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Monday, Dec 27, 2010 - 01:20 SGT
Posted By: Gilbert

Burps And Bingo

I've been slightly more strapped for time than expected these few days, so some scheduled expositions are delayed. How unfortunate.


Burp

My brother passed out from his SCS (formerly SISPEC) medic course, where I noticed that the Standard Obstacle Course had been further simplified; not only has the dismounting jump from the horizontal beam been replaced by steps, the barbed wire below the low ramp is now a concrete platform, presumably halving the height dropped.

The higher-ups probably figured that it doesn't make sense to ruin recruits' knees before an actual war. Frankly, once soldiers get shot at, I would expect them to learn the art of leaping off moderate heights pretty quickly.

The visit reminded me of two things about the army. The not-so-nice side is the interminable waiting around, and we spent an hour and a half just standing around, until the parade began. Time is cheap in the military.

The nice part was the gala buffet after the event, which brought back memories about the meals during my service period. Say what you like, but the army does feed its personnel well - which may have a little to do with my unrefined taste buds. Haven't marched on my stomach since basic training, though. Free Cremo Pilot ice-creams for everyone!

This was followed by another unexpected family trip to IMM (one passport short of JB) yesterday, where I learnt that an employee with a walkie-talkie can keep track of empty parking lots as well as overhead sensors.


Bingo

The night of Christmas Eve was spent at a friend's place, where the hosts spiced things up with a friendly round of Bingo, and very generously added an additional fifty bucks to the pot (had they mentioned this beforehand, the economics student in me would have felt compelled to participate).

What followed was a realisation that waiting for the last number to pop up can get rather annoying, and that having a bunch of numbers marked doesn't appear to mean too much - or does it?

A bit of simulation reveals that given 26 players (assuming one 5-by-5 Bingo card per player), with 75 possible numbers, the expected number of balls drawn before a winner appears (by completing any horizontal, vertical or diagonal line of five) is about 23; with 90 numbers (another common total), it rises to over 29.


More hands saves time - winning frequency vs balls drawn


The more cards there are, the faster the prize is expected to be won - having fifty participants shortens the expected number of rounds to about 20, while a lonely person playing Bingo Solitaire would have to draw approximately 43 balls before winning.

The host also offered a bonus S$50 to the winner, if he completed his Bingo on or before the tenth ball drawn; it seems that he knew that there was little risk of that happening, with this occurring less than 1% of the time with 26 players.


Example card used (Generated by the Free Bingo Sheet Generator)


The Bingo cards used had the 75 numbers distributed totally randomly (i.e. each grid square could contain any number), while it is likely more common in practice to restrict the numbers such that the first column contains only numbers from 1 to 15, the second column numbers from 16 to 30, and so on; this certainly makes looking up the numbers as they are called an easier task.

The non-restricted distribution yields approximately 8 * 1044 possible Bingo cards, while restricting yields about 6 * 1026 cards only, reducing the available combinations by a factor of 1018 - but it would be a dedicated player indeed who repeats a card in either case, assuming that they are truly randomly generated. Also, there's no significant difference in the average speed to Bingo-ing between these two customs.

It is also said that the chances of winning, given any two legal cards, is identical. However (taking the case of 26 cards), if one of the cards has access to the full range of 75 numbers, but the other 25 have only access to half the range (say, 38 numbers), it turns out that the former has a slightly higher chance of winning (about 50% more); with 99 other cards, the advantage increases to about 100% (but the absolute chance is reduced).

Clearly, it would be silly for a crooked Bingo hall to try and cheat in this manner (it would likely be far more efficient to just fix the balls), but this suggests that not all cards are created strictly equal - it depends on the other cards in the population. However, Bingo players shouldn't worry too much about this aspect, since even a near-impossible bias has a miniscule effect, as shown above.


Relation between numbers marked and balls drawn


And, oh, getting one of the numbers on your card called is never bad - that's just common sense. If it's any consolation, those cards which have numbers called earlier do tend to win early too, but of course it's far from guaranteed.

If it isn't the festive season and no Bingo hosts are to be found... well, there's always Seminar Bingo.

[On a side note, it appears as if everybody and his hamster is getting an iPhone nowadays (not you, Mr. Ham, Mr. Robo and Ms. Robo). Will this have an effect on the sense of exclusivity that is attached to Apple products, given that a handphone is perhaps the one gadget that most people need? We'll see...]


Benitez


Not I want to say, but... (Source: Redcafe.net)


Mayhaps he might want to try his hand at managing a Haxball team for a change of scenery? Tactics dominate there!

No change in pretend punting after last week's predictions were postponed due to snow. The draw looks tasty in Arsenal vs. Chelsea, if only because neither side dare lose. So...

P$100 on Arsenal to draw Chelsea (at 2.90)



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