Priyanka I know you like challenges so I am putting here one here for defending.
Question of exploring this paradox has been debated few times around forums. The ones who are saying it is useless in gambling relies on this simple sentence from wikipedia: It serves solely to induce a dependence between Games A and B, so that a player is more likely to enter states in which Game B has a positive expectation, allowing it to overcome the losses from Game A.
Interesting, one of those guys is well respected member Bayes, whose knowledge in math and statistics are more than respectful. He is also programmer and can easily prove any gambling scenario.
Let me copy one of his posts :
Actually, a better explanation of why PP can't work with casino games is because outcomes are independent, but PP requires some interaction between the current game and the previous one. Taken both together, the games do result in an overall negative expectation, but the crucial part is being able to select the game which has a positive expectation given what's just happened. But since what just happened has no effect on expectation in casino games, PP cannot work with them.
Also the famous wizard of odds is clearly saying PP cant be used in casino games:
Personally I don’t see what is so interesting about Parrondo’s paradox but you are not the first to ask me about it so I’ll give you my thoughts on it. The thrust of it is that if you alternate between two particular losing games the player can gain an advantage.
As an example, consider Game 1 in which the probability of winning $1 is 49% and losing $1 is 51%. In Game 2 if the player’s bankroll is evenly divisible by 3 he has a 9% chance of winning $1 and 91% of losing $1. In Game 2 if the player’s bankroll is not divisible by 3 he has a 74% chance of winning $1 and 26% of losing $1.
Game 1 clearly has an expected value of 49%*1 + 51%*-1 = -2%.
In Game 2 you can not simply take a weighed average of the two possibilities. This is because the game quickly gets off of a bankroll remainder of 1 with a win, and often alternates between remainders of 0 and 2. In other words the bankroll will disproportionately play the game with a 9% chance of winning. Overall playing Game 2 only the expected value is -1.74%.
However by alternating two games of Game 1 and two games of Game 2 we break the alternating pattern of Game 2. This results in playing the 75% chance game more and the 9% less. There are an endless number of ways to mix the two games. A 2 and 2 strategy of playing two rounds of Game 1 and two of Game 2, then repeating, results in an expected value of 0.48%.
I should emphasize this has zero practical value in the casino. No casino game changes the rules based on the modulo of the player’s bankroll. However I predict it is only a matter of time before some quack comes out with Parrondo betting system, alternating between roulette and craps, which of course will be just as worthless as every other betting system.
So if they are wrong, where is their flaw in thinking/understanding/application?
You are a coder also. So lets presume you are right and you found a way to apply PP in roulette, can you prove this in your simulation?
I hope you can be generaly precise enough without need for detailed revealing in answering this.
Thanks
Drazen
Question of exploring this paradox has been debated few times around forums. The ones who are saying it is useless in gambling relies on this simple sentence from wikipedia: It serves solely to induce a dependence between Games A and B, so that a player is more likely to enter states in which Game B has a positive expectation, allowing it to overcome the losses from Game A.
Interesting, one of those guys is well respected member Bayes, whose knowledge in math and statistics are more than respectful. He is also programmer and can easily prove any gambling scenario.
Let me copy one of his posts :
Actually, a better explanation of why PP can't work with casino games is because outcomes are independent, but PP requires some interaction between the current game and the previous one. Taken both together, the games do result in an overall negative expectation, but the crucial part is being able to select the game which has a positive expectation given what's just happened. But since what just happened has no effect on expectation in casino games, PP cannot work with them.
Also the famous wizard of odds is clearly saying PP cant be used in casino games:
Personally I don’t see what is so interesting about Parrondo’s paradox but you are not the first to ask me about it so I’ll give you my thoughts on it. The thrust of it is that if you alternate between two particular losing games the player can gain an advantage.
As an example, consider Game 1 in which the probability of winning $1 is 49% and losing $1 is 51%. In Game 2 if the player’s bankroll is evenly divisible by 3 he has a 9% chance of winning $1 and 91% of losing $1. In Game 2 if the player’s bankroll is not divisible by 3 he has a 74% chance of winning $1 and 26% of losing $1.
Game 1 clearly has an expected value of 49%*1 + 51%*-1 = -2%.
In Game 2 you can not simply take a weighed average of the two possibilities. This is because the game quickly gets off of a bankroll remainder of 1 with a win, and often alternates between remainders of 0 and 2. In other words the bankroll will disproportionately play the game with a 9% chance of winning. Overall playing Game 2 only the expected value is -1.74%.
However by alternating two games of Game 1 and two games of Game 2 we break the alternating pattern of Game 2. This results in playing the 75% chance game more and the 9% less. There are an endless number of ways to mix the two games. A 2 and 2 strategy of playing two rounds of Game 1 and two of Game 2, then repeating, results in an expected value of 0.48%.
I should emphasize this has zero practical value in the casino. No casino game changes the rules based on the modulo of the player’s bankroll. However I predict it is only a matter of time before some quack comes out with Parrondo betting system, alternating between roulette and craps, which of course will be just as worthless as every other betting system.
So if they are wrong, where is their flaw in thinking/understanding/application?
You are a coder also. So lets presume you are right and you found a way to apply PP in roulette, can you prove this in your simulation?
I hope you can be generaly precise enough without need for detailed revealing in answering this.
Thanks
Drazen