Parrondo paradox is this thing where two crappy games become profitable when you alternate them in a certain way. It's pretty counterintuitive and has caught the attention of researchers and academics alike.
Basically, you have two games, A and B, and each game has a lower probability of winning than losing. But when you alternate games A and B in a certain way, you end up with a net gain. It's like, whoa, what's going on here?
But after some thinking, I've come to the conclusion that there's actually no paradox. The only reason this theory seems to work is because you choose to play the more advantageous game more often than the less advantageous one. In reality, there are three games/strategies involved instead of just two. The game that's played more often produces a profit that compensates for the losses of the other two games.
It's pretty surprising that the Parrondo paradox is appreciated in academic circles, even though it's not really that mind-blowing. Maybe people just like the idea of finding an advantage in seemingly disadvantageous situations. But we should still be critical and ask ourselves if this theory has a solid foundation or if it's just an illusion.
So, what do you guys think? Have any of you tested this theory? Let's hear your thoughts!
The Parrondo Paradox: Challenging the Illusion
Let's come up with an example we have strategy A which has a 49% chance of winning a unit and strategy B which is composed of strategy B1 with a 74% chance of winning a unit and B2 which has a 9% chance of winning a unit. Strategy B2 should only be chosen if our bank is a multiple of 3. We can see that both strategy A and strategy B are losers in the long run but by alternating both strategies A and B randomly the chances of winning three units before losing three units are greater than 50% so the expected value becomes positive.
Yes, Parrondo basically considers strategy B1 and B2 as one unprofitable strategy B when in fact B1 and B2 are two separate strategies which indeed together are unprofitable but the profit that offsets losses comes from strategy B1 and according to the rules if it is chosen when the bank is not a multiple of three then it will basically be chosen twice as much as B2.
If we look at the transition diagram for game B
and for the situation when it is alternated with game A we can see that the odds of winning 3 units before losing 3 units are greater than 0.5 but it has no applicability since in reality the value of winning is not independent of the odds of success. That is, you can choose a success rate of 74% but the win will be 26 units and the loss 74.
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