a thought on raises... for round 3, it's still fine cause you can bet from 4 to 7, which makes a possibility under 12
but in round 4, why bid BETWEEN 8 and 12, whatever you bid, the total will be higher then 12 anyway so the bid is useless here, unless you have 10 and be stupid enough to bid 10 while youre opponent only have 1 left which would gives you 11. Because whatver you bid, you kill you're opponent by winning unless you're short on elements left, but then you will bid all that you have left anyway.
So just saying, round 4 should be a bet of 8 elements and we skip the bidding phase.