I did a few calculations and it looks like Freebitco.in's expected average payout over time is slightly under 6,000 satoshis per hour.
Looking at the table for payouts in Freebitco.in:
![](https://ip.bitcointalk.org/?u=http%3A%2F%2Fs2.postimg.org%2Fapw2c386h%2Fimage.png&t=665&c=ydOz7rNzEq6l7w)
Although the payout changes depending on the BTC price, the base payout is currently set at 683 satoshis. However, you can also roll higher numbers. That means that out of 10,000 rolls, 9,888.5 will be 683 sats, 100 will be 6,826 sats, 8 will be 68,264 sats, 4 will be 682,640 sats, 2 will be 6,826,404 sats, and only 0.5 will be 682,644,045 sats.
To find the average, we do this calculation:
(683*9885.5+6826*100+68264*8+682640*4+6826404*2+68264045*0.5)/10000 =
~5,850 satoshisProblem is, the vast majority of rolls will be either 683 sats or (rarely) 6,826 sats. Only a small minority of users will ever see higher rolls than these but the fact that some people do skews the mean.