math problem

[rong]

Scenario:

3 people in my office are playing a golf game for money. The rules are a cup is placed at one end of the room and the goal is to putt a golf ball into the cup. Each person puts £10 into the pot and gets 1 shot. If no one scores or everyone scores, they all play another round, again putting £10 each into the pot until only 1 person scores who takes the pot. If 2 people score and one misses then the misser is out and the game continues with the remaining 2 people.

I enter the room, the pot contains £300 with all 3 players who began the game still active. I want to join the game.

Assuming equal golf skill and a fair game, what amount should I add to the pot be fair to all parties for me to join the game at this point?

[BooG690]

$25

[rong]

Explanations required.

[a500lbgorilla]

It depends on what we mean by fair. My first sense is that if you step in and attempt to derive a profit on the back of this being the 10th round of the game, that's unfair. So you would have to chip in money that has no expectation of profit.

-x + .25(330+x) = 0
x = 110

But also, for fairness, your bet shouldn't increase the expectation of anyone already playing.

The normal expectation for that player at this time would be:

-10 + (1/3)(330) = 100, which is cool because everyone is breakeven expectation-wise for having paid up for 10 rounds. If you enter into the race with you 110 entry fee:

-10 + (1/4)(440) = 100, so everything checks out.

[rong]

But if I pay 110 then I've missed out on the 10 previous opportunities to win that my 110 would have bought me. So that's unfair on me.

[a500lbgorilla]

No it isn't. Every round has every actor keeping a running 0 expectation.

Besides, if you enter in less money, you lower everyone else's expectation and increase yours which is doubly unfair.

[a500lbgorilla]

Or you could enter in 10 bucks and have two pools, one where you have no chance at winning the 300 side pool.

[OngBonga]

Deleted my last two because they were wrong.

Ok, so put £100 in and take ten shots (£10 for each shot). If you miss them all, then everyone is even and you carry on from there, taking turns. If you score, then it depends how many shots it took you to score. If say you scored with the 7th, then you effectively paid £70 to reach this far, and should expect a prize of £280. If you score the tenth, you bink the lot. If you hit the 1st but then miss the rest, you only win £40. This would be fair.

[OngBonga]

Also Dan, you're English, no? It's a maths problem, you closet Yank.

[a500lbgorilla]

Deleted my last two because they were wrong.

Ok, so put £100 in and take ten shots (£10 for each shot). If you miss them all, then everyone is even and you carry on from there, taking turns. If you score, then it depends how many shots it took you to score. If say you scored with the 7th, then you effectively paid £70 to reach this far, and should expect a prize of £280. If you score the tenth, you bink the lot. If you hit the 1st but then miss the rest, you only win £40. This would be fair.

This isn't fair because the original 3 have an incentive to decline letting you do it.

[OngBonga]

This isn't fair because the original 3 have an incentive to decline letting you do it.

That's true. But then I can't see how it itsn't an issue of negotiation, by which I mean what's fair is what everyone agrees is fair. I think the side pot is how I'd approach it, you can only win money from the point you start playing.

[supa]

110.

Really it would be a turn around and walk away scenario because

A) After 10 tries nobody's made it, y'all suck and no one will ever win or

B) Everyone has made every shot so far but they have had the advantage of warming up.

[rong]

I think the only option fair to all is to start a new side pot with all 4 of us contributing with the other guys also playing for the main pot. This was all I came up with but wanted a way to get in on the big pot without feeling I'm being fucked over, which is how I'd feel if I had to pay 100 to get in.

[OngBonga]

Do you guys actually do any work?

[rong]

lol they do normally, I do on occasion.

[bikes]

or. wait till they fail and then join in next game. 5 mins of waiting 100 quid saved. OR 5 MINS WAITING 300 QUID LOST. GAAAAAAAAAAAMBOOOOOOOOOL

[rong]

You just wanted to say quid, didn't you?

[kiwiMark]

that's how people get daven'd man

[rong]

You think that should be added to the FTR poker dioctionary?

[KoRnholio]

No it isn't. Every round has every actor keeping a running 0 expectation.

Besides, if you enter in less money, you lower everyone else's expectation and increase yours which is doubly unfair.

This.

Think of it this way: You didn't have a chance in the previous rounds to win, but you also didn't have a chance to lose. Given equal skill, it's a complete wash. Past events/non-events/possible events don't change the present/future EV of this situation.

100 quid (equal share at this point) would be the right amount to get you back "on par" with the current state of the game. It would be the same as starting the game at 100 quid per person, and adding 10 per shot from this round onward.

[celtic123]

The original 3 should take their £100 back and start again This is fairest and no one gets hurt and your not left out.
the next fairest is buy in for £100 and carry on.
then comes buy in for £100 plus an entry fee. When word gets out, more ppl may want in so entry fees and ground rules discourage late entries.game disruption issues.

[kiwiMark]

The original 3 should take their £100 back and start again This is fairest and no one gets hurt and your not left out.

I mean you're probably going to have to tell a teacher to make them start a new game so you can play, but it's all worth it if no one gets hurt.

[rong]

I doubt the most confident of the three will be happy with the already wagered funds being returned to sender.

[rong]

and once again, lol Kiwi

[TLR]

Deleted my last two because they were wrong.

Ok, so put £100 in and take ten shots (£10 for each shot). If you miss them all, then everyone is even and you carry on from there, taking turns. If you score, then it depends how many shots it took you to score. If say you scored with the 7th, then you effectively paid £70 to reach this far, and should expect a prize of £280. If you score the tenth, you bink the lot. If you hit the 1st but then miss the rest, you only win £40. This would be fair.

That makes no sense, we don't have any of the previous scores, in each round all 3 could have missed it or could have hit it

[kiwiMark]

That makes no sense

FYP

[pocketfours]

without feeling I'm being fucked over, which is how I'd feel if I had to pay 100 to get in.

permaban

[swiggidy]

The money in the cup is dead. By paying $100 you have 25% equity and are getting 3:1 odds.

If you're good they would be dumb to let you play. If you're bad you would be dumb to play. Only if you're delusional would you be getting fucked over.

[BooG690]

The money in the cup is dead. By paying $100 you have 25% equity and are getting 3:1 odds.

If you're good they would be dumb to let you play. If you're bad you would be dumb to play. Only if you're delusional would you be getting fucked over.

FWIW, I'd only trust what swig says ITT. The man's fucking smart.

[dranger7070]

FWIW, I'd only trust what swig says ITT. The man's fucking smart.

But this one's a terrorist.

[Luco]

But this one's a terrorist.

And this one has anger issues, possibly steroid related

[dranger7070]

permadaven.

[kiwiMark]

FWIW, I'd only trust what swig says ITT. The man's fucking smart.

But if I only trust what swig says then I can't trust your advice and then I go back to at best having no reason to trust swig more than before you backed him and at worst a reason to distrust your advice and thus swig.

Way to backstab the guy whose opinion you supposedly believe in.

[rong]

Have you been reading labyrinths of reason?

[kiwiMark]

I've been watching 24

[Luco]

Are any of the players girls?

I wouldn't be too comfortable paying $100 to join a game of 3 dudes 1 cup...

[swiggidy]

FWIW, I'd only trust what swig says ITT. The man's fucking smart.

After everything that happened in Vegas I'm amazed this is the impression you left with, but thanks.

But if I only trust what swig says then I can't trust your advice and then I go back to at best having no reason to trust swig more than before you backed him and at worst a reason to distrust your advice and thus swig.

Way to backstab the guy whose opinion you supposedly believe in.

This is why you get the big bucks. And by bucks I mean rep points.

[gingerwizard]

It's 110 not 100 as each of the other 3 players are putting in 10 this round.

Each game is independent given equal skill of the players. The EV of each player if you don't play is

-10 + (1/3)330 = 100

The only fair way for you to enter is for you to pay y such that their EV is unchanged,

-10 + 1/4(330 + y) = 100

Rearranging gives
330+y = 440
y = 110.

[supa]

You can't do math with numbers and letters.

[kiwiMark]

You can't do math with numbers and letters.

It's 110 not 100 as each of the other 3 players are putting in 10 this round.

Each game is independent given equal skill of the players. The EV of each player if you don't play is

-10 + (1/3)330 = 100

The only fair way for you to enter is for you to pay y such that their EV is unchanged,

-10 + 1/4(330 + 110) = 100

-10 + 1/4(440) = 100
-10 + 110 = 100
100 = 100
99999999 = 999999999

tournament gets expensive by my estimations