Posts Tagged ‘Random Numbers’

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Winter Olympics: Bad Math of Figure Skating Scores

February 22, 2018

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Tessa Virtue and Scott Moir win GOLD at Pyeong Chang 2018

                                   Kailani Craine, Australia

figure skating score 9 judges nbclearn

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

figure skating score B

Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

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4. Why the best figure skater doesn’t always win

January 23, 2014

According to the fab NBC video, Mathletes,  nine Figure Skating judges score competitors for the complexity of each element (eg. Triple axel or triple spin jump) and the quality of the performance producing a score out of ten.

Joannie Rochette

Joannie Rochette

Brendan Kerry Australia

Brendan Kerry Australia…..

figure skating score 9 judges nbclearn

This is a typical figure skating score card for one competitor.

The final score, however, is based  on the average for only 5 of these scores. Two are eliminated by random selection (Red Brackets). Then the top and bottom scores are removed and the remaining five scores averaged.

Screen grab NBC Mathletes

Screen grab NBC Mathletes

……………………………………………………

Now consider the IDENTICAL SCORE CARDS

of Skater A & B:

figure skating score A

Skater A:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them)

7.00 + 7.00 + 7.00 + 6.75 + 7.00

……………………………………..

=  34.75/ 5 = 6.95

figure skating score B

Skater B:

Four scores are removed. Two by the random selector (in brackets) and then the top and bottom scores (with line drawn through them). But this time the random selector eliminates two low scores.

The average:

7.00 + 7.25 + 7.00 + 7.00 + 7.00

……………………………………..

=  35.25/ 5 = 7.05

Same score cards but Skater B gets a higher average score than Skater A.

Skater A is, in fact, beaten by a random number selector!!!!

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Gamblers are Losers. Ha! Ha! HA

February 22, 2011

Here is a good exercise that helps us understand random numbers and … that also shows why gamblers lose money.

It comes from Alex Bellos who wrote Alex’s Adventures in Numberland (Bloomsbury) with some additions by Mathspig.

 

 

1. Ask each member of the class to guess, then write down on a piece of paper the result they imagine for tossing a coin 30 times .

 

 

 

 

2. Now ask them to actually toss a coin 30 times recording the result.

 

 

3. Then  ask them to toss the coin one more time. Students who throw Heads will write their first results on the board. And tails their second results.

 

 

4. Finally, see if the class can guess which is which, and calculate the probability of getting those guesses right.

 

 

As Alex Bellos explains, we humans try and impose order on chaos. Our imagined results show a pattern. The real results are more… well, random. The problem is when we write HH we then think it must be Ts turn. It doesn’t matter how many Hs appear in a row, the probablity for the next flip producing a H is still 1:2. Therefore the random results for tossing a coin can have any number of Hs or Ts together!!!!!!!!!!! The longest recorded run for Black on the roulette wheel was 26. See an earlier mathspig post, The Wheel on the Roulette Table went round and round, round and round.

See if you can pick which of the following results A, B, C  or D  was guesswork. The other three are real coin flip results.

In fact, A was the guess.

Gamblers constantly think it’s time for a particular number to be drawn in loot or for a machine to pay out. And they are wrong. Sooooooo wrong……. This is called the gambler’s fallacy. More @ Prevent Gambling Addiction

DO YOU THINK GAMBLERS ARE LOSERS?

DO THE MATHS!!!!

Look at these Las Vegas Casinos …. This has all been paid for by LOSERS….

This …..The Excalibur Hotel Casino    (below)


And this …New York, New York Hotel Casino


And this …The Luxor Hotel Casino


And this … The Venetian Casino

Are you feeling lucky, punk?   Don’t bet on it!!!!!

On the other hand, a maths genius might not need luck. See Maths Makes Money post (following).