Do The Math...Or Not

God plays dice and people play the odds.

So says Dennis. Millions will disagree, convinced that God (or luck) is looking out for them if they trust and obey (or whisper the correct incantation, like "Baby needs a new pair of shoes"). We are equipped with intuitions that are unreliable when it comes to playing the odds. That's why we invented mathematics.

A little test of intuition: when you roll two dice, are you more likely to get a five or a nine total? 

da da da da, da da da da, da da da da...

Got your answer? No cheating. Write it down. 

OK, why did you choose five? Could it be that having five fingers on each hand means you encounter five more often than nine in everyday experience, and therefore judge it to be more likely? 

But you chose nine, didn't you. Could it be that you think the universe is out to fool you so you chose the opposite of what you intuited?

Here is the right answer. (I'm not being clever. I didn't know so I had to work it out.) Five has one chance in nine of coming up. Nine is just as likely, one chance in nine. That was news to me. How about you?

Proof.

There are four ways of getting a total of five: 1+4, 2+3, 3+2, and 4+1. There are also four ways of getting a total of nine: 3+6, 4+5, 5+4, and 6+3. Compare this to a total of 36 possible combinations, six for each die, 6x6=36. The probability of 4/36 reduces to 1/9, as I stated.

Surprised how ignorant your intuition is even for such a simple question? Want more proof? What is the most probable result when you roll two dice? You can choose any number between 2 and 12. Got your number?

Answer: seven is most likely. Proof: there are six ways of getting a total of seven: 1+6, 2+5, 3+4, 4+3, 5+2,  6+1. That is a probability of 6/36. If you work out combinations for a total of six you will get 5/36. Same for eight. The probabilities go down for the other numbers: two has a probability of 1/36 as does twelve. Seven is clearly the most likely total for two dice. What are the odds you guessed seven? No data on that. I'm guessing that you were right because I intuit that you're brilliant.

That's as far as I am going into math, no Gaussian curves or Z scores. I got a C in statistics, which shows I am as intuitive as the next person. So when I play the odds, I am not usually being clever, just guessing. 

Sometimes clever... maybe. For example, I am pretty sure I will get out of bed tomorrow, since I have done it every day for the past decade or so, about 3,650 mornings. The last time I didn't get up, I was in a hospital bed. There will not likely be any reason I can't arise tomorrow, although, for certain, that will happen once in the next decade with increasing probability as the mornings go by. Furthermore, I am pretty sure that when I get to church tomorrow and plug my computer into the TV, I will be able to show the slides and videos I have prepared. Why not? I forgot to tell you about the snow forecast, POP 90%. There is a chance, with good probability, that church will be cancelled, though I don't know the odds because I won't be making the decision. Even if church is on, my computer is twelve years old, in e-hospice with digital death imminent, and God is not an IT nerd on call. 

When it comes to heart attacks, snow days or motherboard failure, the odds are sketchy and your guess is as good as mine. Best laid plans... That's life.