What theory? No-one can flip a coin exactly the same way twice, but I'm not exactly sure what point you're trying to make. In any case, I did point out that when viewed in retrospect, the probability of any specified outcome is always exactly zero or exactly one. I don't know that it takes much theorizing to arrive at that conclusion.

Of course, if you believe in multiverses, one outcome in our universe might be met by an opposite outcome for the same event in one of the other universes.

Even so, artappraiser is correct in pointing out that a public option is a fairly minor component of reform, and that the Senate bill, like the House bill that has already passed, should be judged on its other components as well. Some are excellent, and others are only tiny steps in the right direction. All in all, I found the Senate bill an important step forward, undeserving of the term "incremental", if that term is meant to connote only a very small advance. This would be a major advance if it passes, but of course, getting it passed will be a challenge.

Unfortunately, there is no evidence that mammography before age 50 saves lives. There is no evidence for a net benefit of screening in the 40-49 age group. This has been known for some time, but too many advocacy groups resisted acting on it, and so it has been up to the latest Task Force to bring it to attention again.

In Europe, screening routinely starts after age 50, because the political forces play less of a dominant role.

If the new recommendations are implemented, as I believe they should be, women will still be able to choose screening if they wish, but will no longer be made to feel guilty if they refrain.

In that sense, the push to eliminate prostate cancer screening has preceded the present push to limit the age group for mammography. However, it has been known for some time that screening below age 50 had little or no known benefit, but previous attempts to put this knowledge into a change in policy met political opposition from radiologists and various other advocacy groups in the U.S. In Europe, screening is routinely limited to women age 50 and above.

How these changes would affect younger women is unclear. As you point out, their cancers tend to be more aggressive and faster growing, and therefore more likely to progress despite mammography.

At this point, the new guidelines seem best matched to the evidence, which indicates that screening benefits start to become a net positive around age 50, but which also leave enough uncertainty to justify the decision of individual women in the 40-49 age group to have mammograms, and the decision of others to forego them.

http://democrats.senate.gov/reform/patient-protection-affordable-care-act.pdf

I think it will be hard even for the government, much less the average subscriber of insurance today, to estimate which way his or her premiums will change compared with an unreformed system. Forces tending to reduce premiums will be measures designed to increase healthcare efficiency overall (e.g., bundled payment mechanisms to providers), as well as government subidies to subscribers who qualify but are currently paying all premium expenses themselves. On the other hand, premium costs may go up for some current subscribers at the point where insurance plans are required to meet higher standards for the nature of benefits they offer. Taxes on high end "premium" insurance plans might conceivably be passed on to subscribers of lesser plans, although the extent of this is likely to be small.

Healthy low-risk subscribers in the individual market may see cost increases because insurers can no longer exclude high risk individuals and may therefore raise premiums to cover their extra medical costs. On the other hand, the inclusion of a public option (a "community" option in the Senate version) should reduce costs for subscribers in that market.

Overall, the system is likely to see a cost reduction compared with costs in the absence of reform, but the effect on different individuals will vary in either direction.

At the time the decision was made, no human had all the relevant information, and so for any human, the probability might have been anywhere greater than zero and less than one, but that is because proability is a function of available information and not an inherent property of an event. Retrospectively, we have total information about the play (assuming no vast media conspiracy to deceive us) and so the probability it would fail is now known to be exactly zero. Same play, different probabilities retrospectively and prospectively because prospectively our information was necessarily incomplete and retrospectively it's complete.

In theory, one could go back to the beginnings of the universe and ask whether the outcome of the Patriots/Colts game was determined at that time. It wasn't, but that was because quantum uncertainties would have had 13 billion years in which to operate, and that's enough time not only to affect the results of a 4th down play, but the existence of planet Earth.

Games of chance don't refute these principles, because incomplete information is always guaranteed. As long as all contestants are equally ignorant, the games are fair, and equally "chancy".

Wasn't Belichick once implicated in something called "spygate"?

Seriously, my only real point (outside of my confessed ignorance of insider football) is that complete knowledge at the time of Belichick's decision would have told him it was inevitably destined to fail, and that the incomplete knowledge he had probably should have told him it was likely to fail.

Briefly, probability is not an intrinsic attribute of an event, but rather a reflection of our information about that event. If we flip a random coin of ordinary nature, the probability of a heads is 0.5 if we know nothing else about the coin. However, a computer observing the same coin toss, but armed with knowledge about the coin's center of gravity, its weight, the height of the toss, the initial position, the speed of coin rotation, the wind speed, the slope of the terrain and its elasticity, as well as other important variables, will announce a probability closer to either one or zero, and with total knowledge, would come very close to one or zero. Same coin, different probabilities for us and the computer. Which is correct? They both are, because each is based on a different level of information.

If Belichick had been privy to all relevant information, and the omniscience to process it, he would have known that his decision had a zero (almost) probability of success.

Although cynical leaders will exploit this principle for political gain, their followers are often genuine in their acceptance of faith as a justification for expressing demonic instincts that they would otherwise repress, and in a non-religious ambience, often do.

There is no absolute certainty, but Holder will probably be proved astute for making the choice he made.

First, for some physics. The laws of quantum indeterminancy are more or less averaged out at the macroscopic level at which we operate. This means that for practical purposes on the football field, we live in a deterministic universe. Belichick's decision was wrong at the time it was made, and this conclusion is not altered by the fact that we only learned about its outcome later. If, in fact, he or any other human, had access to all relevant knowledge at the time (which way the wind was blowing, the amount of sweat on the football, the entire history of decisions made by the opposing coach, etc.), he would have known the "gamble" had zero probability of paying off, and would have probably chosen to punt instead (although he might have also seen that as an inevitable failure, in which case he knew the game was lost).

In any case, here's my inexpert take on why it was a bad gamble, and can be summarized by the number 2, taken twice - 2 minutes to play, and 2 yards to go. Because the Colts were 6 points behind with 2 minutes left, they would certainly gamble if pushed. That meant ignoring all alternatives Patriot strategies and gambling that the Patriots would attempt to gain 2 yards via a short pass. This was not inevitable, but likely, because a run had a poorer chance to gain 2 yards, and a long pass is always a gamble for the offense. By focusing almost exclusively on stopping a short pass, the Colts greatly inmproved their chances of success, and that is what happened.

Note that this would have been different if the situation had been fourth down and inches, where a run was a strong possibility. It would also have been different if the situation had arisen in the third quarter, where failure to guard against a long pass might have turned a 6 point deficit into a 13 point one.

Anyway, that's my take on what happened to the Belichick, and as the saying goes, "you can't argue with failure".

If anyone wants to prove me wrong, I forewarn them that I intend to plead ignorance.

We are the only major industrialized democracy that fails to provide comprehensive coverage for all members of society. Our outcomes are worse than all the others

http://www.infoplease.com/world/statistics/infant-mortality-life-expectancy.html

despite the fact that our costs are much higher

http://economix.blogs.nytimes.com/2009/07/08/us-health-spending-breaks-from-the-pack/

These disparities remain striking even when alleged discrepancies in the criteria used for comparison are adjusted. In fact, compared with any one nation, our poor showing might be attributable to factors other than our healthcare deficiencies, but our low rank in comparison with all the others is compelling evidence that the types of reform now likely to pass are overdue.

The quantitation has resulted in the provision in HR3962 of a tiered system comprising basic, enhanced, and premium plans, all of which cover all of the above services, but to a different extent. The basic plan has an "actuarial value" of 70 percent, meaning that for the average patient, the insurer would pay 70 percent of expenses and the subscriber the remaining 30 percent. The other tiers pay higher percentages. Based on past behaviors, the 70 percent minimum is judged to be the minimum value required to adequately protect the health of most subscribers.

A plan with an actuarial value of 70 percent might vary in terms of subscriber cost sharing - in some cases, it would emphasize co-pays or co-insurance, and in others, more of the burden would be placed on deductibles, but even in the latter case, the deductibles would be far less than $5,000. Such a high deductible leads to actuarial values known to be far too low to be of substantial benefit to more than a minority of subscribers.

I expect that something like HR3962 will eventually pass. Although as I said earlier, even a high deductible plan, if mandated, would make the uninsured a bit safer, it would not go nearly far enough, and I don't think such a plan has much chance of being part of the final deliberations in Congress.

Fortunately, that provision will probably be greatly moderated or eliminated in the final bill, although it will be important to keep up the pressure to make sure that happens.