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Author Topic: Math Games  (Read 59739 times)

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faust

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Re: Math Games
« Reply #275 on: February 11, 2017, 03:29:52 am »

Kudos to faust for his R1 submission

I thought about it, but not knowing the mathematical literacy of other people, it just wasn't worth it.
For me it was more like a signal. Also I like to assume perfect rational players.
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faust

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Re: Math Games
« Reply #276 on: February 11, 2017, 03:37:58 am »

What happens if all teams get positive points?
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faust

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Re: Math Games
« Reply #277 on: February 11, 2017, 03:44:02 am »

Will all teams receive the same board?
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Calamitas

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Re: Math Games
« Reply #278 on: February 11, 2017, 04:56:18 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
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Axxle

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Re: Math Games
« Reply #279 on: February 11, 2017, 05:17:06 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
"If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them"

Doesn't sound so great to me
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Calamitas

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Re: Math Games
« Reply #280 on: February 11, 2017, 07:00:54 am »

I was very confused by some of the guesses in that game. Why did so many people guess near 50 in round 1? Why did everyone go for the unstable equilibrium in round 2 instead of the stable one near 4.5? Why does Calamitas' strategy make sense? Why the random square roots UoS? I just tried to guess how far off the stable equilibrium people would be guessing, and in the first two rounds I way underestimated.

Props to faust for submitting an exact fixed point all three rounds.

I picked what I wanted my guess to be to like 1 decimal place.  Then I squared that, picked a random number close to that, and submitted the square root of that, something with a bunch of decimal places.  It was just a lazy way to have a lot of decimal places to make ties less likely.  By the 3rd one I thought there was really no chance of a tie anyway but I just did it to keep the pattern.
But ties are good :-D
"If there is a tie for the winner, each tied player scores 9 points, MINUS 1 per additional player who tied with them"

Doesn't sound so great to me
2x8 > 1x9
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scott_pilgrim

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Re: Math Games
« Reply #281 on: February 11, 2017, 10:05:44 am »

What happens if all teams get positive points?

No one falls into the third category, so no one gets negative points.  (See my post a few posts down.)

Will all teams receive the same board?

No, each team's board will be randomized independently.
« Last Edit: February 11, 2017, 10:51:59 am by scott_pilgrim »
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faust

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Re: Math Games
« Reply #282 on: February 11, 2017, 10:23:05 am »

Okay, so this is not a zero-sum game after all.

Unfortunately, since all teams get different boards, I don't see a good way to coordinate.
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faust

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Re: Math Games
« Reply #283 on: February 11, 2017, 10:24:13 am »

Otherwise we could have all agreed to guess the same spot, making sure nobody gets negative points.
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liopoil

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Re: Math Games
« Reply #284 on: February 11, 2017, 10:24:52 am »

Okay, so this is not a zero-sum game after all.
I was just thinking this too. Potentially problematic
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Re: Math Games
« Reply #285 on: February 11, 2017, 10:44:30 am »

Okay, right, I forgot about that.  Don't post anything publicly yet.
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Re: Math Games
« Reply #286 on: February 11, 2017, 10:51:10 am »

If each team guesses either a red or blue square, scoring will happen normally, and then the negative points will be distributed among the teams guessing blue squares.  If all teams guess the red square, no one will score any points.  I'll update the rules post accordingly.

I apologize for changing the scoring in the middle of the game like this, but I think it needs to be done this way.  Please let me know if you have any concerns about this resolution.
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Calamitas

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Re: Math Games
« Reply #287 on: February 11, 2017, 11:02:16 am »

Okay, so we might want to decide collectively to not submit anything at all.
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faust

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Re: Math Games
« Reply #288 on: February 11, 2017, 11:31:11 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
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Calamitas

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Re: Math Games
« Reply #289 on: February 11, 2017, 11:45:58 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.
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Re: Math Games
« Reply #290 on: February 11, 2017, 11:49:20 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.

But being collective there doesn't increase the total score. It just keeps everyone's score closest to each other.
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Calamitas

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Re: Math Games
« Reply #291 on: February 11, 2017, 11:57:54 am »

Okay, so we might want to decide collectively to not submit anything at all.
That's not a stable strategy; if a single team chooses to go against this consensus, they can only win.
But we might decide to punish them for that in later rounds.

But being collective there doesn't increase the total score. It just keeps everyone's score closest to each other.
Yep, that's why I'm not sure about it here. Probably each team should just do their best.
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Re: Math Games
« Reply #292 on: February 11, 2017, 01:05:25 pm »


Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.


Just want to make sure I am thinking correctly about the scoring

6 teams.  Assume that 3 teams (one of them has 3 players) guess blue, one team guesses red, and two teams miss.

The teams that guess blue: each player on the team gets 3 points (total 21 points awarded)
The team that guessed red: each player gets 12 points (total 24 points awarded)
The teams that missed: divide up the total of 45 points evenly among the 4 players, so each player on the teams that miss get -11.25 points (rounded to -11)

is this right?
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scott_pilgrim

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Re: Math Games
« Reply #293 on: February 11, 2017, 01:27:08 pm »


Scoring is determined as follows (per player):   
Player B guesses the red square:   12
Player B guesses a blue square:   3
Player B does not guess either a blue or red square:   Negative points so that the total points among all players is 0 and the "losing" players all get the same number of points, rounding down if necessary to avoid non-integers.

If each team guesses either a blue or red square, the negative points will be distributed among the teams who guessed blue squares.  If all teams guess the red square, no one will get any points.

*Since there is an odd number of players, there will need to be one team of 3.  I'll list the teams in the next post.


Just want to make sure I am thinking correctly about the scoring

6 teams.  Assume that 3 teams (one of them has 3 players) guess blue, one team guesses red, and two teams miss.

The teams that guess blue: each player on the team gets 3 points (total 21 points awarded)
The team that guessed red: each player gets 12 points (total 24 points awarded)
The teams that missed: divide up the total of 45 points evenly among the 4 players, so each player on the teams that miss get -11.25 points (rounded to -11)

is this right?

Yes, that looks right.
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Re: Math Games
« Reply #294 on: February 11, 2017, 01:58:31 pm »

@scott: is there a solution?
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gkrieg13

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Re: Math Games
« Reply #295 on: February 11, 2017, 02:06:04 pm »

So essentially if we can we want to get the red square because that is the only way to assure that we don't lose points.
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Re: Math Games
« Reply #296 on: February 11, 2017, 02:37:56 pm »

so, if no teams correctly guess a blue or red square then no points are given or taken away?
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scott_pilgrim

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Re: Math Games
« Reply #297 on: February 11, 2017, 02:49:22 pm »

so, if no teams correctly guess a blue or red square then no points are given or taken away?

This is correct
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Re: Math Games
« Reply #298 on: February 11, 2017, 03:37:50 pm »

That is a very good solution, scott.
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Re: Math Games
« Reply #299 on: February 13, 2017, 06:14:20 pm »

/out for the next game.

I am sure I will regret it, but they are coming a bit too fast for me to be able to spend the required time to think them through. Maybe it would be different if we were told in advance what the next game is going to be.
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