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:
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.
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