A Markov disrespect
 

Some may have noticed a request for a layman's explanation of that Parrondo paper. Which no one was prepared to attempt.

http://www.eleceng.adelaide.edu.au/...er/games/ma.htm

However I'll produce my effort here in the hope that a few might actually bother looking at the link, learn something and stop insulting others' intelligence.

Game B is supposed to be negative.

The win chances depend on your position:

0 10%
1 75%
2 75%

Now intuitively that looks positive.

If you assume the 3 slots are equally likely then your win expectation is

(10+75+75)/3% ~= 53.33%

But if you actually use a spreadsheet to repeatedly play the game you find your chances of being in a particular spot end up as:

0 38.46%
1 15.38%
2 46.15%

And that win expectation is precisely 50% = Break Even.

Note that you are spending far more than 1/3rd of your time in ZERO - the Slot of near-Death.

But if you alter Game B by merging it with a negative coin toss with only 49% win chance and repeat the spreadsheet operation then the chance of being on pesky ZERO reduces from 38.46% to 34.51%.

That in turn changes Game B to 52.57%.

Now the average of 49% and 52.57% is clearly better than 50%.

And if you are worried that your taxpayer-funded grants will be taken away because everybody else is bored by such pointless calculations which have absolutely no real-life use, then you title your effort with an eye-catching lie like:

"Losing strategies can win"

I'll take your word for your conclusions jfc. I've got one of those windows 'math' programs with all the maths symbols .....but I still don't know how to use it!