Some time back, I had given the following quiz to my students:
Imagine that you are in my classroom and I have two torches - one with green light and one with red light. The classroom is dark. Let's play a game, shall we? I am going to take one of the torches (red or green) and flash it on the wall. Then I'll flash a torch again (red or green). This way, I'll choose either a red torch or a green torch and flash it on the wall for a total of 20 flashes. There's one condition, however. 60% of the time I'll flash the red torch and 40% of the time I'll flash the green torch. Therefore, I'll flash the red torch 12 times and the green torch 8 times.
Just before each time I flash a torch, I'll ask you to guess which light will come on - red or green? You'll be asked to write down your guess each time before I flash the torch.
Are you ready to play?
Because we are not in a real classroom, we need to find a way to play this game. Here's what I've done. I have already decided exactly when I'll flash the red torch and exactly when I'll flash the green torch. The total of red flashes is already known to you (12) and the total of the green flashes are also known to you (8). What you don't know and are required to guess is the sequence of the flashes. In order to ensure that I do not cheat, I've already made an excel file containing my decision of when I'll flash the red torch and when I'll flash the green torch. The file is attached (and also uploaded in the files section) but encrypted. I'll provide the password to open it when we have finished this game. Before that, however, you've to guess the answers:
1. Red or Green? ____________
2. Red or Green? ____________
3. Red or Green? ____________
4. Red or Green? ____________
5. Red or Green? ____________
6. Red or Green? ____________
7. Red or Green? ____________
8. Red or Green? ____________
9. Red or Green? ____________
10. Red or Green? ____________
11. Red or Green? ____________
12. Red or Green? ____________
13. Red or Green? ____________
14. Red or Green? ____________
15. Red or Green? ____________
16. Red or Green? ____________
17. Red or Green? ____________
18. Red or Green? ____________
19. Red or Green? ____________
20. Red or Green? ____________
Do this quiz, and also think about its connection with portfolio management. The above quiz was adapted from a great book called Calculated Risks.
Anyway, one of my students ("Gautam") gave the following answer:
ANSWER
1 Red
2 Red
3 Red
4 Red
5 Red
6 Red
7 Red
8 Red
9 Red
10 Red
11 Red
12 Red
13 Red
14 Red
15 Red
16 Red
17 Red
18 Red
19 Red
20 Red
This student justified his answer by writing the following:
I don't think that I have any special ability to predict what is in other persons mind. So any other choice would have been completely random and could have produced extreme result. By choosing all red I was sure that I'll right in 60% of cases. I do take risk but only when I understand the risk and if the reward are commensurate to that extra risk. The given case was just too complex for me to calculate the probabilities and see if I can increase my chances of success. Even if I could have calculated all those probabilities, I didn't have that much time. So the best option for me was to choose all red and be happy with 60% success rate.
PS: I do have the ability to break the password of an excel file and thus could have increased my success rate to 100%. But again the reward for that extra effort wasn't there and thus...
MY RESPONSE TO THE ABOVE ANSWER:
Gautam's reasoning has "bounded rationality" written all over it.
Instead of optimizing i.e. trying to get all the answers right, which obviously involves guess work, he chose the simple solution that "satisficed" his pre-determined aspiration level. I repeat here what I wrote about satisficing in my mail of 28 August:
Satisficing is a method for making a choice from a set of alternatives encountered sequentially when one does not know much about the possibilities ahead of time. In such instances, there may be no optimal solution for when to stop searching for further alternatives. Satisficing takes the shortcut of setting an adjustable aspiration level and ending the search for alternatives as soon as one is encountered that exceeds the aspiration level.
Gautam's solution had two huge benefits:
* One, the probability of less overall error. I'll explain this in a moment.
* Second, the solution, which was quick, freed his mind to think of other things in life. I predict that this type of uncluttered thinking will pay Gautam very well in his life.
Those of you who gave the wrong answers indulged in "probability matching" i.e. your answers predicted red flashes 60% of the time and green flashes 40% of the time. The expected payoff from such a strategy can be calculated as follows:
If you predict red 60% of the time and red occurs 60% of the time, then you can expect to be correct on your red guesses 36% (0.6 x 0.6) of the time you predict red. Similarly, if you predict green 40% of the time and green occurs 40% of the time, then you can expect to be correct on your green guesses 16% (0.4 x 0.4) of the time you predict green. Therefore, overall, you can expect to be right 52% of the time (36% + 16%).
The alternate strategy used by Gautam has an expectancy of his being correct 60% of the time. Since 60% is more than 52%, Gautam's strategy is superior even though it explicitly accepts error. His strategy of trying not to be too smart did better than other "smart" strategies.
The analogy with the stock market is obvious.
You would make more money if you explicitly accept error and consistently used Gautam's rule instead of trying to make perfect predictions that are diagnostic of some non-existent rule you believe in.
Life will present you with many opportunities where you can expect to be wrong 40% of the time and right 60% of the time. Any rule that tries to use guessing to reduce the error rate will do worse than Gautam's rule in the long run. Gautam's rule also demonstrates his humility which is one of the most important character traits to have if you want to avoid a miserable life.
Incidentally, it doesn't matter if some of the answers did better than Gautam's. In the long run, following his rule will make you far better off - both financially, and spiritually. In fact, it isn't worth it for me to check any answer that did not match Gautam's answer.
Prof. Sanjay Bakshi
Imagine that you are in my classroom and I have two torches - one with green light and one with red light. The classroom is dark. Let's play a game, shall we? I am going to take one of the torches (red or green) and flash it on the wall. Then I'll flash a torch again (red or green). This way, I'll choose either a red torch or a green torch and flash it on the wall for a total of 20 flashes. There's one condition, however. 60% of the time I'll flash the red torch and 40% of the time I'll flash the green torch. Therefore, I'll flash the red torch 12 times and the green torch 8 times.
Just before each time I flash a torch, I'll ask you to guess which light will come on - red or green? You'll be asked to write down your guess each time before I flash the torch.
Are you ready to play?
Because we are not in a real classroom, we need to find a way to play this game. Here's what I've done. I have already decided exactly when I'll flash the red torch and exactly when I'll flash the green torch. The total of red flashes is already known to you (12) and the total of the green flashes are also known to you (8). What you don't know and are required to guess is the sequence of the flashes. In order to ensure that I do not cheat, I've already made an excel file containing my decision of when I'll flash the red torch and when I'll flash the green torch. The file is attached (and also uploaded in the files section) but encrypted. I'll provide the password to open it when we have finished this game. Before that, however, you've to guess the answers:
1. Red or Green? ____________
2. Red or Green? ____________
3. Red or Green? ____________
4. Red or Green? ____________
5. Red or Green? ____________
6. Red or Green? ____________
7. Red or Green? ____________
8. Red or Green? ____________
9. Red or Green? ____________
10. Red or Green? ____________
11. Red or Green? ____________
12. Red or Green? ____________
13. Red or Green? ____________
14. Red or Green? ____________
15. Red or Green? ____________
16. Red or Green? ____________
17. Red or Green? ____________
18. Red or Green? ____________
19. Red or Green? ____________
20. Red or Green? ____________
Do this quiz, and also think about its connection with portfolio management. The above quiz was adapted from a great book called Calculated Risks.
Anyway, one of my students ("Gautam") gave the following answer:
ANSWER
1 Red
2 Red
3 Red
4 Red
5 Red
6 Red
7 Red
8 Red
9 Red
10 Red
11 Red
12 Red
13 Red
14 Red
15 Red
16 Red
17 Red
18 Red
19 Red
20 Red
This student justified his answer by writing the following:
I don't think that I have any special ability to predict what is in other persons mind. So any other choice would have been completely random and could have produced extreme result. By choosing all red I was sure that I'll right in 60% of cases. I do take risk but only when I understand the risk and if the reward are commensurate to that extra risk. The given case was just too complex for me to calculate the probabilities and see if I can increase my chances of success. Even if I could have calculated all those probabilities, I didn't have that much time. So the best option for me was to choose all red and be happy with 60% success rate.
PS: I do have the ability to break the password of an excel file and thus could have increased my success rate to 100%. But again the reward for that extra effort wasn't there and thus...
MY RESPONSE TO THE ABOVE ANSWER:
Gautam's reasoning has "bounded rationality" written all over it.
Instead of optimizing i.e. trying to get all the answers right, which obviously involves guess work, he chose the simple solution that "satisficed" his pre-determined aspiration level. I repeat here what I wrote about satisficing in my mail of 28 August:
Satisficing is a method for making a choice from a set of alternatives encountered sequentially when one does not know much about the possibilities ahead of time. In such instances, there may be no optimal solution for when to stop searching for further alternatives. Satisficing takes the shortcut of setting an adjustable aspiration level and ending the search for alternatives as soon as one is encountered that exceeds the aspiration level.
Gautam's solution had two huge benefits:
* One, the probability of less overall error. I'll explain this in a moment.
* Second, the solution, which was quick, freed his mind to think of other things in life. I predict that this type of uncluttered thinking will pay Gautam very well in his life.
Those of you who gave the wrong answers indulged in "probability matching" i.e. your answers predicted red flashes 60% of the time and green flashes 40% of the time. The expected payoff from such a strategy can be calculated as follows:
If you predict red 60% of the time and red occurs 60% of the time, then you can expect to be correct on your red guesses 36% (0.6 x 0.6) of the time you predict red. Similarly, if you predict green 40% of the time and green occurs 40% of the time, then you can expect to be correct on your green guesses 16% (0.4 x 0.4) of the time you predict green. Therefore, overall, you can expect to be right 52% of the time (36% + 16%).
The alternate strategy used by Gautam has an expectancy of his being correct 60% of the time. Since 60% is more than 52%, Gautam's strategy is superior even though it explicitly accepts error. His strategy of trying not to be too smart did better than other "smart" strategies.
The analogy with the stock market is obvious.
You would make more money if you explicitly accept error and consistently used Gautam's rule instead of trying to make perfect predictions that are diagnostic of some non-existent rule you believe in.
Life will present you with many opportunities where you can expect to be wrong 40% of the time and right 60% of the time. Any rule that tries to use guessing to reduce the error rate will do worse than Gautam's rule in the long run. Gautam's rule also demonstrates his humility which is one of the most important character traits to have if you want to avoid a miserable life.
Incidentally, it doesn't matter if some of the answers did better than Gautam's. In the long run, following his rule will make you far better off - both financially, and spiritually. In fact, it isn't worth it for me to check any answer that did not match Gautam's answer.
Prof. Sanjay Bakshi
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