I had never heard of the rule of 4 and 2, but it applies to Hold'em, not Omaha and not Big O.
As others have said, your math is wrong. You can't add 10 outs to pair the board plus 9 outs for a flush because one of those cards fits both categories (the 6
) and one of those cards is already in your hand (the T
). So you have 17 outs to make the nut flush, the top boat, or quads.
But wait. You know with certainty that both of your opponents have AK, but you don't yet know if one of them has the K
. There is a 50% chance that one of them has the K
. This reduces your scoop outs by 0.5. So you have 16.5 outs to make the nut flush, the top boat, or quads.
You also have 1.5 outs to hit a non-spade King for a three-way chop. Why 1.5? If both your opponents have a King, then there are 2 Kings left in the deck, but 50% of the time one of those remaining Kings will be the K
, which is a scoop out, not a chop out.
For those 1.5 outs to make Broadway, your equity is 33%. So for simplicity's sake, we can just say you have 17 outs (16.5 + 33% of 1.5).
Now how many unknown cards are there? 52 minus the 5 in your hand minus the 4 on the board minus the 2 Aces and the 2 Kings in your opponents' hands = 39.
17 outs divided by 39 unknown cards = 44%. That's your equity in this hand, and it includes chop outs as well as scoop outs. So, yes, if you're getting 2 to 1, raise every chance you can on the turn.
Just remember: 56% of the time, you're going to miss, you're going to quietly fold to a single bet on the river, and your opponents are going to wonder what the heck you were doing raising and capping the turn when you can't even call a single bet on the end. Let them wonder. Let them think you're crazy or dumb.
You know you made the right decision by raising and capping the turn—that's really all that matters.