Trading Lessons/Insights From Coin Flipping

[nLepwa]

Quote from tradingjournals:

If you have access to a random generator, I see how you can have a positive expectancy. The key is that you see one of the numbers and that you have access to a random generator. Do I get it right? I did not want spell out the method to allow others the opportunity to first think about it.

Guys: the problem posed has a positive expectancy. The person is not wasting your time, in case you want to think about it.

You are right.

Those that don't agree, please play with me!

Ninna

 

[nLepwa]

Quote from walterjennings:

Based on the wording in the original game.

"Choose N1=50 and show that number, flip a coin to decide if N2 is 51 or 49. It should be impossible for them have a chance other than 50% of guessing if N2>N1. Which will lead to positive expectation with the imbalanced payout."

Beats the game. I am assuming there was an error with how it was described if it is actually possible for it to be unbeatable.

There was no error in my wording.

Whether you choose your number by hand or randomly (even uniform distribution) is irrelevant since permission to do one implies permission to do the other.

Ninna

 

[nLepwa]

Quote from u21c3f6:

This goes back to the selection process I wrote in a previous post.

I would choose two numbers that were either both higher or both lower than 50. Then if one of these numbers was selected at random, the chance of guessing correctly whether the other number was higher or lower than the first number selected has a long-term expectation of 50%.

Joe.

Would you be surprised to hear that you can get higher than 50%?

Ninna

 

[walterjennings]

Quote from nLepwa:

There was no error in my wording.

Whether you choose your number by hand or randomly (even uniform distribution) is irrelevant since permission to do one implies permission to do the other.

Ninna

Mind explaining how you would beat the approach I described?

"Choose N1=50 and show that number, flip a coin to decide if N2 is 51 or 49. It should be impossible for them have a chance other than 50% of guessing if N2>N1. Which will lead to positive expectation with the imbalanced payout."

In PM if you don't want to spoil it for everybody else.

 

[nLepwa]

Quote from walterjennings:

Mind explaining how you would beat the approach I described?

"Choose N1=50 and show that number, flip a coin to decide if N2 is 51 or 49. It should be impossible for them have a chance other than 50% of guessing if N2>N1. Which will lead to positive expectation with the imbalanced payout."

If you always choose the same numbers you're really running the experiment only once and therefore can't draw conclusions about the expectancy.

What if I have access to a RNG from which I can draw normally distributed numbers between 1 and 100?
How could I use it?

If you really want me to give you the answer send me a PM.
But I think it would be sad as 95% of what you get from the concept (including the fun) is obtained by searching for the solution.

Ninna

 

[ptrjon]

I did extensive research into methods to maximize return on a roulette table, which is very similar to any application of coin-flip techniques, because there will always be extra transactional costs, like how in roulette there is the house edge.

Through all of my techniques that I programmed, or no matter how I spun it- in the long run, the more money you gamble with, the more you lose, and the more you try to mitigate short term risk, the greater chance you have of long term loss.

 

[rew]

Quote from nLepwa:

Would you play this game with me?

You are allowed to choose any two numbers between 1 and 100.
You reveal to me one of the two numbers.

Now, I must say whether the second number is greater than the first one.

If I guess correctly, you owe me $99.
If my guess is wrong I owe you $101.

So, would you play this game with me?

Ninna

Sure. I'll always pick 2 and then randomly and with equal probability select either 1 or 3. I always show you 2. Obviously you can be right only half the time. So my expected return per bet is $1.

 

[rew]

Quote from walterjennings:

My mistake. I didn't see that I "choose" two numbers. I assumed I randomly generated two numbers between 1-100 and choose a single one to show.

Well, now you're changing the game. Are the two random numbers always distinct?

 

[walterjennings]

Quote from rew:

Well, now you're changing the game. Are the two random numbers always distinct?

Not changing the game at all. I merely misunderstood it originally. Its actually a lot simpler than originally thought, going by the original description of the game.

 

[u21c3f6]

Quote from nLepwa:

Would you be surprised to hear that you can get higher than 50%?

Ninna

Yes. I believe there must be some miscommunication of the rules and/or how the game is to be operated.

Joe.