Recent content by Pujo

Because they have to specify on what flips (1, 4, 5, 7, and 9) they want heads, the odds are EXACTLY the same is if they'd called all heads (those odds being 2^10=1024 to 1). If, on the other hand, they got to say "5 heads and 5 tails" but not specify which tosses were which, then they'd have...

No, This is not just wrong. but spectacularly wrong. Calling heads each time vs. calling heads or tails depending on how you feel on each toss doesn't change the odds, just like calling red on the roulette wheel on each spin is no different from deciding red/black for each spin. You can see...

If a coin is flipped 50 times and the Patriots call it in the air each time, basic probability says they will get it right about 50% of the time (better yet, if the coin is flipped 500 times, they'll be even closer to 50% right). That's so straightforward that I must be misunderstanding what...

There was circumstantial evidence with deflategate like the balls being taken into the bathroom and the "deflator" text, it's just that it was ridiculously short of meeting any reasonable standard of proof. But I wasn't even speaking of evidence, just plausible mechanism. At least with...

This won't get any traction whatsoever. Most of the stories I've read are along the lines of, "Wouldn't it be ridiculous if the Patriots were accused of cheating for this?" There's no plausible mechanism for cheating on the toss, nobody's going to really run with it beyond having click-baity...

Very good analysis. Though I'm not sure if the odds are exactly correct since the coin tosses for the 32 teams aren't independent (every time a team wins a toss, their opponent loses the toss). Conceptually, though, you're dead on. There are lots of teams so it's likely that once in a while, one...

The probability of getting exactly 13 out of 25 tosses correct is 15.5%. The probability of getting 13+ tosses correct is - as expected - exactly 50%.

None of those are relevant to the odds of the flip. The odds are that a fair coin thrown fairly lands on heads are always 50/50. That doesn't mean that you will have an even number of heads and tails, but over a large number of throws (much larger than 25) you'll be damn close. If you're not...

I'm not sure what you're saying here, but a fair coin should have close to 50-50 odds. If you flipped it 1,000 times you're very likely to get close to (but not exactly) 500 heads (it's pretty simple to calculate the standard deviation, but I'll skip it here). With 25 flips, though, it's a lot...

I explained it a bit in the above post, but this is the exact formula:

No, while you're right that any game is 50/50, the chances are that over a large number of tosses, you should get close to an even number of heads and tails. With 25 flips there are 2^25=33,554,432 possible outcomes (e.g, HHHHHHHHHHHHHHHHHHHT, HHHHHHHHHHHHHHHHHHTT, etc). The chances of getting...

Of the problems detrimental to our society, athletes signing with another team once their original team no longer wants them ranks... nowhere.

The only thing that matters is the now. If the Pats didn't want him to sign with another team, they should have offered him a contract. Since they didn't want him, he did exactly what he had to do for himself. Some sports fans apparently think that "team loyalty" and all that other crap is more...

Look, if you've spent your life as a football player, you might also be willing to take a less than ideal situation to extend your football career. This is likely the last game the guy will ever play in (if he even does), I don't think Belichick and Brady are too upset with him for taking one...

Good for Branch, I'm sure he's happy to extend his career even if it's with the Colts. I imagine his impact is going to be very limited. If he shows up on the stat sheet this week, it will be a good game for him. Considering how we needed receivers this year and didn't sign him, I image he...