play it like "close to bet pot" or "easy shove" and wasn't sure which line is optimal. I was thinking like n0rthf4ce but that didn't change anything.

*** RIVER ***
Futgsicht checks
Hero bets €777.00
pop-killer folds
Futgsicht folds

Thx guys for comments.