## A Conversation for Lobster Pots - a Mathematics Game

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### Excellent stuff

OwlofDoom Started conversation Jan 28, 2003

I've never heard of this game, but it has certainly given me some ideas.

I enjoy computer programming, and whenever I learn a new language I tend to try to write the game _Mastermind_ (you know, the one with the coloured pegs). Take a look at my PHP version of said game at .

This game sounds like an excellent idea for a new programming project, especially if I can incorporate an RBS (a primitive form of artificial intelligence) to play as extra players.

The only thing that confuses me from a mathematician's point of view is the stuff about Lottery Days. You say that the players can choose any number (and have to do so), but whichever number they choose they win a hundred quid. I know this is for simplicity's sake, but surely after a few turns, they would soon realise that betting on _seven_ is without a doubt the safest bet, as it's (if I remember correctly) about twice as likely to come up as any other number.

I think this rule would be better if people were given the option of betting on the lottery, and everyone wins if seven comes up (rather than giving those who don't know the magic of seven a significant disadvantage) - obviously there'd need to be something bad about betting too - say you have to bet £20 and you win £120 back or something.

Anyway, after my exams I'll have a look at this as a programming project, and you'll hear about my progress here first .

~ Owl

### Excellent stuff

spook Posted Jan 28, 2003

7 may be the most probable number to appear, however, it does not mean it always comes up. there are other numbers that can appear as well, which means that instead of many people winning, perhaps only 1 person will win.

spook

### Excellent stuff

OwlofDoom Posted Jan 28, 2003

It is quite likely that other numbers will come up. However, if the stakes are equal for each number, surely it is most advantageous for one to bet on _seven_, resulting in a higher probability of winning the same prize. Certainly, if I was playing this game I would always bet on seven as (if you follow a normal distribution, which I believe dice follow) over enough time, it will result in the highest return.

### Excellent stuff

spook Posted Jan 28, 2003

it all depends on how long you play for. of course, a variation could be a distribution of 1 large amount equally between all winners, which would be god for a computer version, however, is not practical in a classroom setting.

spook

### Excellent stuff

OwlofDoom Posted Jan 28, 2003

Anyway, it was an excellently-written article and I enjoyed it a lot. I've been looking for a simple game like this for ages to try out programming something _other_ than Mastermind !

### Excellent stuff

spook Posted Jan 28, 2003

thanks!

and if you are looking for something to program, you could try something like the 24 game (A933121)

spook

### Excellent stuff

OwlofDoom Posted Jan 28, 2003

That's certainly an interesting idea, but it's more a fast-paced multiplayer thingy, which isn't my scene at all!

And "24" is a registered trademark? Amazing!

### lottery

Snowman Posted Jan 28, 2003

maybe you could have odds on the # that comes up as well as betting.

say for the # 7, you get double your money back: £20 bet gets you 40.

but if you bet on 2 and 12, £20 gets you £120.

### lottery

Bagpuss Posted Jan 28, 2003

For the record, 7 is not twice as likely as any other number. 6 and 8 each have a 5/36 chance of coming up, as compared with 6/36 for 7. Nevertheless, as the article describes it a bet of 7 is the only sensible way.

Dividing the winnings isn't so daft in a classroom setting. Why not divide 120 quid? It's divisible by 2,3,4,5,6 and 8, and if you must have a remainder chuck it back to Camelot.

### lottery

spook Posted Jan 28, 2003

and if 17 people choose the right number, consider the time taken to equally divide the amount, and remember that lessons are only 1 hour long usually.

spook

### lottery

Bagpuss Posted Jan 28, 2003

7 quid each, remainder 1. Took me maybe 20 seconds in my head. Besides, the game is supposed to be about maths.

### lottery

spook Posted Jan 28, 2003

aah yes, so it is! but the teacher would be the one to do that, unless, the etacher took the numbers then delegated it to a student to figure out, solving the ultimate problem of everything.

spook

### odds

Snowman Posted Jan 28, 2003

well have the odds of winning almost proportional to the wager, with one # subtly being the winner. then the teacher could leave it to the students to work our for themselves (if they want to have a better chance of winning money in the next lesson) which is the best # to bet on.

just a thought. but i guess with short lessons, the odds will probably not even out, thus making this way pointless

### lottery

OwlofDoom Posted Jan 28, 2003

Re: For the record, 7 is not twice as likely as any other number. 6 and 8 each have a 5/36 chance of coming up, as compared with 6/36 for 7.

Yeah, . That was my mistake. I wasn't exactly _thinking_ earlier, as I'm in the middle of final exams for my degree. You're quite right, but seven _is_ still more likely than six or eight.

### lottery

Bagpuss Posted Jan 28, 2003

Don't worry, I just thought I should make it clear for anyone who assumed you were right.

As for the last part, that depends on parsing.

p(6 or 8) = 10/36 > p(7) > p(6) = p(8).

### lottery

Viojen 2*16+1+3+6=42. Fencing-it's escrime! Posted Jan 28, 2003

Well, our math lessons are only 46 minutes, and if you take into account how long it takes my class to shut up you lose some valuble time. I think I will show this to my teacher anyways. Even though we're a high school class she lets us do fun things every once in a while. ANd especially because we're high school we should be able to divide the bonus without wasting too much time.

### lottery

Viojen 2*16+1+3+6=42. Fencing-it's escrime! Posted Jan 28, 2003

oops! can't spell. I meant

I tried to preview to check the spelling, but I guess I pushed the wrong button.

### lottery

OwlofDoom Posted Jan 29, 2003

Re: As for the last part, that depends on parsing.

!

You know what I mean! I'll rewrite it "the probability of getting six or the probability of getting eight"

Key: Complain about this post

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### Excellent stuff

- 1: OwlofDoom (Jan 28, 2003)
- 2: spook (Jan 28, 2003)
- 3: OwlofDoom (Jan 28, 2003)
- 4: spook (Jan 28, 2003)
- 5: OwlofDoom (Jan 28, 2003)
- 6: spook (Jan 28, 2003)
- 7: OwlofDoom (Jan 28, 2003)
- 8: spook (Jan 28, 2003)
- 9: OwlofDoom (Jan 28, 2003)
- 10: Snowman (Jan 28, 2003)
- 11: Bagpuss (Jan 28, 2003)
- 12: spook (Jan 28, 2003)
- 13: Bagpuss (Jan 28, 2003)
- 14: spook (Jan 28, 2003)
- 15: Snowman (Jan 28, 2003)
- 16: OwlofDoom (Jan 28, 2003)
- 17: Bagpuss (Jan 28, 2003)
- 18: Viojen 2*16+1+3+6=42. Fencing-it's escrime! (Jan 28, 2003)
- 19: Viojen 2*16+1+3+6=42. Fencing-it's escrime! (Jan 28, 2003)
- 20: OwlofDoom (Jan 29, 2003)

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