re: Poker & Interesting idea, any thoughts?
OP's thinking is flawed based on results. If I'm reading it correctly, then the only way that could possibly work is for you to know that checking around will split the pot. But you can't ever really know that, so you're still making a play at a pot you think you might be able to win IF you were going to split anyway.
Also flawed is the thinking abou this -ev for your opponent based on rake. All rakes I've ever seen are capped. Assuming you're playing $50NL online (based on stack sizes provided), then @ PS the rake is $.05 per $1.00 in the pot and is capped at $3.00. If the pot is $8, you shove $50, and opponent calls $50, then the pot is $108. At 5% as above, the rake stops calculating at $3.00 (would be $5.40 if calculated without a cap). So if he calls and you both split then the $108 pot is raked for $3.00 and the $105 split between the two of you for $52.50 each or basically you both made $2.50 of the $8.00 pre-shove pot which equates to giving the poker room $3.00 of a real $8.00 pot because of some goofy theory. Don't feed the rake.
And if you're saying this is live poker opposed to online, then a quick look at Bellagio shows they cap rake at $4.00 max per pot (a $108 pot would pay $3.00 rake btw), so this doesn't matter either.
So the end result is you can pay the $.40 in rake and split $7.60 for $3.80 each, or you can shove and essentially net $2.50 each ($1.30 -ev imo since times you'd do this can cancel out with times your opponents do it after you try it once). Don't feed the rake.