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 win $3 if it is an even number but lose $5 if it is an odd number.

Let us start with $100 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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