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re: Statistics Spinoff Thread: How much would you pay to play this "game of chance"

Posted on 1/15/16 at 1:48 pm to
Posted by UpToPar
Baton Rouge
Member since Sep 2008
23099 posts
Posted on 1/15/16 at 1:48 pm to
I would guess that over say 100 games, the mean amount won would be around $8, so that's how much you should pay. (Maybe $10)
Posted by terd ferguson
Darren Wilson Fan Club President
Member since Aug 2007
114938 posts
Posted on 1/15/16 at 1:48 pm to
quote:

You ask how much to play. He tells you, it costs $X to play the game. OP is asking, what do you think X should be.


$4 but let them call heads or tails... give them a sense of control.
Posted by slackster
Houston
Member since Mar 2009
91874 posts
Posted on 1/15/16 at 1:48 pm to
quote:

If the pot starts at $2 and I risk $1,000,000 then the pot is now $1,000,002 and if I flip tails I receive a payout the size of the pot according to the OP.


The OP shouldn't have called it a 'pot' but rather a 'prize.'

You're thinking of a traditional pot like in card games, but in this instance it is just the prize you win, plain and simple. The longer you flip heads, the bigger the prize.
Posted by foshizzle
Washington DC metro
Member since Mar 2008
40599 posts
Posted on 1/15/16 at 1:48 pm to
If "the house" or for that matter anyone other than me is doubling the pot until I win, then the answer depends on the size of their bankroll. If I get on a real hot streak the pot could grow to a point where they could not double.

If the answer is that there is no limit then I will not play because it's a scam.
Posted by terd ferguson
Darren Wilson Fan Club President
Member since Aug 2007
114938 posts
Posted on 1/15/16 at 1:49 pm to
quote:

You are being intentionally obtuse aren't you? I feel a hook in my jaw.


Only since the point where I realized that the money the player was putting in did not go into the pot.

Now I'm being normal.
Posted by sealedup
BR
Member since Oct 2011
169 posts
Posted on 1/15/16 at 1:50 pm to
but saying $2 is just best case scenario for customer what is the amt that game becomes 50/50 for house and customer?
Posted by Walking the Earth
Member since Feb 2013
17464 posts
Posted on 1/15/16 at 1:55 pm to
I think the OP dicked up his hypothetical but he needs to come back with the "answers" just in case there's some neat math behind all of this with which he's going to boom us.
Posted by Scooba
Member since Jun 2013
20027 posts
Posted on 1/15/16 at 1:56 pm to
So your 1x bet to play the game is basically taking a chance that you will flip enough heads to double the pot to cover your buy in before flipping tails, and "losing" by winning a pot = less than your original bet.

I would consider 4 "heads" in a row lucky. That would lead to a 32$ pot. Any flips beyond that would be a nice payout. I would imagine the casino setting the buy in at 30$. I wouldn't play but I would sit and watch people lose money while drinking complementary crown.
Posted by sealedup
BR
Member since Oct 2011
169 posts
Posted on 1/15/16 at 1:58 pm to
no shite just like u can get house % hold on various games, I'm not going to find a roulette wheel w 35 numbers that would make the game even if just playing numbers and house paying 35/1
Posted by UpToPar
Baton Rouge
Member since Sep 2008
23099 posts
Posted on 1/15/16 at 2:00 pm to
It looks like $6 is about the break even point over many games.

Let's say 100 people each play the game once.

50 people are going to win $2
25 will win $4
12.5 will win $8
6.25 will win $16
3.125 will win $32
1.5625 will win $64

Each of these groups adds up to $100 paid out (50x$2, 24x$4, 12.5x$8, etc.) totaling $600 paid out. $600 paid out divided by 100 games equals $6 per game.
This post was edited on 1/15/16 at 2:02 pm
Posted by Aux Arc
SW Missouri
Member since Oct 2011
2184 posts
Posted on 1/15/16 at 2:02 pm to
I'm guessing the number is somewhere in the range of $15-$20 but I don't have the math reasoning for my hunch.
Posted by STLDawg
The Lou
Member since Apr 2015
4615 posts
Posted on 1/15/16 at 2:03 pm to
Ah, the St. Petersburg Paradox. The only math puzzle/paradox I've seen start more fights is the Monty Hall problem.
Posted by noonan
Nassau Bay, TX
Member since Aug 2005
37016 posts
Posted on 1/15/16 at 2:04 pm to
quote:

No way he setup his scenario correctly.
Or, some aren't understanding it correctly.


He definitely did not explain it well.

But I think I see what he is saying now.
Posted by sealedup
BR
Member since Oct 2011
169 posts
Posted on 1/15/16 at 2:04 pm to
up to par believe ugot right formula but 50 would win $4 it doubles on 1st flip
Posted by UpToPar
Baton Rouge
Member since Sep 2008
23099 posts
Posted on 1/15/16 at 2:07 pm to
quote:

up to par believe ugot right formula but 50 would win $4 it doubles on 1st flip


Nope. 50 would move on to the second flip, but assuming 50/50 odds, half of that 50 would win again, moving on to the third flip. That's why only 25 people would win $4.
Posted by UpToPar
Baton Rouge
Member since Sep 2008
23099 posts
Posted on 1/15/16 at 2:09 pm to
The problem is that, because the pot keeps doubling, it would only take 1 person to flip 7 or 8 times and really screw up the probabilities. If just one person wins $128 or $256, then $6 as the break even point becomes wayyy off.
Posted by tke857
Member since Jan 2012
12195 posts
Posted on 1/15/16 at 2:10 pm to
about tree fiddy
Posted by sealedup
BR
Member since Oct 2011
169 posts
Posted on 1/15/16 at 2:11 pm to
i got u but in the confusing rules it reads to me that it will never be a payout of $2 which will bring the # to $12
Posted by sealedup
BR
Member since Oct 2011
169 posts
Posted on 1/15/16 at 2:13 pm to
true but if you are the house with unlimited bankroll you can charge $1 or $2 dollars extra to start
Posted by Scooba
Member since Jun 2013
20027 posts
Posted on 1/15/16 at 2:14 pm to
quote:

If just one person wins $128 or $256, then $6 as the break even point becomes wayyy off.


True, but all the casino has to do is make enough to win in the long run.

If as you say, the average payout of 100 players is 600$. Lets say the casino sets the game at 8$ to play. You flip at least twice and you make your money back. 3 in a row is a winner. Casino makes an average of 200$ off of every 100 players and the chance of someone winning 128$ is < 1 in 100.

My numbers aren't as clear as yours but does that make sense? I may be way off...
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