# Math is hard says the Guardian

The polls were wrong. And because we are obsessed with predicting opinions rather than listening to them, we didn’t see it coming. So, the world woke up believing that Republican candidate Donald Trump had a 15% chance of winning based on polling predictions – roughly the same chance of rolling a six if you have two dice. Despite those odds, the next US president will be Donald Trump.

A six? Two dice. So, 1/6 for a six on either. Two dice, 1/3 of getting a six. 33%, not 15%.

Now, if you want to say the chance of rolling six with two dice then…..5/36….13.9%

No wonder The Guardian had problems with polling.

Thanks to Eagle Eyed Spotter Peter Fletcher

## 26 thoughts on “Math is hard says the Guardian”

1. Not a third, but 11/36. There are 36 permutations of results. Ten of those permutations will show one six. One of those permutations will produce two sixes.

2. A six? Two dice. So, 1/6 for a six on either. Two dice, 1/3 of getting a six. 33%, not 15%.

You’re wrong too.

The chances of not getting a six with one die are 5/6, so the chances of not getting six with two are (5/6)^2, or 25/36, which leaves 11/36, or just under 11%, of getting a 6.

The gamblers would like you to play chuck-a-luck.

(With an n-sided die, if you roll n of them, your chances of not getting a 6 as n approach infinity is 1/e, which is about 3 in 8.)

3. TedS

How is 11/36 11% ? Do tell.

Mathematics are difficult indeed.

4. Maths aside, are the Guardian really saying that they trusted the polls? After the last three British elections? What fuckwits.

One thing I noticed about this election is that Americans are well aware of the recent British votes, and so they didn’t trust the polls. Clinton was campaigning till the midnight deadline: that’s not the behaviour of someone who really believes she’s got it in the bag.

The first election in which everyone goes in distrusting the polls. Fascinating times.

And The Guardian didn’t even notice.

5. SquanderTwo: “Maths aside, are the Guardian really saying that they trusted the polls?”

Of course they did! They were telling them what they wanted to hear.

6. 2 die, 36 possible outcomes. There’s at least one 6 on 11 of them (2 6’s on one).

11/36 = 1/5 to get a 6 or 30.5%

compared to

1/6 for a single die or 16.7%

7. Squander Two
November 9, 2016 at 10:46 am

Maths aside, are the Guardian really saying that they trusted the polls? After the last three British elections?

*And* the last 4 American ones.

8. There are 5 ways of rolling a 6 with two dice. 1.5, 2.4, 3.3, 4.2 and 5.1. So the guardian was quite close. I think Tim has read it as rolling exactly one 6, rather than a total of 6.

9. The polls were a pack of deliberate, shaped lies.

And the reappearance of this cancerous old chestnut is a larf:

“And because we are obsessed with predicting opinions rather than listening to them,”

No you lying shite, the left listen to nothing except their own cockrot. You were obsessed with trying to force your opinions on others.

The “we must listen more” is just boilerplate bullshit the CM gang bring out every time they fail.

10. The LA Times was consistently calling it for Trump, and it explained why: traditional polls adjust results for age cohorts, gender, etc. They do not adjust for political affiliation. We know that Republicans are less likely to pick up the phone, so the raw answer is skewed Democrat. The LA Times adjusted for that.
This was all public knowledge, so the question becomes why is was under-reported? I think history will show that the political class died in 2016. RIP

11. Misunderstanding across the cultural divide. Yanks play craps, not snakes’n ladders. So presume a two dice roll to make a six. (& not far off 15%)

12. The chance of getting one six is:

First, getting six on the first die.

Secondly, the second die is eaten by the dog so it doesn’t give a result.

So the joint probability is about zero.

13. bongo,

> There are 5 ways of rolling a 6 with two dice. 1.5, 2.4, 3.3, 4.2 and 5.1. So the guardian was quite close. I think Tim has read it as rolling exactly one 6, rather than a total of 6.

This might vary between dialects, but I would say that “roll a six” means rolling an actual six on at least one of the dice, whilst “roll six” means getting a total of six.

14. If you have a couple of pennies spare, now would be a good time to use them up buying stock in political polling companies.

15. To summarise:

The probability of rolling ‘a’ six (i.e. one or two sixes) with two dice is the complement of the probability of rolling no sixes = 1 – 25/36 = 11/36 ~ 30.6%

The probability of rolling exactly one six with two dice is, by counting, or by subtracting the 1/36 probability of two sixes from the previous result, 10/36 = 5/18 ~ 27.8%

The probability of rolling ‘six’, in the craps or Monopoly sense is, again by counting, 5/36 ~ 13.9%

So both Graun and TW are wrong.

16. Oh, and here’s a good one: what is the expectation value of the number of times one will have to roll a fair die to get a six? That’s harder than it looks to work out.

17. It was always obvious, just as with Brexit, that the polls were under-reporting Trump support. When all the educated establishment types do their best to tell people that they are evil morons for supporting Trump (or Brexit), then it’s no surprise that when educated establishment types ask people their opinion in surveys, a lot of those people keep schtum.

Some say that the pollsters deliberately ignored this well-known factor so as to make it appear that Clinton, and Remain, were going to win. If so, that was a bad idea. With the EU referendum, for instance, it appears that a lot of Remainers — young Remainers, especially — didn’t bother to vote because they thought it was in the bag.

18. ‘The polls were a pack of deliberate, shaped lies.’

Well put, Mr Ecks.

Up until near the election, polls are used to SHAPE opinion, not measure it. Usually, the polling companies come into line with reality at election time, to protect their reputation. I think they so desperately wanted Hillary they sacrificed their reputation to stump for her to the end.

Joyful times!

19. “…we are obsessed with predicting opinions rather than listening to them…”

Ahem.
“…we are obsessed with controlling opinions rather than listening to them…”

FTFY.

20. I see “the markets” have been caught off-guard. Who were they listening to, and why?

21. @Tim N: “I see “the markets” have been caught off-guard. Who were they listening to, and why?”

I assume they weren’t. Just another excuse to push some share trading from the investment side of the business to the stockbroking side to pocket some commissions before Christmas.

22. Ha ha they’ve updated it to say a total of six! Well done Tim.

Also I notice that CIF comments are not allowed: -)

23. The polls were worse than expected – I had adjusted for their usual bias to the left-wing (or lefter-wing) party and was still shocked when my wife woke me to say that Trump was winning.

24. The rumour is that 85% of Guardian on-line articles are not read even once.

I can see why they do not like maths.

25. “I had adjusted for their usual bias to the left-wing (or lefter-wing) party and was still shocked when my wife woke me to say that Trump was winning.”

Ditto, I expected a toss-up, with one of them winning by a couple of electors. I was shocked by how big Trump’s landslide was.

I almost feel sorry for Clinton at this point, because even her election fraud abilities were massively overstated.