AFAIK it’s when you can predict its value from the preceding sequence. It’s why, most computer programming languages use pseudo random numbers rather than random numbers – if you know the seed and the algorithm, you can calculate the next value. If you need true randomness, you need an external source of entropy – for example a plate that detects particle impacts – which themselves are not purely random (they’re chaotic) but for all intents and purposes, they might as well be (you’d need a particle-level model of the universe to make the prediction).

I’m not sure how this is handled formally, but I think a number stops being random when you know its value.

So in this case the ‘player’ has had a run of luck in the sense that he started on a O and that he got more X’s than O’s.

Add an O to the end, so that the observations are equal, not the transitions, and the sequence looks very different.

Looking at a sequence with equal number of transitions may well be more suitable, but perhaps the subject should have been asked if any part of the chain represented a streak of luck, rather than the whole chain.

That is such a better example than I had ready that I don’t know where to begin. Trouble is, I work on low level stuff – neural networks and how they form abstractions from percepts in a hierarchical chain. I always forget about the big things with teeth.

* note to self – include more lions in justifications *

In sports “runs” another likely contributor to misperception is player desire not only to perform, but to anticipate correctly. When I start hitting the treble 20 I feel I’ve made a transition into a state where all is working as it should be.

I think this is why most people who’ve played anything competitively would agree that it’s a lot easier to believe the people you’re playing against are scoring at random than that you yourself are conducting Bernoulli trials.

I think the book you;re thinking of is Life’s Grandeur by SJGould. Not one of his better ones.

just replace (3) with i got some deer antler fur supplements (yes they exist)
and (4) with therefore, supplements work and you get a taste of my day at work

It seems PAT (a teaching union) are callin gon the Govt. to undertake further research on Wi-Fi because a member has complained of becoming ill following the installation of Wi-Fi in their school. Strangely enough when n=1 the whole sample seem to exhibit the problem!!

the evolutionary pressure to develop an instinctive grasp of stats is fairly low…. i don’t know anybody who got themselves dead from misunderstanding the stats…

You’ll often get people saying they’ve lost their touch after a break, when really it’s your opponents that have fixed their tactics.

You’ll also have a roghly equal number of relatively bad runs, when you’re being marked by an above-average player.
I suppose that this is technically a winning run due to the lack of opponents skill, rather than an ‘in the zone’ increase in your own.

Of course, you’ll also have winning runs due to luck – which often seem like skill.

It wouldn’t be hard to statistically test for “winning streaks” in athletes. E.g. I compile the batting performance of a cricketer for an entire season – for every delivery they faced, I record how many runs they scored and whether they got out. Now I extract at random just one of those deliveries, and give you all the rest of the data (in random order.) Your job is to give odds on what they scored in the delivery I withheld. Now suppose instead of giving you the season’s data all mixed up, I gave it to you in two lumps: deliveries faced by that player in the same week as the withheld one, and the rest. Could you better predict the score of the withheld delivery with this extra information?

Program a computer to do this, feed it lots of different ‘withheld over’s, and for lots of batsman…

Of course, at best you establish a correlation, not a cause. The correlation might (e.g.) be more to do with whether the captain had told them to play for safety or for quick runs, or the skill of the opposing bowler , rather than whether the batter is ‘in the zone’.

‘I try not to think with my gut. If I’m serious about understanding the world, thinking with anything besides my brain, as tempting as that might be, is likely to get me into trouble.’