BTW - I've been chewing on this one for a few days and finally broke out the spreadsheet. And basically, there is no wrong answer - though I think the math supports a touch higher on the river bet sizing strictly to protect our range.
Attached are two spreadsheets, one with the $1,374 size and one with $2,500 like I had suggested. You'll see that they are both +EV with basically negligible differences.
Also, this is assuming the villain range of
JJ,77,55,AQs-A2s,KJs,QTs,J7s,AQo-A7o,KJo,J7o
Looking at the spreadsheets you'll see only about $300 difference in the EV result between the two river sizes. But you'll notice that betting $1,374 is only slightly (less than $200) better than checking back river. Additionally, by betting $2,500 we can rep our entire range and keep ourselves more balanced.
So, this is what I was trying to say - but didn't do a very good job. I also didn't actually do the math - sorry for the laziness.
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