I'm a bit math challenged, I do admit. However I must say I was bit impressed with myself recently viewing my old college transcripts to see that I got B's in a couple of calculus classes. Wow. If I remember right that was mostly because I had had the same courses in high school getting C's. Second time was easier. My arithmetic was great ... I felt almost like there was a scaffolding in my mind where the numbers would jump around and add themselves up almost by itself. Interestingly this probably came from a game we played as boys; hand held calculators had just come out, and one of us five boys would give a long string of numbers, adding and subtracting them, figuring it up on the calculator, while the other four did it in our heads seeing who would get it right.

But the higher maths wasn't happening with me. Decades later, I was in a swimming pool with a math professor, and I asked her: "What is calculus anyway?" If I remember right she said, "For figuring the area under the curve." "Oh," I said, eruditely.

Fast forward to my seminal gambling career. Two math anomalies:

1: A 2-point conversion is about a 40% proposition, ranging from upper 30's to upper 40's in various seasons and levels of play. For 30 years on 2-point tries at the end of games which affected covers, I was on the wrong side of every one, except one. I started gathering witnesses for the streak with phone calls to other punters telling how the upcoming play would surely go. Right, right, right, right, right ... etc. One time the play went my way. It was the Ohio State/Wisconsin game, Clarett title year. OSU scored in the 4th quarter to go up 19-14, as a 6 pt. favorite. For my lungs I needed the dog. They missed it; a wild throw way over everybody's head out of the end zone. I just watched the play for the first time ever last night and I still can't believe I won that game. So the idea is: what kind of anomaly is this, going like 1-99 in 100 or so trials. How many standard deviations from the expectation is that, and is it randomly feasible? As I said I didn't see this play at the time, so therefore every single one I did see went against the result I needed. Jeez, in writing this I only now realized that the 40% thing doesn't even matter, because it wasn't about whether they made it or not, but about how whether they made it or not matched up with what I needed. Anyway, I've always had it in my head that this is an utterly impossible statistical result. Not sure if that's legit.

2. PLO. For over 30 years, when starting with a 2-pair hand, I failed to ever flop a set to this 3.5/1 shot. Well over the last 50 of these I showed to other players to verify/establish. Never. 0-for. Approximately 200 trials. How many standard deviations from the expectation is that, and is it a feasible possibility under normal concepts of randomness?

For #1, if we assume approximately half of the situations were conversions you needed your team to make and the other half were ones you needed the other team to miss, then you're saying you went 0-50 in the former and 1-49 in the latter, approximately. The probability of that would be .6^50 * (50*.6*.4^49 + .4^50) = 1 in 1.284*10^29.

For #2: the probability of missing the flop with two-pair in the hole is 44*43*42/(48*47*46). The chance of that happening 200/200 times is 1 in 1.532*10^23

If your memory is right, that is some out-of-this-world runbad or some riggage.

Thank you for taking it seriously and not going straight to, "Nope. Can't happen. You made it up." It backs up my claim that none of it is really random, only shortcutted as so generally.

On the 2-pointer thing, there is a factor in play that I usually need the favorite to miss it or the dog to make it, and I'm imagining that 2-pointer success rate is often skewed more heavily in favor of the favorite (make on O, stop on D) than realized. That would be an interesting study, what percent of 2-pointer tries are successful for faves versus successful for dogs. Not sure about that, just an idea.

The PLO thing is just super bizarre stuck on zero. Super bizarro.

You didn't comment on how many standard deviations from the mean either of these is. I realize it is hard nay impossible to take literally, and I presume any mathematician would consider it impossible and be willing to shove that it wouldn't ever happen. That would be justified, I'm sure, by any standard take on reality, which of course, mathematicians are known for. Once you get over 5 SD's or so it is getting pretty inconceivable, right?

(*I had another 2-pair starting hand in PLO the other night. J-J-8-8 double-suited red. I just can't tell you how little drama there is about if I'm gonna flop a set to it. Nope. I did flop a straight flush draw, and made a loose call in last position with good odds (150 against 1000). On the turn I tripped the jack. (Two times previously in this streak that I remember I tripped on the turn and won a huge pot.) So now i had the second set and a straight flush draw. Check, check to me, one player behind me, the pre-flop raiser. I fired the pot, he insta-raised. A-9-7-J board. Shorthanded 5 player game. So I need help. My trusty deuce of spades came on the river. So anyway, the live streak that goes 0-for-200 on a 3.5-to-1 shot.)

I'm guessing there is some other factor at play for #1. If the 40% stat is just a broad average, the average in various matchups might be a lot different like you said. Still, we'd need to massage the numbers drastically for the resulting probability to not be astronomically low. Even if we change the average in your 1-49 spots to 60% and the average in your 0-50 spots to 30%, that's still only 1 in 2*10^17, harder than winning the Powerball jackpot twice in a row with one ticket each time.

Re: standard deviations, that's just another way of expressing the same information. For the Omaha, 0-200 is 7.8224 SD's below the mean, in this case the maximum possible. Technically that's not exactly what you want, but since we're working with a Binomial distribution I think it's close. More precise would be to (numerically) integrate the standard Normal pdf until reaching the z-score yielding our probability. But 1/10^23 is definitely below 5 sigmas. 5 sd's would be about 1 in 3.5 million, a walk in the park compared to your mush job!

If you were not lying or being cheated, then your results means that the probability that God exists (and is punishing you for your posts on the religion forum) is over 50%

I am not joking.

I'm going to have to take that under consideration, I think.

At the level of improbability this reaches, some form of human or systematic error becomes far far far more likely an explanation. There are a variety of cognitive biases that explain this far better than 'just bad luck'.

I realize that, which is one reason I was verifying via turning hands up (or showing to neighbors when possible), and making calls about the two point conversions. Sklansky's reply is sage in that it goes to metaphysics, and that is exactly where I ultimately was forced to go by way of explanation. Not god per se, but wider, more scientific metaphysics. That is where the explanation is imo.

You should not take his response as evidence that god exists. You should take it as pointing doubt at your claims. From where I'm standing, your claim is so unbelievable that other explanations are virtually guaranteed to be the case. You are not far off being likelier to quantum tunnel your way through the nearest wall. Knowing the amount I do about the propensity of the senses to lie, for memory to be faulty, for cognitive biases to prioritise survival mechanisms over truth-telling mechanisms, it's exceedingly unlikely you're telling the truth. If you're convinced you're telling the truth, it's still more likely you're just mistaken.

Would you like me to link you to some articles that talk about false memories and how easy they are to implant, and the evolutionary mechanisms that require that possibility?

I know exactly what he meant and I know he doesn't believe in god. I'm one of the greatest sports statisticians of all times, and I realize exactly what the claim and the biases are. Everything you just said is in my rear view mirror, though you couldn't have been expected to know that. It's the obvious the knee jerk reaction/explanation. I'M TURNING THE HANDS OVER AND THEY ARE O-FOR. I started that about 10 years ago.

Sklansky's point was that he would change his metaphysics/worldview before he would accept either of those statistics at face value ... even if a bit facetious in so doing. My point on that was that his non-literal "conversion" to belief in god is in the right direction if taken literally in that the explanation is indeed metaphysical.

Probability provides a projection for expected results for trials where we have incomplete information. Yes? Is there something that has complete information?

So I had never written anything about this 2-point conversion anomaly until this week. I had described it to a few people who of course were incredulous. Today I'm one of the few people on earth who has Penn St. + 7.5 (bought at -155). As the game wore on OSU was ahead and it was painfully obvious Penn St couldn't score, so I took OSU to win laying -250. Got a 7.5 point middle working in a low scoring game.

Penn St. has miracle score with 29 seconds left to cut it to 8, standard play is kick to cut to 7. Nope, idiot Franklin trying to prove something that he has already utterly disproven, goes for 2. And needless to say, it's no good. I haven't seen the play.

So I had a perfect ticket today, 3 other games and 2 fights, except for the 2-pt. conversion miss which shouldn't have even been tried.

I don't believe you, just from reading this thread. You say above that you are one of the greatest sports statisticians of all time, and yet you need to come to this forum to ask for the likelihood of a couple basic stats problems? And then you need someone to calculate the SD for you?

And kicking the extra point when down 8 points late in the game is no longer standard. People have finally started doing something that was figured out decades ago (and which Sklansky credits to Chip Reese), which is that going for two in that situation increases your odds of winning. Now that everyone uses analytics in football, it's become the standard play to go for two when down eight. The fact that you seem very ignorant of stuff like this and yet have a delusionally high opinion of yourself makes it plain to an outside observer that your record of bad luck is also a delusion.

I will say though, for people who have been on this board long enough, there was a post in I think BBV long, long ago where someone posted a graph from PokerTracker that showed them running some impossible amount below all-in EV. Like over 250,000 hands at medium stakes and he should have been up a million and was break-even, or something ridiculous like that. I've always wondered what the real story was behind that. If anyone can find the thread, I'd love to see it, but bear in mind in may have been on the old UBB forums.

Sports statistician would be very different than the discipline of statistics, obviously, as in just the keeping of the statistics from the games. Which means things like winning national sports statistics trivia contests in Las Vegas, and does not mean so much as ever having taken a statistics class. I intentionally said sports statistician in this sense to delineate it in that regard.

THE STREAK ENDED LAST NIGHT

In a 6 hour session of PLO last night, this 2-pair in the hole not flopping a set for 30 years (playing about once a week for 5 hours or so live play, 200+ trials), the seventh time I had 2-pair last night (5-card), I flopped bottom set. I had about 280 left way late about 2 AM on the button, ready to go. I had 7-7-8-8-9 ds. 1-2-5 game. I straddle on button. Somebody makes it 30, I make it 120, He blows it open clearing it out and the flop is K-9-7. I actually held against his nut flush draw and aces. That ended the streak in which for the last 5 years I have tabled or showed neighbor the 2-pair whiff about the last 60 times, going 0-for-60 sets. This includes last night in which I was showing them to the guy next to me. On this all in hand for fun I said, "Here, touch the hand." He did and the streak ended. The streak is a thing, and gargantuan anomalies are a thing.

I of course don't blame people for not believing it, and fully expect that reaction, indeed am surprised at anyone taking it as real. But I looked at it. I lived it. And if you bring a lie detector expert and your money, you get to pay me off. There's no delusion here re this. Nyoop.

Texas did it in the de facto national championship game in 1969. Quite a dramatic thing. I'll never forget the surreal moment when a guy called Happy Feller then kicked the XP on the next TD to beat Arkansas 15-14. It's really kind of the game that gave birth to college football as a TV extravaganza. It wasn't such a thing before that, even the mega games.

Luv your candor and directness ("I don't believe you ..."), but when somebody is clearly making light of their own mathematical ability, you don't get to then accuse them of being delusional about how good they think they are. That won't work. I get that you weren't making the distinction between sports statistics and statistics as an academic discipline.

I am very interested in your comment on the obscene run bad example you gave. I remember Caro writing about such things as well. I love that subject. I love streaks and somehow they find me. For instance, one streak I love is Joe DiMaggio's 56 game hitting streak MLB amazing record. But that was not Joltin' Joe's longest professional hitting streak, and you get to pay me off, as others have, if you bet that it is (he hit in 61 straight in the Pacific Coast League's San Francisco Seals in 1933).

You feel me? So I gave that question to a bartender in NYC and he went wild saying he would make a fortune. Another guy same night tried to bet me that Joe D. appeared twice in the list of 20 longest MLB hitting streaks, but the other one was Dom, not Joe. So I win again. I do streaks.

Somehow I won 31 times in a row in the PLO game, full sessions not hit and run, and when I asked around the longest I ever heard was 24. Of course they take it as bragging, but I was trying to discuss anomalies, not being a great player. Caro indeed wrote about this too, some guy that won 68 in a row or something by winning one or two or ten dollars and cashing out, doing it a few times a day, totally bogus. But my streak was more like, "What are the odds that someone with an established 65% win rate would win 31 in a row?" And that number, which I needed help with, is anomalous in a sense.

I've just been involved in some incredible streaks. What can I say?

7 two pair starting hands last night and 4 sets flopped. Streak finally really eased up. After 0-for-200+ on the 3.5/1 shot.

Why does dividing by 303 always yield a repeating fraction??

It does?

For non-zero whole numbers < 303 ??

Because 1/303 repeats and any integer multiple of a repeating decimal either repeats or ends in .9 repeating, in which case it can also be written as the next decimal value before the 9s (e.g. .9 repeating = 1, .09 repeating = 0.1, etc.)?

It can probably be easily shown that 1/(prime power) repeats for all primes not 2 and 5, and any algebraic combination (rational multiples, sums of rational multiples) also repeat.

So, basically, p/q repeats in base 10 when q has a prime other than 2 or 5 in its factorisation, I think. And p,q co-prime obvs: 606/303 doesn't count.