Parrondo’s Paradox

A combination of losing strategies will result in a winning strategy if they are combined together.

1st Game:
You lose 1 every round.  2nd Game: Depending on the amount you have, you win3 if it is an even number but lose 5 if it is an odd number.  Let us start with100 to play each game independently.

1st Game:
By the 100th round, you have lost all your money.

2nd Game:
1st round – 100 +3 = 103 2nd round -103 – 5 =98
3rd round – 98 +3 = 101 4th round -101 – 5 =96
5th round – 96 +3 = 99 6th round -99 – 5 =94

Basically, you progressively lose money till you have lost all your money.

Combination of 1st & 2nd Game playing them alternately:
1st round (2nd game) – 103 +3 = 106 2nd round (1st game) -106 – 1 =105
3rd round (2nd game) – 105 +3 = 108 4th round (1st game) -108 – 1 =107
5th round (2nd game) – 107 +3 = 110 6th round (1st game) -110 – 1 =109

As you can see, you progressively earn money ($2 per 2 rounds).

Application:
In terms of investing, single investments with a negative long-term returns combined together will create a diversified portfolio with a positive long-term returns.

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