A bit of talk about gambling today... We've been telling A to talk with one of his teachers about an issue he is having. He won't talk to his teacher. I think he doesn't think it will help - plus, he is probably embarassed to do so.
So we discussed the possible outcomes of having such a conversation:
- Possibility 1: he gets no benefit.
- Possibility 2: he gets a small benefit, e.g., a good suggestion from his teacher.
- Possibility 3: he gets a large benefit, e.g., his teacher gives him better grades.
I emphasized that none of the possible outcomes had a negative value. Thus, even though he might think that the most likely outcome is zero, the fact that the possibility of positive outcomes exists makes this a worthwhile thing to do. Its value is the probababilty of each outcome mutiplied by each outcome's value.
I compared this with the value of a bet: heads you get $1. Tails you get nothing. A immediately knew the value of such a bet was 50 cents. And he understood it was worth betting up to 49 cents in such a bet. We spoke about other types of bets, e.g., the lottery, and about how ussually their cost is higher than their value.
Of course, one thing is understanding this "stuff", and a very different one is talking with your teacher... Oh, well.