### Why I don't agree with lottery Scrooges

It's traditional for those with some grasp of probability to belittle those who enter the National Lottery. 'Clearly idiots,' they say. 'These people don't understand probability, or they wouldn't play.'

I must admit, I've taken this stance a little in the past. Imagine, I've said, that the lottery balls came out one Saturday as 1, 2, 3, 4, 5, 6. There would be questions in the House no doubt. A new scandal to rival phone hacking - how could the National Lottery draw be so obviously rigged? Last Saturday's draw numbers were 4, 9, 13, 15, 18, 40 (as the website kindly sorts them into numerical order, I don't know what order they were drawn in). But in drawn order, that sequence of numbers had exactly the same probability of coming up as 1, 2, 3, 4, 5, 6.

Our natural suspicion of the ordered set arises because it makes it more obvious just how unlikely it is that a particularly sequence will be drawn - yet the same goes for the numbers on your ticket. It is ridiculously unlikely that your numbers will be drawn. So why bother? It's a waste of money.

But here's the thing. I play the lottery. Every four weeks I allow myself £10 to play. No more - very tightly controlled. I don't enter the main Lotto draw, but rather the Thunderball draw, which has lower winnings (£500,000 for matching a full set) - but that would be enough to change my life, I don't want to be multi-millionaire, and the lower jackpot comes with better odds. Even so, it's an immense longshot. So why do I do it?

Essentially it's a kind of utility that conventional economics is not very good at reflecting. If the sum involved is so small that I can consider it negligable (we're talking a coffee and cake for two at Starbucks per month), then I can effectively mentally lose it and easily offset it against a very low chance of winning a rather exciting amount. To add to the benefit side of the equation, with this style of play I get a win about once every couple of months. This will inevitably be for between £3 and £10, but there are still a few minutes of delicious anticipation after getting the 'Check your account' email from the National Lottery when it could be oh so much better.

One of the important factors in making the decision to play rational to me is I totally forget about my entry unless I do get one of those emails. I don't anxiously check my numbers. I don't know what my numbers are. As far as I am concerned, once the payment has been made the money has gone, just as if I had spent it on those coffees. That way, any win is pure pleasure, because it has no cost attached to it. Let's face it, the only thing I'm likely to get the day after a visit to Starbucks is indigestion.*

All in all, then, I say pish and tush to those who put down lottery players. If it's done in the right frame of mind, and in a controlled fashion, why not? Of course you aren't going to win the jackpot. But is there anything wrong with having a dream? After all, one thing is certain. If you don't take part you will certainly never win anything.

* This is not casting aspersions on Starbucks, espresso-based coffee always gives me indigestion.

1. I'm with you on this one Brian. Compared to the utter banality and disappointment that comes with most products costing a few quid on the high street - such as from coffee chains etc, the occasional frisson from a little flutter appears to be quite good value.

And if you can apply rationality to such things, using the 'lucky dip' function appears to be the one way of slightly tipping the "expected return on your investment" in your favour as you are less likely to pick numbers that are shared by others.

2. Good point, M. Canard. Those who try to apply purely monetary values to these transactions know nothing of frissons and flutters.

I also take the point about the lucky dip function. I either use this or play the game 'can I pick a set of numbers other people wouldn't like,' which can be very entertaining (if you are easily entertained). I don't pick 1,2,3,4,5,6 - though until I recently I assumed no one would pick these, but apparently they're quite popular.

### Why I hate opera

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### Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

### Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope