> Now WHO (WORLD HEALTH ORGANISATION) wanted to know if the AIDS
> virus could pass through condoms. So they experimented and tested
> condoms. They didn't test 2,000,000,000 or 2,000,000: they only
> tested 500.
Number of permutations in the above example: Two. Either the virus will pass through condoms or it won't. Thus the example is hardly relevant here.
Now consider how may different ways a player can get a hand of 15, and how many different hands the dealer can have with an upcard of Seven, and calculate the probability of each. The number of permutations and associated probabilities will run into the tens if not hundreds of millions, and each must be taken into account to get an absolutely accurate determination of how the player should play the hand of 15 vs. 7.
Now, can some shortcuts be taken? Sure. You could get approximate probs of the result of hitting, standing, doubling the 15 at each count, and average probs for each final hand for the dealer at each count, and then cross-multiply to get approximate win, push, lose probs.
But the key word there is "approximate." With today's computing power, even using brute force methods, getting EXACT information is really rather easy for any competent programmer.