Game theory, Parrondo’s paradox and how combining two losing strategies can result in winning strategy.

Juan Parrondo is Spanish physicist how introduced a new concept in game theory– Parrondo’s Paradox. It is an interesting concept- what it states is if two losing strategies are combined i.e. played alternatively, they can result in a winning strategy.

Can two losers come together and use their complementary skills to device a winning strategy? Sounds ridiculous, but Juan Parrondo thinks it is possible.

Take two games- game A and game B, if played exclusively each will result in loss, but when played in combination can result in win.

Let game A be you lose Rs.1 every time you play game, and game B is you count money you have, if it is an even number you win Rs. 3, else lose Rs.5.

Now if you start with Rs. 100, and play game A exclusively, you will lose all your money in 100 rounds (lose Rs. 1 every time you play, so in 100 rounds you lost Rs. 100)

If you play game B exclusively, then also you will lose all your money in 100 rounds. You can use excel sheet to make calculations. Ex. you start with 100, since it is even number you get Rs. 3, so you have Rs. 103, since 103 is odd number you lost Rs.5, so now you are left with Rs. 98, which is even number so win Rs. 3, total now is Rs. 101, which is odd, so lose Rs.5 and so on…

Now use combination of games i.e. first plays B, then A, then again B, then A i.e. BABABA…, you will start winning.

Here you start with Rs. 100, under game B you win Rs. 3 as 100 is even number, so you are left with Rs. 103, now play game A i.e. lose Rs. 1, so you are left with Rs. 102, now play game B, win Rs. 3 as 102 is even, back to game A and lose Rs.1 and so on. With every BA game combination you gain Rs.2.

If you have losers in your team, don’t give up on them, study their competencies and see if combination can deliver a win.

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