On one of those late night shows I came across the Sikkim Mega Super Lotto lottery or something like that where six numbers are picked up and a winner declared depending on how many of your numbers match up to the selected six. As the beautiful hostess accompanied by a somber man who is supposedly some govt. person roll the container to secure the six numbers I wonder how many people actually win this in a lifetime. (By the way I could never figure out what is the need for that person even though he is the sponsor in some way.
I remember that this was a mega craze some years back with Playwin and Super lotto. Cut to 2008 and there is a similar craze in the stock markets “The market has gone down , now is the right time to buy! It will rise…” Both these events are linked, heres how ---
First regarding Super Lotto --
The idea is to pick 6 numbers and match them to six selected from 51 numbers. Sounds easy. The odds of doing so?
If you programmed a computer to randomly generate six different numbers every second taken from the numbers 1 through 51, you would have to wait nearly seven months before every combination came up at least once.
The odds of matching 6 of 6 numbers are 1 in 18,009,460;
5 of 6 are 1 in 66,702;
4 of 6 are 1 in 1,213;
3 of six are 1 in 63.
The odds of winning anything are 1 in 60.
So for the less mathematically inclined, If you buy 100 tickets a week, you can expect to win the jackpot on average every 3,463 years. If you buy Rs 12,50,000 worth of tickets a week, you can expect on average to win about every 14 years. If you expect to live 50 more years, you should buy Rs 350,000 worth of tickets a week if you want to have a good chance of winning the jackpot in this lifetime. Of course, if you do, you may not even break even. You could well be about Rs 100,000,000 in the hole, depending on when you win.
However, if you would be satisfied with getting 5 out of 6, you will have a much easier go of it. You are likely to get 5 out 6 every 12.8 years on average if you buy 100 tickets a week. However, you will have spent nearly Rs 30,00,000 to win about Rs 75,000.
Phew so basically all it means is that the chances are slim. But wait this is just statistical and real life is different. You may never win regardless of how often you play and how much you spend. For e.g. there is a one in two chance of a coin flip coming up heads, but in reality heads might come up more or less than five times in ten flips.
Now the Sensex --
Most retail investors investing on hunches and without proper analysis run similar odds like above. Now to the fallacy that what goes down will come up. Even in super lotto you might think that you can beat the odds by either selecting numbers that have not been chosen in recent drawings, or by selecting numbers that have come up more frequently than expected in recent drawings. In either case, you are committing the gambler's fallacy. The odds are always the same, no matter what numbers have been selected in the past. This fallacy is commonly committed by gamblers who, for instance, bet on red at roulette when black has come up three times in a row. The odds of black coming up next are the same regardless of what colors have come up in previous turns. Dice players frequently commit this fallacy. When they see a player make his point several times in a row, they think the odds of him making his point again diminish. They don't. Those odds are fixed and they never change. For example you see people saying a lot of times just like that without any economic analysis, over a cup of tea but with all the worldly wisdom ‘The markets have tanked for long enough now they will rise”…. And what do we say --- Correct ‘The Gamblers Fallacy”.
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