Advanced Mafia Calculus e1
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  1. #1

    Advanced Mafia Calculus e1

    the game is a k shot roulette such that k>=3.
    The min bet is 1 points.
    There's 1 guy who bet 10000 points
    There's n other players such that 1<=n<=11, who bet 100 points each.
    Assume everyone are cowards who only pulls the gun once.
    Assume the gun never jams.
    Assume your max bet is 11100 points.

    Chapter 1
    Q1. Assume k=12 and n=2, how many points should you bet for maximum profit?

    (Hint: derive the equation once and find it's root!)
    Last edited by Tauntshaman; November 24th, 2019 at 10:47 PM.
    CHOO CHOO, THE SQUIRREL GOD CALLS THOSE RIGHTEOUS AND FAITHFUL! FLOCK TO THE SQUIRREL MESSIAHS ARMS!

  2. #2

    Re: Advanced Mafia Calculus e1

    Fuck this equation is actually really long.

    Was not expecting it to get this big. You got me T_T
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  3. #3

    Re: Advanced Mafia Calculus e1

    Yeah, I'm pretty sure I haven't made any mistakes and this does rest on solving a quartic.

    The quartic in question doesn't seem to have any nice ways of being simplified. You'd just have to plug it into the quartic formula.
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  4. #4

    Re: Advanced Mafia Calculus e1

    One can demonstrate that the average profit can be written as a function of the player's bet, like so:

    E(profit)=0.25*( (10,000B)/(B+200) + (200B)/(B+10,100) - B )

    Then, one can differentiate this equation w.r.t B and solving for its extrema (which will sadly be equivalent to solving a quartic).

    Lastly, one can plug all these extremum values for B (along with 1 and 11100) back into the function and uncover which extremum yields the largest value for E(profit).

    There are some issues with this approach. E(profit) merely represents the average amount of profit you're extremely likely to make after betting the same amount in this same scenario 100s of times. In reality you may run out of cash long before your average profit is E(profit)! Hence, this answer is highly theoretical.
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  5. #5

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by Tauntshaman View Post
    the game is a k shot roulette such that k>=3.
    The min bet is 1 points.
    There's 1 guy who bet 10000 points
    There's n other players such that 1<=n<=11, who bet 100 points each.
    Assume everyone are cowards who only pulls the gun once.
    Assume the gun never jams.
    Assume your max bet is 11100 points.

    Chapter 1
    Q1. Assume k=12 and n=2, how many points should you bet for maximum profit?

    (Hint: derive the equation once and find it's root!)
    the root is Distorted because he is the root of all evil (tbh the same could be said to me aswell but then others call me chaotic neutral)
    May The Heart Be Your Guiding Key

  6. #6

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by yzb25 View Post
    One can demonstrate that the average profit can be written as a function of the player's bet, like so:

    E(profit)=0.25*( (10,000B)/(B+200) + (200B)/(B+10,100) - B )

    Then, one can differentiate this equation w.r.t B and solving for its extrema (which will sadly be equivalent to solving a quartic).

    Lastly, one can plug all these extremum values for B (along with 1 and 11100) back into the function and uncover which extremum yields the largest value for E(profit).

    There are some issues with this approach. E(profit) merely represents the average amount of profit you're extremely likely to make after betting the same amount in this same scenario 100s of times. In reality you may run out of cash long before your average profit is E(profit)! Hence, this answer is highly theoretical.
    YOU GOT THE IDEA CONGRATS but no this is not the correct answer.

    Plug in your equation into desmos and it yields:
    10.png
    However, this is only valid [9800,+infinity) due to the rule that u can't bet more than all others' bet combined. for example, in a 3-man roulette, if the other 2 ppl bet 5 and 10 pts each, and you bet 60, you bet will be automatically lowered to 5+10=15pts

    Obviously on [9800,10200] there isn't a critical point, thus this is no the correct answer
    CHOO CHOO, THE SQUIRREL GOD CALLS THOSE RIGHTEOUS AND FAITHFUL! FLOCK TO THE SQUIRREL MESSIAHS ARMS!

  7. #7

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by Tauntshaman View Post
    YOU GOT THE IDEA CONGRATS but no this is not the correct answer.

    Plug in your equation into desmos and it yields:
    10.png
    However, this is only valid [9800,+infinity) due to the rule that u can't bet more than all others' bet combined. for example, in a 3-man roulette, if the other 2 ppl bet 5 and 10 pts each, and you bet 60, you bet will be automatically lowered to 5+10=15pts

    Obviously on [9800,10200] there isn't a critical point, thus this is no the correct answer
    I'm confused about what the permitted range of betting is. Your first post says it's between 1 and 11100, this post suggests it's between 1 and 10200. Both of these ranges include 1225.

    Also, regardless of what the cutoff ranges are, so long as you plug in your minimum permitted value, your maximum permitted value and then any extrema within the permitted range, you will find the highest.

    Or did I mess up my equation?
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  8. #8

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by yzb25 View Post
    I'm confused about what the permitted range of betting is. Your first post says it's between 1 and 11100, this post suggests it's between 1 and 10200. Both of these ranges include 1225.

    Also, regardless of what the cutoff ranges are, so long as you plug in your minimum permitted value, your maximum permitted value and then any extrema within the permitted range, you will find the highest.

    Or did I mess up my equation?
    Also that's one freaky ass graph. I kinda like it.
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  9. #9

  10. #10

  11. #11

    Re: Advanced Mafia Calculus e1

    Now that I think about it, it makes sense that betting between 1 and 2 thousand is the best. It's high enough to drown out your opponent's gains if the 10,000 loses, while still being a very small bet relative to 10,000.
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  12. #12

  13. #13

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by yzb25 View Post
    Now that I think about it, it makes sense that betting between 1 and 2 thousand is the best. It's high enough to drown out your opponent's gains if the 10,000 loses, while still being a very small bet relative to 10,000.
    The guy attempting to bet 10k can always only put in as much as all other players combined. You do not get 10k from him if you don't bet 10k yourself. Hence the only way to gain 100% profit is to bet 1.

  14. #14

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by Kenny View Post
    The guy attempting to bet 10k can always only put in as much as all other players combined. You do not get 10k from him if you don't bet 10k yourself. Hence the only way to gain 100% profit is to bet 1.
    So, after all the bets are made, if someone's bet is larger than the sum of the other bets, their bet gets reduced to the sum of the other bets?

    Am I right in thinking that the loser's pot is split proportionately to how much each person bet?

    omg that explains what Taunt was saying I'm sorry XD
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  15. #15

    Re: Advanced Mafia Calculus e1

    What about the order? With 12 shots and 4 players, on average each player will die 1/4 of the time, sure. But won’t the person going first, on average, pull the trigger the most and therefore get a larger share of the pot?

    Or is the order also random?
    Have you ever heard the tragedy of Darth Jar Jar the wise?

  16. #16

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by aamirus View Post
    What about the order? With 12 shots and 4 players, on average each player will die 1/4 of the time, sure. But won’t the person going first, on average, pull the trigger the most and therefore get a larger share of the pot?

    Or is the order also random?
    if u assume everyone only pull once than order doesn't matter. for example, in a 3 shot roulette with 3 players:
    the first player has 1/3 chance to die
    the gun has 1/3 chance to fire in the first round, hence the chance of second player getting to pull is 2/3. and out of that 2/3 there's a 1/2 chance the gun will fire, 2/3*1/2=1/3
    similarly, the third player has 1/3 chance to pull and 1/1 chance for the gun to fore, thus making it 1/3 also




    ...and the share is only dependent on your initial bet and extra pulls, not the "forced" ones
    CHOO CHOO, THE SQUIRREL GOD CALLS THOSE RIGHTEOUS AND FAITHFUL! FLOCK TO THE SQUIRREL MESSIAHS ARMS!

  17. #17

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by Varcron View Post
    My great math skills lead me to believe that the answer is 42, as 42 is always the correct answer.
    The answer is 2 Celsius degrees, obviously.
    Quote Originally Posted by S-FM Hey peter View Post
    There are two wolves inside you. One is addicted to crack. The other one is also addicted to crack. You are addicted to crack.
    Quote Originally Posted by Stealthbomber16 View Post
    MM IS AN ANTI-VAXXER
    Quote Originally Posted by The Lawyer View Post
    Besides your lamp and your refridgerators, do you find anyone else suspicious?

  18. #18

    Re: Advanced Mafia Calculus e1

    Quote Originally Posted by Tauntshaman View Post
    if u assume everyone only pull once than order doesn't matter. for example, in a 3 shot roulette with 3 players:
    the first player has 1/3 chance to die
    the gun has 1/3 chance to fire in the first round, hence the chance of second player getting to pull is 2/3. and out of that 2/3 there's a 1/2 chance the gun will fire, 2/3*1/2=1/3
    similarly, the third player has 1/3 chance to pull and 1/1 chance for the gun to fore, thus making it 1/3 also




    ...and the share is only dependent on your initial bet and extra pulls, not the "forced" ones
    let's say the 6th shot is the kill-shot.
    So person 1 pulls twice total and lives
    Person 2 pulls twice total and dies
    person 3 pulls once and lives
    person 4 pulls once and lives

    Doesn't person 1 get a bonus for pulling more times?
    Have you ever heard the tragedy of Darth Jar Jar the wise?

  19. #19

    Re: Advanced Mafia Calculus e1

    If my understanding is correct, that'd mean that when B<9800 the equation radically simplified because the 10,000's are replaceed with "200+B" in the original equation I posted:

    E(profit)=0.25*( (B+200)B/(B+200) + (200B)/(2B+300) - B )

    ---> E(profit)=0.25*( 200B/2B+300 )

    The maxima evidently becomes 9800. You can prove this without the graph again by deriving for extremums (realizing there's no extremums) and then evaluating all the endpoints of each function.
    Quote Originally Posted by Blinkstorteddd02 View Post
    naz, he's claiming to have been at your house last night and infected you. I know u were drunk but PLEASE try as hard as you can to remember... That burning you felt the next morning when you went pee was from me, not him.

  20. #20

 

 

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