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Take a chance

This small article is aimed at people who do not understand the laws of chance. If you know and understand chance theory, skip this at the *risk* of boredom. If however you believe that you can influence chances at the roulette table, or fear plane crashes as a serious danger, then read on.

Many people don't like chances, many others do. The former want security and control, the latter are not so much concerned about that. However usually both want to minimize negative effects and maximize positive ones. But how can you be in control if things are in the hands of random chance? The answer is that you can have partial control.
With random effects, there is a simple law that states risk = chance x effect. For instance if you can choose between an action that will gain you 10 "units" of money with a chance of 20% and another action that will gain you only 4 units but with a chance of 60%, then the latter option is the best. The average gain of the first option is 10x(20/100)= 2 units, the average gain of the second option is 4x(60/100)= 2.4 units.
The gain is not guaranteed, but then again neither option guarantees anything. It is well possible that if you try both options 3x in a row that the first will gain you 30 units and the latter 0. The chances of that happening though, are slim. Actually, that chance is 20%x20%x20%x40%x40%x40% = 0.0512%, not much at all ... In the game of chance it is important to be aware of both chances and effects.

dice However people tend to overrate large gains (and losses) and underrate chances. Many of us participate in a lottery, hoping to win the jackpot or at least a substantial prize. They forget that all the money that some players win, is coming from other players and that the lottery organization is scraping off a substantial amount to handle all organziation and make a profit for itself too. Many lottery organizations refund 20% or less of the original inlay as prize money. Sure, you might hit the jackpot, but it is far more likely that you pour more money into the gamble than you get out of it. If you want to get rich, try another way.

Here is another example, taking a negative view. We 21st century people travel a lot. In travel, there is always a risk of accident. Some ways of travelling are more risky than others. Many people are afraid to board an airplane. Suppose it is hyjacked, or crashes down because of a mechanical failure! Yet they have no compulsion of boarding their car everyday and drive through heavy traffic, even if aware that many more people die in road accidents every year than in airplane crashes.
Airway corporations advertise this fact as much as they can, claiming that flight is actually the safest way to travel, as it has the lowest casualty rate per kilometer traveled. What they forget to mention is that one usually travels a lot more kilometers per journey in an airplane than one does in a car. What is a good safety rate? Casualties per km? Per hour? Per journey? The answer is that a good rate is what you think is a good rate.

Chances of random effects can be modified by repetition. Everybody understands that the chance of 4x red in a row at roulette is smaller than 2x in a row. But how much? Some dumbheads think that the row-length being 2x as long, the chance is 2x lower. Of course the chance for 2x in a row is ½x½ = ¼ and the chance for 4x in a row is ½x½x½x½ = 1/16, so it is 4x lower.
There is another, more common but equally serious misunderstanding. Suppose we are playing roulette and the ball has hit red 2x in a row already. What is the chance that it will hit red 2x more in a row at this point? Many people think that that comes 4x in a row, so say 1/16. In fact, the ball or anything else that determines its way has no memory whatsoever of the previous two rolls, so the only things that matter are the chances of the upcoming two rolls. The chance of hitting red 2x more is just ½x½ = ¼.
Of course at the start of the 4-row series the chance of hitting red 4x was 1/16, but halfway it comes down to just ¼, as the first two rolls are no longer in the realm of chance, they are known.

Looking back the reader can state that all this comes down just common sense. And indeed it does. Calculating chances is common sense. Just don't forget to calculate and don't act on "feeling" alone. Feeling is more often wrong than you think, but numbers don't lie - and that is the last rule here.