Raising AK in big blind vs 3 limpers

[SeaEagle]

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See, this is where you guys are losing me. A flush draw or any half decent draw whatsoever is folding the turn never whether you raise preflop or not.

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With an unraised pot there's only 3.25BBs in the pot on the turn, so a flush draw is getting just about the right price at 4.25-1. I was showing him folding just to make Eric's point about why the unraised pot makes more EV.

One of the things about his formula is that it makes the "loose players" analysis pretty easy. If we assume that the opponents are really bad and will always play the same way regardless of the pot size then we get:

assumption: Big pot is 24sbs. Small put must then be 24-4 or 20sbs. If AK goes to showdown, the smallest post possible is 18.5, so 24 is probably a decent average.
assumption: AK wins 80% of the time. This isn't really all that important because AK wins the same amount of time in both sitations now.
assumption: postflop investment for AK is always 5.

EV Raise: 24 - (.2*24) - 5
EV Check: 20 - (.2*20) - 5

You can easily see that in the worst case, where pot size never matters to opponents, there is a constant 4 - (.2*4) or 3.2 EV advanage to the raise when AK hits. And using Eric's estimates, AK has about a .8 advantage when he misses.

When we subract out the extra bet the PF raise costs, we get an overall advantage of 1/3 * 3.2 + 2/3 * .8 - 1 or about .6.

So, in the very worst situation that I can think of, it's still solidly profitable to raise PF. If the players play more correctly, it's even better.