Jump to content

Portfolio Type II -- The Dice Game


Skyline

Recommended Posts

can anyone PLEASE guide me with the last two questions??? how to determine the costs and payout?? and how do you count the probability of winning when there are multiple players??? HELP HELP HELP :help: :help: :help: :help: :help:

I think its pretty straight forward. I assume you have calculated the probablity of the either the bank/player(s) winning. You can determine the cost/payout simply by choosing how much money you wish to circulate. From how I define of "fair", the costs and payout should be set so that if both the bank and the player(s) start off with $1000, after 200 tries of the game they will still have roughly that amount. So create such a situation. Well pick a number for the cost, I choose $25. Say the probability of the bank winning is 0.25 and the probability of the player winning is 0.75 . The payout should be determined as the cost divided by the probability. Thus, the bank will win $100 if they win and the player $33.3... You will find that in the long run that the costs, payout and probability cause equalibrium and that after infinite games, they should still have roughly the same balance.

  • Like 6
Link to post
Share on other sites

I think its pretty straight forward. I assume you have calculated the probablity of the either the bank/player(s) winning. You can determine the cost/payout simply by choosing how much money you wish to circulate. From how I define of "fair", the costs and payout should be set so that if both the bank and the player(s) start off with $1000, after 200 tries of the game they will still have roughly that amount. So create such a situation. Well pick a number for the cost, I choose $25. Say the probability of the bank winning is 0.25 and the probability of the player winning is 0.75 . The payout should be determined as the cost divided by the probability. Thus, the bank will win $100 if they win and the player $33.3... You will find that in the long run that the costs, payout and probability cause equalibrium and that after infinite games, they should still have roughly the same balance.

thank you soooooo much!!!!! :props: I highly appreciate the help!

one question: if the bank wins, will the player have to pay again on top of the cost of the game?

thanks a lot!!!

Link to post
Share on other sites

can anyone PLEASE guide me with the last two questions??? how to determine the costs and payout?? and how do you count the probability of winning when there are multiple players??? HELP HELP HELP :help: :help: :help: :help: :help:

I think its pretty straight forward. I assume you have calculated the probablity of the either the bank/player(s) winning. You can determine the cost/payout simply by choosing how much money you wish to circulate. From how I define of "fair", the costs and payout should be set so that if both the bank and the player(s) start off with $1000, after 200 tries of the game they will still have roughly that amount. So create such a situation. Well pick a number for the cost, I choose $25. Say the probability of the bank winning is 0.25 and the probability of the player winning is 0.75 . The payout should be determined as the cost divided by the probability. Thus, the bank will win $100 if they win and the player $33.3... You will find that in the long run that the costs, payout and probability cause equalibrium and that after infinite games, they should still have roughly the same balance.

There's a slight mistake there. The probability of the bank winning doesn't matter. The bank only "wins" the cost; there is no payout to the bank. However, the rest of what you said about the payout is true. The payout when the player wins would have to be 25/0.75 = $33 (it's best to keep it to rounded figures). What this is means is:

The player will (probably) win 3 games out of 4. The cost of playing 4 games is $100. The payout out of winning 3 games: $99. So all-in-all, the bank is making $1 on every four games. Had the payout been $34, the payout for winning 3 games would be $102. The bank would be making a loss of two dollars on every four games. The bank will choose to use $33 for payout because it maximizes the appeal to the player, while still making a profit on the long run.

So to answer your last question, Desy; No, the cost is all the player pays.

Edited by genepeer
  • Like 3
Link to post
Share on other sites

  • 1 month later...

Can somebody give me some guidance on step 3? To me, it looks similar to step one. I mean the probability doessn't seem like changing when the dice are rolled twice, but I know that my predictions are not correct, so I'm asking you guys.

it will be different since the highest score will be noted.

hint:

Ann's chance of getting 1 in the first roll is 1/6

Ann's chance of getting 2 in the first roll is 1/6

Ann's chance of getting 3 in the first roll is 1/6

Ann's chance of getting 4 in the first roll is 1/6

Ann's chance of getting 5 in the first roll is 1/6

Ann's chance of getting 6 in the first roll is 1/6

Ann's chance of getting 6 in the second roll is 1/6

so the chance for Ann to score a 6 will be....? (consider the opposite case too, where Ann gets a 6 in the first roll and anything in the second roll)

  • Like 1
Link to post
Share on other sites

  • 1 month later...

so who has finished this task and is able to give a little more guidance?

so in the fourth question, the player will win if their score is higher than the bank's and the player will lose (i.e. the bank will win) if their score is the same with the bank's? what will happen if the player's score is lower than the bank's?

wouldn't the best game be a fair one? like when the probability of winning for the player and for the bank are the same?

can anyone hint me on the last question with multiple players?

A casino is created to make money in the long run so the bank has to make profit i think so it can't be a fair game

Link to post
Share on other sites

Pleease, can anyone guide me with the second question?

what's your problem? quote me please so I can reply to you once I go online.

Pleease, can anyone guide me with the second question?

what's your problem? quote me please so I can reply to you once I go online.

i have a problem in step 2 too. what does " ann can roll her die a second time and will NOTE THE HIGHER SCORE OF THE TWO ROLLS but bob rolls only once" mean? does it mean that the SUM of ann's rolls have to higher of the score of bob OR EACH of her scores must be higher than his? moreover, what is the sequence of rolling? firstly she, then he and again she or not? I'm a bit confused with this point. please help

Link to post
Share on other sites

i have a problem in step 2 too. what does " ann can roll her die a second time and will NOTE THE HIGHER SCORE OF THE TWO ROLLS but bob rolls only once" mean? does it mean that the SUM of ann's rolls have to higher of the score of bob OR EACH of her scores must be higher than his? moreover, what is the sequence of rolling? firstly she, then he and again she or not? I'm a bit confused with this point. please help

basically it means:

ann rolls twice

bob rolls only once

the order of rolling is not set and it doesn't matter anyway

you know if ann's score > bob's score, ann wins vice versa but if ann's = bob's, bob wins.

that ann's score is not the score of each roll in this case. it's just the highest score from the two rolls.

it doesn't matter who rolls first, second or last.

Link to post
Share on other sites

i have a problem in step 2 too. what does " ann can roll her die a second time and will NOTE THE HIGHER SCORE OF THE TWO ROLLS but bob rolls only once" mean? does it mean that the SUM of ann's rolls have to higher of the score of bob OR EACH of her scores must be higher than his? moreover, what is the sequence of rolling? firstly she, then he and again she or not? I'm a bit confused with this point. please help

basically it means:

ann rolls twice

bob rolls only once

the order of rolling is not set and it doesn't matter anyway

you know if ann's score > bob's score, ann wins vice versa but if ann's = bob's, bob wins.

that ann's score is not the score of each roll in this case. it's just the highest score from the two rolls.

it doesn't matter who rolls first, second or last.

i have a problem in step 2 too. what does " ann can roll her die a second time and will NOTE THE HIGHER SCORE OF THE TWO ROLLS but bob rolls only once" mean? does it mean that the SUM of ann's rolls have to higher of the score of bob OR EACH of her scores must be higher than his? moreover, what is the sequence of rolling? firstly she, then he and again she or not? I'm a bit confused with this point. please help

basically it means:

ann rolls twice

bob rolls only once

the order of rolling is not set and it doesn't matter anyway

you know if ann's score > bob's score, ann wins vice versa but if ann's = bob's, bob wins.

that ann's score is not the score of each roll in this case. it's just the highest score from the two rolls.

it doesn't matter who rolls first, second or last.

you said "it's just the highest score from the two rolls" so taking an example, ann is rolling 3 and 6. while bob 5. who wins in that moment and why? ann because the sum (9) is bigger than 5 or still ann because she got 6 while bob still 5? thanks a lot

Link to post
Share on other sites

you said "it's just the highest score from the two rolls" so taking an example, ann is rolling 3 and 6. while bob 5. who wins in that moment and why? ann because the sum (9) is bigger than 5 or still ann because she got 6 while bob still 5? thanks a lot

lol, the task doesn't mention sum anywhere in it, so no please don't think about the sum at all.

ann wins because her score (which is the higher score from 3 and 6, which is 6) is higher than bob's (which is 5).

another example, ann gets 1 and 2 while bob gets 4. ann's highest score is 2, which is lower than bob's so bob wins.

Link to post
Share on other sites

Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do.

If Ann and bob roll once, the probability is 15/36

If Ann rolls twice and Bob rolls once, the probability is 125/216

If Ann and Bob each roll twice, the probability is 505/1296

So based on that I know that the denominator of the equation is 6^(A) times 6^(B)

(A = number of rolls Ann gets, B = number of rolls Bob gets)

But I have no Idea how to figure out what the numerator would be.

Any Help?

Link to post
Share on other sites

Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do.

If Ann and bob roll once, the probability is 15/36

If Ann rolls twice and Bob rolls once, the probability is 125/216

If Ann and Bob each roll twice, the probability is 505/1296

So based on that I know that the denominator of the equation is 6^(A) times 6^(B)

(A = number of rolls Ann gets, B = number of rolls Bob gets)

But I have no Idea how to figure out what the numerator would be.

Any Help?

You are right about the denominator. However, the numerator is much more complicated. To get the numerator, you must look at the cases carefully and generalize how you got every case, using variables. I can't give you formula and it is not a simple equation as you say.

Link to post
Share on other sites

Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do.

If Ann and bob roll once, the probability is 15/36

If Ann rolls twice and Bob rolls once, the probability is 125/216

If Ann and Bob each roll twice, the probability is 505/1296

So based on that I know that the denominator of the equation is 6^(A) times 6^(B)

(A = number of rolls Ann gets, B = number of rolls Bob gets)

But I have no Idea how to figure out what the numerator would be.

Any Help?

yes there is a formula, but it is very complicated. since i did this portfolio, i'm less willing to give out much guidance. my one and only hint: sigma notation.

Link to post
Share on other sites

Is there an equation to figure out the probability that Ann wins for a given amount of rolls each player gets? for example if you want to know what is the probability that Ann wins if both Ann and Bob roll 4 times. there's got to be a simple equation to figure it out. Otherwise its going to take ALOT of calculating to do.

If Ann and bob roll once, the probability is 15/36

If Ann rolls twice and Bob rolls once, the probability is 125/216

If Ann and Bob each roll twice, the probability is 505/1296

So based on that I know that the denominator of the equation is 6^(A) times 6^(B)

(A = number of rolls Ann gets, B = number of rolls Bob gets)

But I have no Idea how to figure out what the numerator would be.

Any Help?

i was wondering how did u get 505 over 1296 . For the first two questions you are right. but the third one, i think it is 295 over 1296
Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...