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ALSO AVAILABLE ON YOUTUBE: LECTURES ONE THROUGH TEN ON IDEOLOGICAL CRITIQUE



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Thursday, October 2, 2014

CLEAR EVIDENCE OF A MISSPENT OLD AGE


The various solitaire programs on my computer keep track of how I do, and this morning, as I played my four thousand two hundred and twenty-second game of old-fashioned solitaire [on this computer], I paused to look over my record.  My win percentage is 16%, or, more precisely, 16.6%, which is almost exactly one in six.   [Interesting aside:  A while back I decided to start using the un-do facility to see whether I could up my win percentage.  Contrary to expectations, it has had no effect at all on the number of games I win.  Odd.]

My longest win streak is five.  Simple math tells me that I have a 1 in 7776 chanced of winning five games in a row, assuming that I always play with the same degree of skill and that the computer is not deliberately feeding me easy or hard games.  Since I have played 4,222 games in all, there have been 4,218 five-game runs, so one run of five wins is not out of line with expectations.  My longest loss streak during the same period of time is 54.  [I should report that as the losses piled up, I became morbidly curious just how long I would go without a win.]  Slightly more tedious math tells me that there is a 6.6 in 10,000 chance of a run of fifty-four losses, making the same assumptions.  This is a chance of roughly 1 in 1515.   Now, there are 4,168 fifty-four game runs in the 4,222 games I have played, so one run of fifty-four losses is well within the expectable.  [My gut tells me there is something wrong with this reasoning.  I was never any good at probabilities.  Do I have this right?]

1 comment:

Sheryl Mitchell said...

I think that your logic is correct, although I get 4,169 runs of 54, not 4,168 as you had.

By my calculation the expected, or mean, number of runs of 5 wins in 4,218 trials is 0.53, with 1 win being within one standard deviation of the mean. So you did better than would be expected, but still inside the one standard deviation range.

The expected, or mean, number of runs of 54 losses in 4,169 trials is 0.23, with a single occurrence lying between 1 and 2 standard deviations. So, if it wasn't for bad luck...

Interestingly, there is no "top down" analytical answer to the question of what the probability is of winning at solitaire. And Monte Carlo simulations don't seem to work either. So it is hard to say where your win rate is in relation to the theoretical value.