@TPmarketwatch@rossium I just asked Claude and it seems that the answer is 1 by symmetry of recurrence-still a little unsure on the geometric argument itself, but the symmetry idea: that returning to position 1 resets the probabilities makes sense.
@TPmarketwatch@rossium I think it's
1/2 chance that you don't fall on the first step: ie you are now 2 steps away.
1/4 chance of moving forward twice once you are two steps away.
I may be missing something-it does seem that your logic presumes they stay 1 step away instead of moving backward.
@TPmarketwatch@rossium Could be wrong but I think you need to account for the probability of getting to any given distance from the edge in the first place, not just the probability of moving to the edge after starting at the distance.
@TPmarketwatch@rossium But to get to the state where he would need to fall in 2 steps is only a 1/2 probability (he has to move back once). 1/2 probability of moving back once, 1/4 chance of moving forward twice afterward means a 1/8 total probability of that scenario. And so on.
@rossium I see people suggesting 1, but I don't see why the probability has to be 100% just because it goes on infinitely; infinite sequences don't necessarily diverge.
@rossium 2/3?
1/2 for moving forward
(1/4)(1/2) for moving back then forward twice
(1/8)(1/4) for moving back twice then forward three times
Geometric sequence: (1/2)/(1-1/4)=(1/2)/(3/4)=2/3.
@michaelknowball@will_nba_hater The Cavs are just as good as the Pistons and the Spurs are a juggernaut just like OKC. Knicks only lucked out avoiding Boston, but if they swept the team that beat Boston, I'm not sure how much resistance the Celtics would've put up.
@CanadianCatCP If you're talking about elite offensively minded coaches, Russ had Sean Payton. The reason he didn't accomplish anything is because he was done by that point.
Pretty obviously Russ in Seattle is better than Stafford in DET, but Seattle Russ vs LAR Stafford is a fair convo.
@MidBallKnower@nickercolano Always better to have positive camp reports than not, but wouldn't put too much stock into them. Bryan Edwards and Marquez Callaway once got WR1 talks for the Raiders and Saints. Don't think anybody knows them anymore.
Hopefully MHJ and BTJ can bounce back this year though.
@MidBallKnower@nickercolano Not saying that he won't exceed 675, just saying that the reasoning is a bit off. Certainly, I could see him in the 450-650 range or the 1200+. Definitely has potential to get back on track but still, I would take say an MHJ over him right now.
@MidBallKnower@nickercolano Yes, but he was forcefed the ball as the supposed #1 option most of the year. It's like saying that a disappointing first round WR who puts up 700 yards in Year 1 will put up more as they grow. Often, they regress as their role declines.
@BreidenFehoko Brunson has 7 playoff series wins with the Knicks as the #1 option. Melo had one. Brunson also has 3 second team all NBA's and a top 5 MVP finish as arguably the biggest playoff riser in the league.
@npparikh Of course, not to question your judgment. It's just that sometimes professors assign mountains of work not realizing that it's not feasible. If your students can/have been able to handle it, all power to them.
@npparikh Even without it being strictly STEM, I found 120 pages of qualitatively & history focused architecture, 150 pages of dense econ, 40 pages of philosophy, and 25 hours on problem sets and labs to be my absolute limit last term, and that was without non-academic cares.
@npparikh Still, *hundreds* for a single course seems excessive-the most I'd assign as a professor would be 200 in a heavy week. Just too many classes and other academic priorities for students to handle more, let alone any consideration of recreational freedom.
@r0ckstep@vjoshuaadams He's saying that no matter the moment in time, we look upon the next generation with disdain for not meeting the academic standards we hold them to.