Probability is an interesting subject to me. Nearly anything you can think of can happen, it’s just that most outrageous things are not likely to happen. One way to measure probability is how many times would something likely have to happen for a specific behaviour to appear. Like throwing a die. One could expect to roll a 6 one out of every six tosses, or 1 in 6 (1/6); because you are waiting for a specific outcome (6) out of a possible six outcomes (1,2,3,4,5,6) and each outcome is equally likely to happen on each throw. What about rolling a six two times in a row? That would be 1/6 * 1/6 or 1/36. So if you threw a die twice 36 times–on average one of those pairs of tosses would both be six.

I want to share something very unlikely that happened the other night. My dad and I were playing backgammon. Under most circumstances the best roll in backgammon is double 6’s and the worst is a 1 and a 2. Imagine my dad’s consternation when he rolled a 1 and 2 at a critical time near the end of the game. Imagine his feelings when he rolled another 1 and 2 two turns later, and then his horror when he rolled a 1 and 2 on the very next roll! That was two in a row and 3 out of 4. He could hardly believe his luck. His next toss was something different but then he rattled off four (1,2) pairs in a row! Four in a row! We stared at each other in disbelief with each toss and as I marched to victory. We couldn’t believe what we were seeing.

I just had to know how unlikely this turn of events was. There are 36 possible two die combinations and two of them are (1,2) and (2,1). So every toss you have a 2/36 or 1/18 chance of throwing a (1,2). The chances of this happening four times in a row is basically 1 over 18^4 which is 1/104976. While that doesn’t seem ultra high in our culture of exaggeration (How many times have you said or heard someone say “That was a million to one odds!”?) think of how big of a number 104976 is. It is really hard to fathom that many of anything tangible. Keep in mind that this says 1 in every 104976 times you throw four pairs of dice. Does that mean 419,904 individual tosses? Or can the 4 tosses “overlap” one another?

I wonder how many times an average game playing adult has thrown a pair of dice in their life. Let’s give an average game playing life span of 70 years, that’s generous. That equals 25,550 days to play dice games. But I doubt that many people average a game a week for 70 years, but we’ll put that in. That’s 3,650 games. This is where it gets tricky. How many times do you throw the dice in each game. Obviously some games are more dice intensive than others. I’m going to throw a number out there, you can refute it if you want, of 50 tosses per game. That equals 182,500 tosses of a pair of dice over a life time. And I think that’s probably high.

Keep in mind that probability doesn’t say that something will happen after a certain number of tries, or even within a set of a certain number of tries. It only says that if you collect data over a lifetime of the event (throwing four pairs of dice) you can expect to see an average of one instance of all (1,2) out of ever 104,976 tries, or about 0.00095% of the time.

Another thing that facisnates me and yet I don’t understand is how would you “distribute” that probability. Would you say that if everyone (who plays games) throws about 200,000 pairs of dice in their life that one out of every two people will throw (1,2) four times in a row? Or does it happen often throughout every day? Let’s be ultra conservative and say that 1,000,000 people (about 0.02% of the worlds population between the ages of 10 and 74 accordnig to the US Census Bureau’s International Database Aggregation Tables) throw a pair of dice four times every day in the world. Does that mean that about 95 people are going to see this happen every day?

I don’t know the answers. And I only have lots more questions, but I find it facsinating. I’ll come back some time with some quantum mechanics discussions my brother Brian and I have had about probability as well. Those are always fun.