Search Results: "byron"

1 July 2016

Joachim Breitner: When to reroll a six

This is a story about counter-intuitive probabilities and how a small bit of doubt turned out to be very justified. It begins with the game To Court the King (German: Um Krone und Kragen ). It is a nice game with dice and cards, where you start with a few dice, and use your dice rolls to buy additional cards, which give you extra dice or special powers to modify the dice that you rolled. You can actually roll your dice many times, but every time, you have to set aside at least one die, which you can no longer change or reroll, until eventually all dice have been set aside. A few years ago, I have played this game a lot, both online (on as well as in real life. It soon became apparent that it is almost always better to go for the cards that give you an extra die, instead of those that let you modify the dice. Intuitively, this is because every additional die allows you to re-roll your dice once more. I concluded that if I have a certain number of dice (say, n), and I want to have a sum as high as possible at the end, then it may make sense to reroll as many dice as possible, setting aside only those showing a 6 (because that is the best you can get) or, if there is no dice showing a 6, then a single die with the best score. Besides for small number of dice (2 or 3), where even a 4 or 5 is worth keeping, this seemed to be a simple, obvious and correct strategy to maximize the expected outcome of this simplified game. It is definitely simple and obvious. But some doubt that it was correct remained. Having one more die still in the game (i.e. not set aside) definitely improves your expected score, because you can reroll the dice more often. How large is this advantage? What if it ever exceeds 6 then it would make sense to reroll a 6. The thought was strange, but I could not dismiss it. So I did what one does these days if one has a question: I posed it on the mathematics site of StackExchange. That was January 2015, and nothing happened. I tried to answer it myself a month later, or at least work towards at an answer, and did that by brute force. Using a library for probabilistic calculations for Haskell I could write some code that simply calculated the various expected values of n dice for up to n = 9 (beyond that, my unoptimized code would take too long):
1:  3.50000 (+3.50000)
2:  8.23611 (+4.73611)
3: 13.42490 (+5.18879)
4: 18.84364 (+5.41874)
5: 24.43605 (+5.59241)
6: 30.15198 (+5.71592)
7: 35.95216 (+5.80018)
8: 41.80969 (+5.85753)
9: 47.70676 (+5.89707)
Note that this calculation, although printed as floating point numbers, is performed using fractions of unbounded integers, so there are no rounding issues that could skew the result. The result supported the hypothesis that there is no point in rolling a 6 again: The value of an additional die grows and approaches 6 from beyond, but judging from these number is never going to reach it. Then again nothing happened. Until 14 month later, when some Byron Schmuland came along, found this an interesting puzzle, and set out a 500 point bounty to whoever solved this problem. This attracted a bit attention, and a few not very successful attempts at solving this. Eventually it reached twitter, where Roman Cheplyaka linked to it. Coincidally a day later some joriki came along, and he had a very good idea: Why not make our life easier and think about dice with less sides, and look at 3 instead of 6. This way, and using a more efficient implementation (but still properly using rationals), he could do a similar calculation for up to 50 dice. And it was very lucky that he went to 50, and not just 25, because up to 27, the results were very much as expected, approaching value of +3 from below. But then it surpassed +3 and became +3.000000008463403. In other words: If you have roll 28 dice, and you have exactly two dice showing a 3, then it gives you better expected score if you set aside only one 3, and not both of them. The advantage is minuscule, but that does not matter it is there. From then on, the results behaved strangely. Between 28 and 34, the additional value was larger than 3. Then, from 35 on again lower than 2. It oscillated. Something similar could be observed when the game is played with coins. Eventually, joriki improved his code and applied enough tricks so that he could solve it also for the 6-sided die: The difference of the expected value of 198 dice and having 199 dice is larger than 6 (by 10 21...)! The optimizations that allowed him to calculate these numbers in a reasonable amount of time unfortunately was to assume that my original hypothesis (never rerolling a 6 is optimal), which held until n < 199. But this meant that for n > 199, the code did not yield correct results. What is the rationale of the story? Don t trust common sense when it comes to statistics; don t judge a sequence just from a few initial numbers; if you have an interesting question, post it online and wait for 16 months.

4 May 2013

Ian Campbell: Taking over qcontrol upstream, releasing qcontrol 0.5.0

Taking over Qcontrol upstream When I took over the qcontrol package in Debian, back in October 2012, I was aware that upstream hadn't been active for quite a while (since late 2009). I figured that would be OK since the software was pretty simple and pretty much feature complete. Nevertheless since I've been maintaining the package I've had a small number of wishlist bugs (many with patches, thanks guys!) which are really upstream issues. While I could carry them as patches in the Debian package they would really be better taken care of by an upstream. With that in mind I mailed the previous upstream (and original author) Byron Bradley back in February to ask if he would mind if I took over as upstream. Unfortunately I haven't yet heard back, given how long upstream has been inactive for this isn't terribly surprising so having waited several months I have decided to just go ahead and take over upstream development. Thanks Byron for all your work on the project, I hope you don't mind me taking over. Since it is unlikely that I will be able to access the old website or Subversion repository I have converted the repository to git and uploaded it to gitorious: I don't expect I'll be doing an awful lot of proactive upstream development but at least now I have a hat I can put on when someone reports an "upstream" issue against qcontrol and somewhere which can accept upstream patches from myself and others. I'm still deciding what to do about a website etc. I may just enable the gitorious wiki or I may setup an ikiwiki software site type setup, which has the advantage of being a little more flexible and providing a neat way of dealing with bug reports without being too much overhead to setup up. In the meantime its been almost 5 years since the last release, so... New Release: qcontrol 0.5.0 This is a rollup of some changes which were made in the old upstream SVN repository but never released and some patches which had been made in the Debian packaging. What's here corresponds to the Debian 0.4.2+svn-r40-3 package. The 0.4.2 release was untagged in SVN, but corresponds to r14, new stuff since then includes: As well as the change of maintainer I think the addition of the daemon mode warrants the bump to 0.5.0. Get the new release from git or

15 January 2011

Dirk Eddelbuettel: Allen Toussaint with Don Byron and Nicholas Payton

Lisa snagged us some sort of subscription to the CSO's jazz series and last night was a first concert resulting from this. In town were Allen Toussaint with a three piece rhythm section as well as Don Byron (also here) on clarinet and tenor saxophone, and Nicholas Payton (also here) on trumpet. Given Allen Toussaint's live-long association with New Orleans, there was a lot of music inspired by the town, including a modern rendition of an old Sidney Bechet tune as well as other material came from his most recent album The Bright Mississippi. And, given Allen Toussaint's fame in Rhythm and Blues circles, there was lot of R&B too. I found the program to be a little uneven and unbalanced that way---but it was still a great show, and he surely brought the house down. He is a charming old school performer, and maybe the audience warmed his heart right before the concert started with a quick Happy Birthday rendition as yesterday was in fact his this 73rd birthday! Don Byron and Nicholas Payton were, as expected, stellar in their own right. A nice night out.

27 February 2007

David Welton: php4, php5, objects and cloning

We take a very simple class:
class Foobar  
var $myvar = 1;
function Foobar()  
function printit()  
    echo "var is " . $this->myvar . "\n";
function incr()  
    $this->myvar += 1;
$f = new Foobar();
$a = $f;
$b = $f;
And run it with PHP4 and PHP5:
davidw@byron:/tmp$ php4 foobar.php 
var is 1
var is 1
davidw@byron:/tmp$ php5 foobar.php 
var is 1
var is 2
Apparently it's possible to use the clone function to do what we want with PHP5, but... that means we have to track down every single place in the code where there is something like $foo = $bar. And hope that we got them all, because otherwise subtle bad things might happen. The codebase I've inherited isn't great to begin with, and hunting down every object copy is bound to be torture. Ouch. Update It's been pointed out that my description of exactly what's happening internally isn't correct. However, from my point of view, the end result is the same: a massive search and replace operation in order to obtain the "old" behavior by using clone. Most likely, this means that we won't be able to upgrade soon, which means that we won't be able to take advantage of some of the nice new PHP5 features, which will slow down other works in progress. For want of a nail...

15 January 2007

Russell Coker: top 10 girl geeks

We have a list of 10 (famous) girl geeks from CNET and one from someone else.

The CNET list has Ada Byron, Grace Hopper, Mary Shelly, and Marie Curie. Mary Shelly isn't someone who I'd have listed, but it does seem appropriate now I think about it. Marie Curie is one of the top geeks of all time (killing yourself through science experiments has to score bonus geek points). I hope that there are better alternatives to items 4, 7, 9, and 10 on the Cnet list.

The list from someone else has 9 women I've never heard of. If we are going to ignore historical figures (as done in the second list) but want to actually list famous women then the list seems to be short. If we were to make a list of women who are known globally (which would mean excluding women who are locally famous in Australia, or in Debian for example). The only really famous female geek that I can think of is Pamela from Groklaw.

The process of listing the top female geeks might have been started as an attempt to give a positive list of the contributions made by women. Unfortunately it seems to highlight the fact that women are lacking from leadership positions. There seem to be no current women who are in positions comparable to Linus, Alan, RMS, ESR, Andrew Tanenbaum, or Rusty (note that I produced a list of 6 famous male geeks with little thought or effort).

Kirrily has written an interesting article on potential ways of changing this.

1 April 2006

Andrew Pollock: [life] More animal fostering

A mother and her litter of five kittens (four boys and a girl) were dumped at the animal shelter that Sarah volunteers at, and they needed a temporary home for about 5 weeks until they're old enough to be weaned, de-sexed, and put up for adoption, so they have taken up temporary residence in the spare room. They're about three weeks old at the moment, and very uncoordinated. The mother is only about 8 months old herself, and very affectionate. It's interesting watching her reaction to her kittens mewing. It'll be fun watching them grow up. They're a bit too small to be playful yet, but they're starting to develop their own personalities. Sarah named them: