If you’ve got, say, a school physics exam,you know what the physical laws are.You’re given the information.So in theory, you should be able to get the right answer.If your answer is surprising, then you’vedone something wrong in the working.But it’s not a kind of difficult level of ignoranceto escape, in theory.The second level of ignorance according to Poincarewas one where you know what the rules are,but you lack the information necessary to carry outthe calculations accurately.And he used roulette as an example.So a roulette table, you start a ball spinning round and round.And he observed a very small change in the initial speedof the ball could have a very dramatic effect on whereit ends up, because it’s going to becircling this table over time.And nowadays mathematicians referto this as sensitive dependence on initial conditions.And popularly it’s known as the butterfly effect. Learn more about math and luck in context of casino at CasinoSlots.

There’s a talk in the ’70s where a physicist pointed outthat a butterfly flapping its wings in Brazilcould cause or perhaps prevent a tornado in Texas.These very small changes, which Poincare first observed,could have a very large effect later on.And then we’ll say that the results is random.It’s down to chance.But really, it’s a problem of information.Then comes the third degree of ignorance.And this is where we don’t know the rules.Or perhaps they’re so complex, we’llnever be able to untangle them.And in this situation, all we can do is watch.Watch over time and try and gain some understandingof what we’re observing.And it’s really this level of ignorancewhen gamblers started targeting roulette that they focused on.They didn’t try and untangle all of these physical laws.They just said, well, let’s just watch a load of roulettespins at a table and see if there’s a bias.See if there’s something odd going on with this table.But this raises the question of whatdo we actually mean by odd.What do we mean by biassed?And while Poincare was thinking about roulette in France,on the other side of the channel,a mathematician called Karl Pearson was alsothinking about roulette.And Pearson was fascinated by random events.As he said, we can’t have any true sense of what nature does.We can only observe and try and make inferenceson those observations.And he’s really keen to collect random data to test outthese kind of ideas.On one occasion he spent his summer holiday flipping a coin25,000 times to generate a data set to analyse.And he was also interested in roulette.

Now fortunately for him at the time,the Le Monaco newspaper would publishthe results of all the roulette spinsin the casinos at Monte Carlo.Now for Pearson this is a fantastic data set.He wants to test out his ideas about randomness.You’ve got all these previous roulettespins to test it out on.And he started looking at ways to understand whether theywere random or not.And a roulette table, of course, you’vegot these black and red numbers.And then you’ve got zero.If you take out the zero, over timeyou’d expect the proportion of black and red to be even.You’d expect it to be 50/50 over time.And when Pearson looked at the data,he found that red came up 50.15% of the time.This was over about 16,000 spins.So according to his calculation, this wasn’t that implausible,that actually that kind of deviationfrom the expected value is reasonable giventhe kind of data set he had.But then he continued.