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Posers and Puzzles

Posers and Puzzles

  1. Donation Acolyte
    Now With Added BA
    25 Jan '03 16:46
    This one's not hard if you spot the answer, but I think it deserves a little explanation (sorry royalchicken, no elaborate proofs required):

    Vaknso and Rhymester are playing a game. Vaknso tosses a coin 10 times, Rhymester only 9; both record the number of heads they got. If Vaknso gets more heads than Rhymester, he wins; otherwise Rhymester wins. Assuming neither cheats, what is the probability that Rhymester wins?
  2. 25 Jan '03 19:00
    50/50.. if im right if im wrong!
  3. Donation Acolyte
    Now With Added BA
    25 Jan '03 19:14
    Originally posted by peterh
    50/50.. if im right if im wrong!
    But why 50/50?
  4. Subscriber Chris
    Site Admin
    25 Jan '03 19:17 / 2 edits
    Originally posted by Acolyte
    This one's not hard if you spot the answer, but I think it deserves a little explanation (sorry royalchicken, no elaborate proofs required):

    Vaknso and Rhymester are playing a game. Vaknso tosses a coin 10 times, Rhymester only 9; both ...[text shortened]... uming neither cheats, what is the probability that Rhymester wins?
    I'm afraid I don't know why. But the answer is 50/50, because there are 110 possible outcomes, and vaknso wins 55 of them. Actually there it is... some of them must be draws...

    I cheated and resorted to programming to solve... (sorry about the formatting, this poorly designed site doesn't deal with indentation properly )

    int totalCombos = 0;
    int vaknsoWins = 0;
    for (int vaknso=0; vaknso<=10; vaknso++)
    {
    for (int rhymester=0; rhymester<=9; rhymester++)
    {
    totalCombos ++;
    if (vaknso > rhymester)
    {
    vaknsoWins ++;
    }
    }
    }
    float ratio = (float)vaknsoWins / totalCombos;

    System.out.println(vaknsoWins + "/" + totalCombos + " = " + ratio);

  5. Subscriber Chris
    Site Admin
    25 Jan '03 19:19
    So I completed the program to give me all the facts...

    Vaknso Wins: 55/110 = 0.5
    Draws: 10/110 = 0.09090909
    Rhymester Wins: 45/110 = 0.4090909
  6. Donation Rhymester
    and RedHotTed
    25 Jan '03 19:25 / 1 edit
    Well I'm no mathematician but if we tossed it the same number of times it would be 50%. I'm tossing it one less time so Vaknso would have the advantage - so less than 50% chance of me winning.
    He's tossing it 10% more than me so he has 10% more chance of winning. So 6 to 4 on for Vaksno to win. 60% for Vaknso which leaves a 40% chance of me (Rhymester) winning.

    Rhymester
  7. 25 Jan '03 19:55
    i reckon its 50/50- if they both had 9 each then 50/50 and they both have 50/50 on the extra go (the 19th go) theres no need for any more throws because someone would have won! surely there cannot be a draw on a toss of a coin?and surely there cant be a draw if best out of 19? im no mathematician either..so there could be plenty of thisand this:'(:'(.....
  8. Subscriber Chris
    Site Admin
    25 Jan '03 19:56
    Originally posted by Rhymester
    Well I'm no mathematician but if we tossed it the same number of times it would be 50%. I'm tossing it one less time so Vaknso would have the advantage - so less than 50% chance of me winning.
    He's tossing it 10% more than me so he has 10% more chance of winning. So 6 to 4 on for Vaksno to win. 60% for Vaknso which leaves a 40% chance of me (Rhymester) winning.

    Rhymester
    And what about your draws...
  9. Subscriber Chris
    Site Admin
    25 Jan '03 19:58
    Originally posted by peterh
    ...surely there cant be a draw if best out of 19? im no mathematician either..so there could be plenty of thisand this:'(:'(.....
    It's a draw if Vaknso gets 5 out of 10 and Rhymester gets 5 out of 9...
  10. 25 Jan '03 20:07
    p.s....if this is anything like the ''don''question then im going to look a bit silly!
  11. Donation Rhymester
    and RedHotTed
    25 Jan '03 20:18 / 1 edit
    OK then 33.3% and that's my final offer

    I think the first 9 tosses would cancel each other out probability wise and I would have a 1 in 3 chance on the tenth toss.

    Rhymester
  12. Standard member royalchicken
    CHAOS GHOST!!!
    25 Jan '03 21:21
    Acolyte-Don't you think it a bit dangerous to be pitting vaknso and Rhymester against each other ? There could be riots...
  13. Donation Rhymester
    and RedHotTed
    25 Jan '03 23:49
    Originally posted by royalchicken
    Acolyte-Don't you think it a bit dangerous to be pitting vaknso and Rhymester against each other ? There could be riots...
    Baggies I keep the coins when it's all over!

    Rhymester
  14. Donation Rhymester
    and RedHotTed
    29 Jan '03 08:46
    Originally posted by Rhymester
    OK then 33.3% and that's my final offer

    I think the first 9 tosses would cancel each other out probability wise and I would have a 1 in 3 chance on the tenth toss.

    Rhymester
    So, was I right?
  15. Donation Acolyte
    Now With Added BA
    29 Jan '03 09:16
    The answer is 50/50: note that if they both get the same number of heads, Rhymester wins.
    Vaknso gets an extra toss; if he gets tails, he's at a disadvantage because he now has to get more heads than Rhymester to win; if he gets heads, he's at an advantage because (over the remaining 9 tosses each) Rhymester has to get more heads than him to win.