To those of you who have read my columns for years, you know I remain apolitical. So what I’m going to write is not political commentary in any way but a simple example of how you can get numbers to say whatever you want.
If I ask someone if we generally have Democrats or Republicans as President, what’s the correct answer? My guess is that it will largely depend on what message the responding person is trying to convey.
After all, we’ve had Democrats for the last 4 years. Or have we had Democrats for 4 of the last 12 years? Or have we had Democrats for 12 of the last 20 years? Or have we had Democrats for 12 of the last 32 years? visit KaptenPoker
So depending on your point of view, we might have Democrats as President for 100% of the last few years, 33% of the last few years, 60% of the last few years or 37.5% of the last few years. I could easily put this in terms of% Republican years and the numbers would be all over the place too.
On the one hand, mathematics is an exact science. On the other hand, it can easily get distorted to say whatever the messenger wants. Throw in the fact that most people don’t fully understand all the nuances of things like probability and it’s very easy to be misled by those who want to.
Last week, my son, who was in kindergarten brought home a project he did at school. They roll the single die several times and record the results. Check the chart for calculated results (this exercise is for this purpose – calculating)
When I first saw this, my initial reaction was “it looks like it’s dead loaded”. Of course, I say this tongue on the cheek. But, it’s starting to make me wonder about how other people might react and what the real probability is for each of these occurrences. Obviously, we expect an average of 5.5 rolls for each number. How outrageous are these results? Could it be dead loaded?
Well, I can’t speak to death justice. Unless there is evidence to the contrary, I have to assume that it is a fair die or at least as fair die as you get in board games. I doubt it is approved by GLI or NGCB, but I would argue that it is fair.
To begin with, let’s get rid of what might be misunderstood about this project. Just because the mean is 5.5 does NOT mean the probability of 5 is the same as the probability of 6. They are close, but the probability of 5 is 18.5% and the probability of 6 is 17.3%.
So, what is the probability that the number will appear 8 times? An astronomical 8.7%. In other words, it is somewhat common, although not the most frequent occurrence. It takes one number that comes up 15 times before we find something that is rarer than 1 in 10,000.
And, like I said at the start, we can all make the numbers say what we want with a little bit of hand. The numbers presented here depend on one another. In 33 reels, if one number appears 8 times, there are only 25 more rolls for the other 5 numbers. It’s NOT the same as me rolling the dice 33 times and just counting how many 1s I got and then repeating it all over and over again. The results in this case will vary from the examples I present.
So what’s the point of all this? Pay close attention when someone is just throwing a lot of numbers at you. You have to make sure that you are comparing apples to apples.
Numbers are rotatable and it usually takes a lot of important information to get a complete picture of what’s going on. Most importantly, very little of what actually happened was “outside the norm,” meaning the game was not rigged.
The final part of the Expert Strategy is knowing what to expect and is by far the largest and in many cases the most important aspect of the strategy. In our little die case, rolling 1 eight times is perfectly normal. However, if you play a game based on that and start to convince yourself that the dice have been rigged, you may find yourself believing that 1 is really more likely than the other numbers and then change your strategy based on that.
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