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+--- Thread: Math puzzles! (/showthread.php?tid=48625)
Math puzzles! - XTOTHEL - 2011-11-07
XTOTHEL Wrote:6 x 6 x 6 = 216 total combos
5 x 5 x 5 = 125 combos without the number YOU guessed.
125/216 = 57.9% chance that you lose.
ok...
67/216 combos that you get 1x, 31.0%
18/216 combos that you get 2x, - 8.33%
6/216 combos that you get 3x - 2.78%
1 x 0.31 + 2x 0.0733 + 3x0.0278 = 0.54
Math puzzles! - shouri - 2011-11-07
XTOTHEL Wrote:ok...
125/216 = 57.9%
67/216 combos that you get 1x, 31.0%
18/216 combos that you get 2x, - 8.33%
6/216 combos that you get 3x - 2.78%
1 x 0.31 + 2x 0.0733 + 3x0.0278 = 0.54
bolded numbers are incorrect.... also, you forgot to include something in that last equation.... loses have to be taken into account too... not just wins.
Math puzzles! - Kalovale - 2011-11-07
In all the likelihood of winning, 1/36 nets you 3x bet, 2*(5/36) nets you 2x bet and the rest nets you 1x bet.
On average: 3/36 + 20/36 + 25/36 = 1.33x the bet money.
With a 42% chance to win at 133% bet money, on average you win 42%*133% = 55.9% of the bet money, and lose 57.9% of the bet money per bet.
Not entirely sure I'm not speaking nonsense here, but whatever.
Math puzzles! - shouri - 2011-11-07
Kalovale Wrote:In all the likelihood of winning, 1/36 nets you 3x bet, 2*(5/36) nets you 2x bet and the rest nets you 1x bet.
On average: 3/36 + 20/36 + 25/36 = 1.33x the bet money.
With a 42% chance to win at 133% bet money, on average you win 42%*133% = 55.9% of the bet money, and lose 57.9% of the bet money per bet.
Not entirely sure I'm not speaking nonsense here, but whatever.
Lol, take your time next time.... you can't win 55.9% and lose 57.9% of your money xD
it's 1/216 gets you 3x bet (other errors too).
Math puzzles! - Kalovale - 2011-11-07
Oh, there's the possibility of winning the other dice when you get double-win too. Hmm..
And I don't see why I can't win those amounts on average.
Math puzzles! - shouri - 2011-11-07
Also, the rest doesn't net you 1x bet.... you sure CAN get 1 x bet... but you can also lose your bet... meaning -1x bet
Math puzzles! - Kalovale - 2011-11-07
shouri Wrote:Also, the rest doesn't net you 1x bet.... you sure CAN get 1 x bet... but you can also lose your bet... meaning -1x bet
I was accessing only winning bets.
Math puzzles! - shouri - 2011-11-07
Kalovale Wrote:I was accessing only winning bets.
yeah, noticed that after. too lazy to edit xD
Math puzzles! - Kalovale - 2011-11-07
E.g: A 6-6-6 guess with 6-6-6 results will gain as much as a 6-6-3 guess with 6-6-3 results.
Silly me, it doesn't matter.
Math puzzles! - Mibs - 2011-11-07
You people are crazy lol.
I wish I was good enough at math for this.
Math puzzles! - shouri - 2011-11-07
Mibs Wrote:You people are crazy lol.
I wish I was good enough at math for this.
I didn't learn to do this 'til I got to college (never took stats)... but plenty of people learn to do something real close to this during high school D:
Math puzzles! - Shidoshi - 2011-11-07
(5/6)^3 chance to get (-1) - ~58%
3 * 1/6 * (5/6)^2 chance to get (+1) - ~35%
3 * (1/6)^2 * 5/6 chance to get (+2) ~7%
(1/6)^3 chance to get (+3) ~0.5%
Averages to -0,0787
Math puzzles! - shouri - 2011-11-07
Shidoshi Wrote:(5/6)^3 chance to get (-1) - ~58%
3 * 1/6 * (5/6)^2 chance to get (+1) - ~35%
3 * (1/6)^2 * 5/6 chance to get (+2) ~7%
(1/6)^3 chance to get (+3) ~0.5%
Averages to -0,0787
Love the avatar btw... and yes you're correct.
When betting a dollar you're only receiving back about 92 cents (aka losing out on about 8 cents per game). Let's say six people play a minute a game, with a house minimum of $5 per play... the even though they only lose out on 8% per play... the house gets to make over $100 an hour off of them
6) Another gambling game! (probably a bit easier this time)
Let's check the license plates of the next twenty cars we see and notice the last two digits of each plate. I'll bet you $20 that at least two of the cars will have plates with the same last two digits. So you win if there is no match... you lose if there is a match.
"Hmm.... since we're worried about the last two digits... there are 100 choices ranging from 00 to 99. The chance of two of them matching is 1/100 for two chars... so since there's 20 cars, there's about a 20/100 chance that they make.... or 80% chance I'll win...sweet... let's start."
ex Plate1: F567RET plate2: E967WER match up. (Just pretend ALL plates are like this "letter-number-number-number-letter-letter-letter", ignoring custom plates.)
The bet is $20 at 1:1 (aka if you win, you get $20, if you lose you lose $20). This may or may not be bad odds to play at.... what if you were offered 5:1 (aka a bet of $20 can net you $100 if you win).
Math puzzles! - nRxUs - 2011-11-07
What's the question? Whether you should play?
If that's the question then of course not, you have to take into account permutations and make a binomial distribution which shows that the chances of you losing are over .9.
Similar to that question of if you have at least 30 people in the room there is a huge chance that at least two of them share the same birthday. Permutations win.
Math puzzles! - Shidoshi - 2011-11-07
The chance that all twenty car plates will be different is:
100!/((100 - 20)! * (100^20)) = 13,04%
Or the complementary, the chance that at least one plate will be the same is 86,96%
So the odds are extremely against the guy betting they'll all be different (even a 1:5 bet is disadvantageous).
Not gonna calculate the expected value here, it's not hard though.
For a group of N possibilities, the chance that in n different picks all will be different is:
N!/((N - n)! * N^n))
Math puzzles! - shouri - 2011-11-07
nRxUs Wrote:What's the question? Whether you should play?
If that's the question then of course not, you have to take into account permutations and make a binomial distribution which shows that the chances of you losing are over .9.
Similar to that question of if you have at least 30 people in the room there is a huge chance that at least two of them share the same birthday. Permutations win.
Chance of losing is NOT over .9 actually. Also remember, the pay out is IMPORTANT. If you had a 90/10 chance (only 10% chance of winning)... but the pay out was higher than 10:1 it'd be worth playing... even with the high chance of losing.
The questions are as follows:
is it worth it to play at a 1:1 payout? You pretty much answered this part. (aka, no)
is it worth it to play at a 5:1 payout? This one's a bit trickier. You'll have to calculate the EXACT percentages to see if 5:1 is a good payout or not.
Math puzzles! - Kalovale - 2011-11-07
Lol, that dice problem, I went from guessing one dice to guessing three dice without even knowing what happened.
Math puzzles! - shouri - 2011-11-08
Shidoshi Wrote:The chance that all twenty car plates will be different is:
100!/((100 - 20)! * (100^20)) = 13,04%
Or the complementary, the chance that at least one plate will be the same is 86,96%
So the odds are extremely against the guy betting they'll all be different (even a 1:5 bet is disadvantageous).
Not gonna calculate the expected value here, it's not hard though.
For a group of N possibilities, the chance that in n different picks all will be different is:
N!/((N - n)! * N^n))
Good good. Since you have the percentages already... the expected value is -1*86.96 + 1*13.04=-73.92 cents, if the pay out is 1:1. even at 5:1 the pay out is -1*86.96 + 5*13.04=-21.76... you'd need 7:1 payout for the game to be worth it for you.
Time for some darts trivia/problems
For reference, in darts, you throw darts at a circular board sectioned off into 20 pieces... think of cutting cake into 20 slices. The numbers 1 through 20 are mixed through the "slices" and landing there gives you that many points. There are also small sections which double or triple the score. So it's possible to get triple 11, for 33 points in one shot. The very center is a circle with another circle around it. The very center is worth 50 points, and the small ring around it is 25 points.
![[Image: 250px-Dartboard.svg.png]](http://upload.wikimedia.org/wikipedia/commons/thumb/4/42/Dartboard.svg/250px-Dartboard.svg.png)
The goal in the particular game I'll ask about is to start off at a score (say 300) and work your way down to exactly zero. If you hit a 20, your score drops from 300 to 280. If you're at 5 and hit a 20, you stay at 5 (no going into negatives).
7) What's the lowest score that cannot be scored with one dart throw?
8) What is the lowest score that you can be left with where the game CANNOT be finished in two darts?
9) What is the lowest score that you can be left with where the game CANNOT be finished in THREE darts?
10) Is it possible to score 100 points using three triples? what about four triples?
11) There are four ways to score 26 points using a triple then a double... name them. Ex: triple 1 and double 6 gets you 15. But you must find 4 ways to get a 26 this way.
Try and answer only 1 question at a time to let others have a shot at solving 'em. Also, number your response please
Math puzzles! - rethic - 2011-11-08
7) 23?
Math puzzles! - ShinkuDragon - 2011-11-08
11:
hit 10*2 and 2*3
7*2 and 4*3
4*2 and 6*3
1*2 and 8*3
woo, new title
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