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Diwali, Loaded Dice and a Warning
Today is Diwali or Deepawali - one of the most beautiful of all
festivals. Nothing looks more beautiful than a series of lit earthen
lamps on the roofs and the boundary walls of a house. But knowing human beings, we can always expect a (somewhat) negative aspect to Diwali. Gambling!
Gambling comes in two forms - cards and dice.
While playing dice one would generally assume that the probability of any of the 6 numbers coming up is the same - 1/6. However, most gamblers play with two dices and that's where luck stops laying a part. The probability of the numbers 2 to 12 is no longer the same.
Have a look:
Dice#1 -- Dice#2 -- Total
1 -- 1 -- 2
1 -- 2 -- 3
1 -- 3 -- 4
1 -- 4 -- 5
1 -- 5 -- 6
1 -- 6 -- 7
2 -- 1 -- 3
2 -- 2 -- 4
2 -- 3 -- 5
and so on and so forth. Notice than the sum of 2 will never again occur.
The probability works out to be as follows:
Total -- Probability of Occurrence
2 -- 1/36
3 -- 2/36
4 -- 3/36
5 -- 4/36
6 -- 5/36
7 -- 6/36
8 -- 5/36
9 -- 4/36
10 -- 3/36
11 -- 2/36
12 -- 1/36
Notice a pattern? The middle numbers have more probability of occurrence.
However, the problem is compounded because of manufacturing process. The dice people play with are not perfect dice. They are "loaded". As a result the probabilities change.
Most of the players I have seen playing are a little (and that is an understatement) drunk. And no one thinks of probabilities while playing. So instead of starting Diwali with pots of luck they end up losing money.
So, is it safe to stick to cards? Again most of them play with more than one deck and depending on the game the probabilities are not equally distributed. So beware there too.
Diwali is a beautiful festival. There are a lot of ways of enjoying it. Drinking to the gills and gambling is not one those.
Just a thought: did Shakuni know more about probability than Yudhisthira? You bet!
Gambling comes in two forms - cards and dice.
While playing dice one would generally assume that the probability of any of the 6 numbers coming up is the same - 1/6. However, most gamblers play with two dices and that's where luck stops laying a part. The probability of the numbers 2 to 12 is no longer the same.
Have a look:
Dice#1 -- Dice#2 -- Total
1 -- 1 -- 2
1 -- 2 -- 3
1 -- 3 -- 4
1 -- 4 -- 5
1 -- 5 -- 6
1 -- 6 -- 7
2 -- 1 -- 3
2 -- 2 -- 4
2 -- 3 -- 5
and so on and so forth. Notice than the sum of 2 will never again occur.
The probability works out to be as follows:
Total -- Probability of Occurrence
2 -- 1/36
3 -- 2/36
4 -- 3/36
5 -- 4/36
6 -- 5/36
7 -- 6/36
8 -- 5/36
9 -- 4/36
10 -- 3/36
11 -- 2/36
12 -- 1/36
Notice a pattern? The middle numbers have more probability of occurrence.
However, the problem is compounded because of manufacturing process. The dice people play with are not perfect dice. They are "loaded". As a result the probabilities change.
Most of the players I have seen playing are a little (and that is an understatement) drunk. And no one thinks of probabilities while playing. So instead of starting Diwali with pots of luck they end up losing money.
So, is it safe to stick to cards? Again most of them play with more than one deck and depending on the game the probabilities are not equally distributed. So beware there too.
Diwali is a beautiful festival. There are a lot of ways of enjoying it. Drinking to the gills and gambling is not one those.
Just a thought: did Shakuni know more about probability than Yudhisthira? You bet!
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