William M. Briggs

Statistician to the Stars!

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Two New Dice Games: Animosity & Disdain

Laissez les bons temps rouler!

Summer and time for doing plenty of nothing. Like playing a rousing game of 10,000, sometimes called Farkle, Dix Mille, or “Didn’t we just play that yesterday?”

There are many variants to 10,000 as there are economists’ opinions on the GDP, but this link is closest to the game I know.

The problem with 10,000, while it’s fun in a pleasant sort of way, is that it doesn’t sow as much discord and domestic disharmony as I like to see. Every player is against only himself and the cruelty of the dice. Whereas in a proper game players are at each others’ throats.

Best news is that no politics of any kind is ever discussed during play of the games below. No rule forbids this, but the flow of play precludes it. Thus, while the game appears to increase bad feelings, it actually decreases them globally. Progressives and conservatives, atheists and believers, and the froward and shy may play together and George Zimmerman’s name never is mentioned.

333 or Animosity

Normal: Play starts and continues right or left. See Scoring Table below. Player rolls and can keep his score or assign it to the player on his left (if playing left, or vice versa). He must then roll again and must keep score on second roll. Player to his left, if assigned the thrower’s first roll, loses his next chance to roll. A straight or triple immediately reverses play.

Example: Player rolls (1,2,3) and play had been going left. It switches to right. Player may keep the 12 points for himself or assign it to the player to his right. After scoring, play moves to right and proceeds as usual.

Endgame: Once any player meets or exceeds 333 points, play continues once more around in current direction, but scores can no longer be assigned. Each player begins an accumulation, adding scores on successive rolls. The accumulation may continue as long as successive rolls are larger than or equal to previous rolls.

Example: The current potential victor has 342 and play is to left. Next player is at 280 and rolls a (1,1,2). This isn’t enough to put him over 342, so he rolls again. Next two rolls are (4,4,5), which is higher than (1,1,2), then (2,3,5), which isn’t, so this player loses and the next player moves to the endgame.

Disdain

Normal: Play is much like in Animosity, except that the endgame accumulation rule is in effect the entire game and the play never reverses direction. Player rolls and at any time in his accumulation may stop and keep his score or assign it to the player on his left. He must then roll again and must keep score on second accumulation. As above, the successive roles must equal or exceed the previous roles in the accumulation. Player to his left, if assigned the thrower’s first score, loses his next chance to roll.

Endgame: Exactly as above.

Notes: Both games have been played and tested. Both have produced much fun. Gamblers like Disdain; analytical folks prefer Animosity.

Scoring Table

The three dice are summed. If the throw is a “straight”, the sum is multiplied by two. If the throw is triples, the sum is multiplied by three.

Roll Score Prob
1,1,2 4 0.0139
1,1,3 | 1,2,2 5 0.0278
1,1,4 6 0.0139
1,1,5 | 1,2,4 | 1,3,3 | 2,2,3 7 0.0694
1,1,6 | 1,2,5 | 1,3,4 | 2,2,4 | 2,3,3 8 0.0972
(1,1,1) | 1,2,6 | 1,3,5 | 1,4,4 | 2,2,5 9 0.0880
1,3,6 | 1,4,5 | 2,2,6 | 2,3,5 | 2,4,4 | 3,3,4 10 0.1250
1,4,6 | 1,5,5 | 2,3,6 | 2,4,5 | 3,3,5 | 3,4,4 11 0.1250
(1,2,3) | 1,5,6 | 2,4,6 | 2,5,5 | 3,3,6 | 3,4,5 12 0.1389
1,6,6 | 2,5,6 | 3,4,6 | 4,4,5 13 0.0833
2,6,6 | 3,5,6 | 4,4,6 | 4,5,5 14 0.0694
3,6,6 15 0.0139
4,6,6 | 5,5,6 16 0.0278



(2,2,2) | (2,3,4) 18 0.0324
(3,4,5) 24 0.0278
(3,3,3) 27 0.0046
(4,5,6) 30 0.0278
(4,4,4) 36 0.0046
(5,5,5) 45 0.0046
(6,6,6) 54 0.0046

Notes: All possibilities are show, sorted; the order of the dice do not matter. A (1,2,3) is the same as a (2,1,3) or (2,3,1), etc. Parentheses around the roll indicate a straight (sum times two) or triple (sum times three) and thus also a switch. Chance of a reversal (straight or triple) is 5/36, or about 1/7.


Bonus third game! 222 or Unnamed as yet

Normal: Play starts and continues right or left. Player rolls and can keep his score or subtract it from player to his left (if playing left, or vice versa). A straight or triple immediately reverses play. No player can have less than 0 points.

Example: Player A rolls (1,2,3) and play had been going left. It switches to right. Player A may keep his 12 points or subtract them from player to his right. After scoring, play moves to right and proceeds as usual until next switch.

Endgame: Once a player meets or exceeds 222 points, play continues once more around in current direction, except that scores can only be added to players’ tallies, and only accumulated if successive rolls are larger than or equal to previous rolls. Players may stop at any time and tally score.

Example: Player A hits 230 so play moves to B, who is at 180. He rolls a score of 12, which isn’t enough to beat A, so he rolls again but must beat or tie 12 points on next roll. Suppose his second desperation roll is 14, for a total of 26, which still isn’t enough to beat A, so he will roll again. If he doesn’t beat or tie 14 on the roll, he is out. And so on across the board.

Notes. Haven’t played 222 yet, but would be delighted to hear reports of any attempts.


3 Comments

What Regression Really Is

Bookmark this one, will you, folks? If there’s one thing we get more questions about and that is more abused than regression, I don’t know. So here is the world’s briefest—and most accurate—primer. There are hundreds of variants, twists and turns, and tweaks galore, but here is the version most use unthinkingly.

  1. Take some thing in which you want to quantify the uncertainty. Call it y: y can be somebody’s income, their rating on some HR form, a GPA, their blood pressure, anything. It’s a number you don’t know but want to.
  2. Next write y ~ N(m, s), which means this and nothing else: “Our uncertainty in the value y takes is quantified by a normal distribution with central parameter m and spread parameter s.” It means you don’t know what value y will take in any instance, but if you had to bet, it would take one of the values quantified by the probabilities specified by the mathematical equation N(m,s).
  3. We never, absolutely never, say “y is normally distributed.” Nothing in the universe is “normally distributed.” We use the normal to quantify our uncertainty. The normal has no power over y. It is not real.
  4. The probability y takes any value, even the values you actually did see, given any normal distribution, is 0. Normal distributions are bizarre and really shouldn’t be used, but always are. Why if they are so weird are they ubiquitous? Some say insanity, others laziness, and still more ignorance. I say it’s because it’s automatic in the software.
  5. Collect probative data—call it x—which you hope adds information about y. X can be anything: sex, age, GDP, race, anything. Just to fix an example, let x1 be sex, either male or female, and let y be GPA. We want to say how sex informs our uncertainty of a person’s GPA.
  6. Regression is this: y ~ N(b0 + b1*I(sex=Male), s).
  7. This says that our uncertainty in y is quantified by a normal distribution with central parameter b0 + b1*I(sex=Male) and spread parameter s. The funny “I(sex=Male)” is an indicator function and takes the value 1 when it’s argument is true, else it equals 0. Thus, for males, the central parameter is b0 + b1 and for females it is just b0. Pause here until you get this.
  8. This could be expanded indefinitely. We could write y ~ N(b0 + b1*I(sex=Male) + b2 * Age + b3 * Number of video games owned, s), and on and on. It means we draw a different normal distribution for GPA uncertainty for every combination of sex, age, and numbers of video games. Notice the equation for the central parameter is linear. Our choice!
  9. Regression is not an “equation for y”. Regression does not “model y”. Regression only quantifies our uncertainty in y conditioned on knowing the value of some x’s.
  10. The b’s are also called parameters, or coefficients, or betas, etc. If we knew what the values of the b’s were, we could draw separate normal distributions, here one for men and one for women. Both would have the same spread, but different central points.
  11. We do not ordinarily know the values of the parameters. Classically we guess using some math which isn’t of the slightest interest to us in understanding what regression is. We call the guesses “b-hats” or “beta-hats”, to indicate we don’t know what b is but it is just a guess. The guesses are given the fancy title of “estimates” which makes it sound like science.
  12. Ninety-nine-point-nine-nine percent of people stop here. If b1 is not equal to 0 (judged by a magical p-value), they say incorrectly “Men and women are different.” Whether or not this is true, that is not what regression proves. Instead, if it were true that b1 was not equal to 0, then all we could say was that “Our uncertainty in the GPAs of females is quantified by a normal distribution with central parameter b0 and spread s, and our uncertainty in the GPAs of males is quantified by a normal distribution with central parameter b0+ b1 and spread s.
  13. Some people wrongly say “Males have higher GPAs” if b1 is positive or “Males have lower GPAs” if b1 is negative. This is false, false, false, false, and false some more. It is wrong, misleading, incorrect, and wrong some more, too. It gives the errant impression that (if b1 is positive) males have higher GPAs, when all we can say is that the probability that any given male has a higher GPA than any given female is greater than 50%. If we knew the values of the b’s and s, we could quantify this exactly.
  14. We do not know the values of the b’s and s. And there’s no reason in the world we should be interested, though the subject does seem to fascinate. The b’s are not real, they are fictional parameters we made up in the interest of the problem. This is why when you hear somebody talk about “The true value of b” you should be as suspicious as when a politician says he’s there to help you.
  15. What should then happen, but almost never does, is to account for the uncertainty we have in the b’s. We could, even not knowing the b’s, make statements like, “Given the data we observed and accepting we’re using a normal distribution to quantify our uncertainty in GPA, the probability that any given male has a higher GPA than any given female is W%.” If W% was equal to 50%, we could say that knowing a person’s sex tells us nothing about that person’s GPA. If W% was not exactly 50% but close to it—where “close” is up to each individual to decide: what’s close for one wouldn’t be for another—we could ignore sex in our regression and concentrate on each students’ age and video game number.
  16. This last and necessary but ignored step was the point of regression; thus that it’s skipped is an argument for depression. It is not done for three reasons. (1) Nobody thinks of it. (2) The p-values which say whether each bi should be judged 0 or not mesmerize. (3) Even if we judge the probability, given the data, that bi is greater than 0 is very high (or very low), this does not translate into a discernible or useful difference in our understanding of y and people prefer false certainty over true uncertainty.
  17. In our example it could be that the p-value for b1 is wee, and its posterior shows the probability it is greater than 0 is close to 1, but it still could be that, given the data and assuming the normal, the probability any given male has a GPA larger than any given female is (say) 50.01%. Knowing a person’s sex tells us almost nothing about this person’s GPA.
  18. But it could also be that the p-value for b1 is greater than the magic number, and the posterior also sad, but that (given the etc.) the probability a male has a higher GPA than a female is (say) 70%, which says something interesting.
  19. In short, the b’s do not tell us directly what we want to know. We should instead solve the equation we set up!

Obviously, I have ignored much. Entire textbooks are written on this subject. Come to think of it, I’m writing one, too.



31 Comments

Submit! Update

Source.

Source.

A 27-year veteran of the Utah Air National Guard said he was reprimanded after he wrote a letter objecting to a gay wedding in the West Point chapel and was later told to prepare for retirement because his personal beliefs about homosexuality were not compatible with the military’s policies.

Source

LGBT rights advocates chalked up a win on Wednesday as a Senate committee passed the Employment Non-Discrimination Act, a bill that would ban workplace discrimination based on sexual orientation and gender identity.

Source.

Jodi Rose, Australian Artist, Marries 600-Year-Old French Bridge Le Pont du Diable

Though their union is not legally recognized in France, Rose said it’s just as strong as any other marriage.

“While I respect those whose romantic and sexual feelings are oriented towards objects, mine is a symbolic affair, a pagan / animist view of the spiritual vibration in everything,” she wrote on her blog, Bridgeland. “He understands that I love other bridges — and men — ours is a love that embraces the vagaries of life, as materialized in the swirling currents of the river that flows beneath his magnificent body.”

Source

Hey, who are you to say it’s wrong. No, seriously: I ask you. Who are you to say it’s wrong? Did not the Supreme Court confirm that marriage is no longer to be based on biology but on feelings? Feelings. Oh, whoa, oh, feelings! Gmarriage for everybody!

And listen. You can have any opinion you want in these great United States. As long as its government approved.

Update

Transgender at 6:

Maryland couple decided to listen to their 5-year-old daughter’s urgent and persistent insistence that she was a boy, after a psychiatrist told them it would be healthy to let the child live as a boy…

Psychiatrists, as we know, are rarely mistaken, they being in a scientific field which in no way is subject to fad, whim, and misinformation. Source.

A photography studio in New Mexico was fined years ago under the state’s Human Rights Act for refusing to accept a lesbian couple’s request to photograph their commitment ceremony because it was contrary to the owners’ Christian beliefs.

Source.

Remember, as some commenters below have reminded us, all rights, including the right to take photographs, come from the blessed government. Vengeance is mine; I will repay, saith the government. Amen. It is government which gets to decide what is right and wrong, what is good for us and what bad. This cannot be questioned.


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Finally landed. But still way behind with emails!


35 Comments

See The Dancing Briggs

Another rapt audience

Another rapt audience

A reminder that the purpose of this site is mercenary and that I am sitting in the queue waiting to be flagged down and hired by you.

It turns out, much to my surprise, and to your eventual delight, that my specialty is venturing forth and lecturing those businesses interested in understanding uncertainty. Any that use numbers, probability, statistics, data to make forecasts or other guesses of the future or in an attempt to explain why what happened happened in the way it happened.

I have left a trail of enthralled audiences literally from coast to coast. Indeed, I have developed a permanent stoop from cramming my extended frame into airlines seats designed for emaciated Oompa Loompas.

Particularly, if you use the old ways of doing statistics it’s guaranteed that you’ll be too certain, that you’ll be too confident in the decisions you make, that you’d be better off casting a more skeptical eye.

If you’re interested in parting with some of your training budget, I’m here to help. See my Contact Page or email matt@wmbriggs.com


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I’m on the road now and behind in answering emails.


2 Comments
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