Katweezel: "You can safely throw your BS chart away for 44 V 4 because the conclusion was based on trillions, billions or many millions of hands simulated. So the long-term recommedation is go with the math. But let's face it; you are never going to be playing for the long-term. In fact, you are always in the short term. You will be lucky to see one million hands, let alone one hundred million."
OK, are you INCAPABLE of understanding the explanation that I have made a trillion times on this web site already???? The computer's simulation of trillions of hands is a COMPUTATIONAL TECHNIQUE to estimate the expectation on the hand, but that expectation applies even to a SINGLE hand played, and the strategy on that hand may not even be a close decision. It would be stupid to play suboptimally even for one hand.
Let me give an example. You have a coin that is heavily weighted in favor of heads, maybe in the 90% heads to 10% tails ballpark. Then, we run a computer simulation of a gazillion hands and determine that the heads probability is in fact 88.763%. It took us a gazillion to get the accuracy to determine that the probability is 88.763%, as opposed to 88.91% (that's the number being thrown around by the numerically illiterate). Now that we have our 88.763% answer, we can forget about the gazillion hands. It doesn't matter how we came to this 88.763% answer. We could have just as easily read this answer off the tablets Moses brought from the mountaintop (or, we could have computed them using exact combinatorial analysis, without resorting to simulation). It doesn't matter. The simulation was simply a computational method to get the answer. NOW, we know the coin is 88.763% in favor of heads. You are going to play the game one time only. Are you going to stupidly call tails, and then rationalize that by saying that you aren't going to be playing a gazillion flips?
The expectation applies even to a single flip, and just because the computer ran a gazillion trials doesn't mean that the strategic decision is close.
Let me try one more example, since obviously this point hasn't sunk in yet. There are two tables of Russian Roulette offered at the casino. Each table has a specially constructed gun that has one million slots, but we don't know how many bullets. Through computer simulation of gazillions of times pulling the trigger, we find that the first table has 5000 bullets in the gun (so 0.005000 chance of death), while the second table has 1 bullet in the gun (so 0.000001 chance of death). You are going to play this Russian Roulette only once. Even though you aren't going to play many times, it would be pretty stupid to choose the table with 5000 bullets in the gun.
Note also that our simulation of gazillions of hands was just a computational method to figure out how many bullets were in the guns; equivalently, we could have gotten the information from the dealer, who could have told us that at the beginning of the shift, she loads one gun with five thousand bullets, and the other gun with one bullet.
If you want to make a foolish play, abandoning BS so that you can gamble by splitting 44 v 4, then knock yourself out. But please stop defending the play by using incorrect arguments that completely misrepresent the meaning of statistical estimation techniques.