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July 31st, 2002

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06:06 am - Numbers of the day
I need your help with a troubling integer sequence.

What numbers follow next in this sequence and why?


I have been told the following numbers, but I can't work out the logic. Even the good old Integer Sequence Encyclopedia has failed me. As is usual with these things, the person who set the puzzle claims that it can be done with "6th grade math", the sequence is infinitely long and that "no mundane or earthly knowledge is required to solve this puzzle... and in fact it might just hurt your chances".

Many thanks in advance to any bright sparks who can see what I'm missing.

Right, now I have that important public announcement out of the way I can retreat into a <lj-cut> to talk at length about poker.

I have a huge deal of respect for poker as a card game. Much of this is due to "Late Night Poker", a TV show broadcast on Channel 4 here in five short seasons over the last couple of years. It does a remarkably good job of illustrating a (relatively simple version of) a complicated game to a specialist audience.

Voiceover host Jesse May, plus a colour commentator in the established sports broadcast traditions, give a tremendous summary of what's going on. I suspect that much of the commentary is scripted and edited, because it's far too good to be live. Furthermore, they know exactly when to be quiet and let the action (and the players) speak for itself. This is a cut above 99% of sports commentary. Jesse has a wonderful voice and a tremendous range of timbres, which vary from ever-so-slightly-wistful to so-enthused-only-dogs-can-hear-him.

However, much of the appeal is the effortless way in which they establish a mythos and build up the reputation of the players. In just a few short hands, they effectively communicate a sense of the players' characters. Obviously, there's no telling whether they're sticking to the truth or taking us for a ride - but it's subtle, yet works to a T. Furthermore, their little cute names and in-jokes lull the viewer into an intimate shared experience, giving the impression that the game is played between what Jesse might call "ramblin', gamblin'" folk without the traditional lawless excesses of the Wild West.

It's quite possible that ealuscerwen may be laughing her socks off by this point. I shall respectfully defer to her authority if she is.

Incidentally, my view of Jesse is favourably affected by his book, "Shut Up And Deal", which is a novel containing not so much a story as a semi-stream-of-consciousness blend of vignettes, mingling together the demonstrably true with the deliciously plausible. I borrowed my copy of it from Nick Parish, who owns the book but hates it. Furthermore, Jesse also writes a lovely column for The Good Gambling Guide which only perpetrates the mystique further. Entertainingly, he frequently promotes lots of losing bets supposedly placed by his team of backers. His "Meal Wars" column - a solo appearance to date - is also highly entertaining. I don't think the guy is physically capable of writing a dull paragraph; if he wrote about a trip to the post office in the patent May style, it would be as florid a wander as any of Stuart Hall's famous football-and-Ozymandias reports.

To top it all off, his e-mail address is clearly visible by his columns. If you send him a polite mail, he will make a respectful reply. Now maybe I'm just being more of a fanboy than usual, but you can't get the same degree of service from John Motson. It's not just Jesse, either. Lots of the top, and not-so-top, players maintain their own web sites and post away quite happily to each other on online message boards. They are very ordinary, literate, intelligent, personable people who just happen to play an extraordinary game. The immediacy of connection between the lowest and highest levels of play may be nearly unmatched in many fields of endeavour.

(You can tell I'm writing this at 5am. I haven't used nearly enough parenthetical remarks yet.)

Anyway, not a little due to the success of Late Night Poker, poker in the UK is on a gentle upswing at the moment, and this leads to bluffers like me poking their noses in where they aren't necessarily required. Every board game which has a "start player" marker that rotates around the table starts to inspire tribute lines like "So tell us about that dealer button, Barney" and "So there's a hundred and fifty pounds in the pot - even before the players get to see their cards!". Truly it is one of the finest set-pieces in the business.

But one thing leads to another and more gamers than ever before are coming into contact with poker - or, at least, I'm coming into contact with more gamers than ever before who are themselves in contact with poker.

Now one of my fundamental ("religious", if you will) positions on gaming is that a good game should be as entertaining when not played for money as it is when played for money. Furthermore, I don't like playing games as much as I dislike losing money, especially when you know the swine who's taking advantage of your misfortune. Admittedly this comes from the guy who offered 7/2 against someone turning up at a games convention and consequently lost 70p as a result, but that sort of thing is just plain funny. I'd offer the same bet again tomorrow, I'm convinced it offers lousy value. The guy in question was really too busy to turn up and will probably regret taking the time off work.

Another reason that I don't want to play poker for money ever again is that my lifetime record at money poker is currently 43p to the good and believe in quitting while I am ahead. The backstory here is a one-pound-a-head tournament two ManorCons ago, where the guy who was organising it paid for me to enter just so he would get more opposition. Then he found he only had 93p in change and I figured the overlay on offer was good enough for me to break the habit of a lifetime. Frankly it wasn't a particularly good poker tournament - six entries and we paid three, with the third prize (which I took) being a half-your-original-stake-back insult prize of 50p. It was also that tournament in which I witnessed someone get a legit Royal Flush at Texas Hold 'Em in person, doubtless for the only time in my life. How we all chortled at the irony of wasting a Royal Flush on a pound-a-head jolly.

Still, from time to time I encounter a group of (normally board) gamers who are prepared to play poker for laughs without a financial stake - and a freeze-out tournament is the most convenient way to structure this. Almost all the time we play No Limit Texas Hold 'Em, because it's what we know from the TV. One of these days we will finally learn that you need lots and lots of low-valued chips and relatively few high-valued ones, not vice versa as per most sets of board game funny money.

I maintain that the concept of "being in the game" is an effective enough motivator to get people to take the game seriously; being out of the game is a punishment at the "you can't play with us any more" schoolchild level which is the ultimate danger in any game, a fate to be avoided. The fact that elimination games have somewhat gone out of fashion, for the best of reasons, makes poker's inherent elimination structure all the more special. If you want a slightly higher stake, you can say "winner chooses the next game". (If you want a higher non-financial stake still but are in one-gendered company then you can always play Mental Strip Poker. I don't think there's any evidence to suggest that's ever reached a stage of evolution further than "grand thought experiment", as is the case of most of the ideas in the Global Ideas Bank. In this case, I suspect "grand thought experiment" may be quite fully evolved enough.)

However, we ended up playing it at the games club tonight. There are eight players in the game: Nick M, who fancies himself as a playa with the ladies but not a player at poker, Peter S, who apparently used to play for low stakes with his housemates and picked up wicked streaks of wins by exploiting the fact that one friend used to inadvertently perform The People's Eyebrow (years before either The Rock or Vic Reeves ever thought of it) every time he was running a bluff, Brian McI, who plays as tight as a duck's buttocks and has a haircut to match, your protagonist, who likes to read up on the subject but is quite glad not to be playing for money, Matt H, who is quiet enough that I must have met the guy thirty times and am still not completely sure of his name, and three children with a combined age of possibly thirty-seven.

Anyway, the kids are still at the stage of learning what a good five-card hand is (no, a run of three cards doesn't count for anything) and what sort of pre-flop hands might get them there. They play very fast and loose to the point where anything less than a six-way flop is a rarity. Now this is the point where I start to doubt my principles and suspect that they might not quite play the same way if there were a real stake. Unfortunately, the only thing I could ever win from them would be bloody Pokémon cards - and I'm not convinced that I could sell them back to them if I did win them because they'd all go off and play the Dragonball Z CCG instead.

The whole reason I decided to make a poker-themed LJ entry tonight is that in the fifth or sixth hand tonight, we had a silly number of pre-flop raises which lead to the big stack going all in... and all the kids decided to follow. (Hey, they'd been playing for fully 30 or 45 minutes and were probably starting to get bored.) Consequently we ended up having a main pot and four - four! - side pots. Thankfully, the second biggest stack hit a straight draw on the river. He was in all the pots, being the biggest all-in player, so we didn't have to go through and try to remember who was and wasn't in each side pot. The upshot of it was that we went down from eight players to four in a single hand and that's something you don't see on Late Night Poker very often.

The game was a little more sensible after all the kids were eliminated (I got out of that hand with my A8 after the pot was triple-re-raised just after my first, single-big-blind, bet - a move which saved me a tidy packet) in one fell swoop but I got knocked out a little later, finishing third, so no place for me at the semi-final table. (I went all-in as first to speak of three with KJs, the chip leader called with 95, 9 paired the board and my two missed.) There was very, very nearly a remarkable comeback when we got down to heads-up (by this time I was acting as dealer, which I always enjoy) but one big hand settled it.

It's probably playing at playing poker rather than actually playing poker, but a good time was had by all anyway.

(Not much off 2000 words in a little over an hour.)

Current Mood: Insomnolent
Current Music: the dawn chorus

(10 comments | Leave a comment)


Date:July 30th, 2002 10:21 pm (UTC)


Are you sure about that last number? It's quite odd that the numbers would increment list up to 800ish, then suddenly drop to 311.
[User Picture]
Date:July 31st, 2002 01:35 am (UTC)

Good evening, and welcome to the show

As a mathematics graduate, I'm probably the last person to have a go at this, but as an expert in the fine art of google, I can furnish you with the answer. Unless you want the answer, don't click here.
As a simple clue, consider the length of each term in the series. What is it that reaches 2 digits at its 5th term, 3 digits at its 11th term?
[User Picture]
Date:July 31st, 2002 03:32 am (UTC)


"I have been told the following numbers, but I can't work out the logic."

This is probably a good thing. Being too busy to play with this properly, I have up after 5 minutes and was very glad I did when I read the answer.

The person who set the problem takes an information-theoretic view and regards it as a good problem because the solution can be concisely expressed as an algorithm. However, from a game design perspective (we are doing this for fun, right ?) the sequence isn't a very interesting one because it's far too arbitrary, having no interesting mathematical properties, being one of a set of 362980 sequences amongst which it does not stand out as special and being in any case relative to a particular numerical base.

Also, "no mundane knowledge" can be a bit of a relative thing. For example, I just made up this sequence:


(It does appear in the Encyclopedia, FWIW) Now this sequence is a lot more interesting to humans, particularly humans who watch gameshows, than it is from a detatched mathematical perspective.
[User Picture]
Date:July 31st, 2002 05:40 am (UTC)
I read the solution at the link provided in an earlier comment. In my opinion, this is not a fair problem.
[User Picture]
Date:July 31st, 2002 09:36 am (UTC)


Hmm. Which of the four good comments should I reply to? I know, none of them.

Many thanks to those who have pointed me in the right direction. D'oh, indeed. Being able to find something on Google when you can't find it on the integer sequence encyclopedia - who'd have thought it? (To be fair, looking on Google is the sort of thing that I probably should have thought of trying myself.)

On the whole, I grudgingly concede this is a fair puzzle. (It's a grudging concession because it is, overtly, a fair puzzle, but I wasn't smart enough to think of the technique required.) After all, there are only a fairly limited number of techniques you can use in a reasonable integer sequence puzzle and this is just one that I hadn't encountered before.

I take Dom's point about the substitution cipher in use not being an interesting one. For instance, it might have been an easier-to-crack puzzle (a fairer puzzle? a more fun puzzle?) if the cipher used was, say,
1234567890 <-> 0123456789 or <-> 2345678901 or <-> 4567890123 or <-> 0987654321. However, there is a sense of internal logic to it - when you write out 0,1,4,9,16,25,36... then you write each digit for the first time in the order 0149625387, which is the clue from which you get the cipher 1234567890 -> 0149625387. It's not as if the substitution cipher used has been plucked at random from the 10! possibilities, even if it is a bit too clever and obscure for me to have spotted.

A difficult and clever puzzle. If Dom couldn't get it in five minutes then I don't feel so bad about not getting it myself. :-)
[User Picture]
Date:July 31st, 2002 09:52 am (UTC)

Re: Ahhhh....

Don't be so modest, Chris, I'm sure you're way better at that kind of thing than I am !
[User Picture]
Date:July 31st, 2002 11:39 am (UTC)



Can I be laughing my socks off but respectfully abdicate all authority, please?

[User Picture]
Date:July 31st, 2002 11:47 am (UTC)

Re: Request

Ooh, go on, but only because you asked nicely.

WANTED: poker authority. Absolutely no money paid whatsoever. Applicants must have own dealer button, "Anecdote FM" radio channel (all poker anecdotes, all the time) and sleeveful of aces.
Date:July 31st, 2002 01:46 pm (UTC)
*brain has melted*

I honestly don't have a clue, but the reason for that is twofold:
a) I'm totally crap at Maths - I was kicked off an A/S Level Pure Maths course two weeks before we went on study leave because if I took the exam, I was going to drag the school averages down.
b) Logic is something I don't do. Explains why, despite A's in four A-levels [/boast], my IQ according to the latest online test I took was 91.

[User Picture]
Date:July 31st, 2002 03:02 pm (UTC)


Worry not. This is a very inconsequential integer sequence, even among the inconsequential field of recreational integer sequences.

Being refused permission to take an exam to protect a school's average is hypocritical and scandalous. I was discussing changes in education policy with worrals' boyfriend t'other day; he argued that nobody would choose to return to the days when schools' performances were catalogued but not published, though maybe this is an argument that either

(a) "average protection" of the type you have experienced is counter-productive with regards to the essential education provision purposes of schools


(b) the most popular stats are recording unhelpful details.

Unfortunately, case (b) is trickier to deal with than it might at first appear. Schools shouldn't be able to deny their students the right to take exams just to protect their averages - however, schools' averages shouldn't be punished in the instances that their students decide for themselves not to take exams at the last minute. Trying to come up with a metric which will identify the circumstances under which each student stops studying for an exam is, probably, practically impossible, so we probably aren't going to get a more useful metric.


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