I have game data that should indicate a learning curve.

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It is from Windows Draw One Solitaire. Before I played Draw One, I played Draw Three. Draw One is easier to learn and win than Draw Three, but I learned to play Windows Solitaire by playing Draw Three first (and a lot). My success rate in Draw Three was less than 20%. Before Windows Solitaire, I learned to play Klondike Solitaire with playing cards ... the physical-manual equivalent of Windows Solitaire.

I have game data for Windows Draw One Solitaire that begins with a success rate of 50% and rises to 90% as I learn the game and its allowances. When I plot a linear trend line for the data, it starts at 50% and ends above 90%. I understand that. When I plot a trend line for log, exponential, or power, I get what looks to be the top right half of a classic learning S curve. I can see a flattened S-curve in the plotted data, but the log trend line, for example, rises steeply where the data do not, and levels out below the level of my recent success data.

I am trying to correlate my success rate to certain specific developments in my understanding of the game.

The log trend line does not look like a learning curve because it rises steeply at the start from 50%. Is it possible that the fact that the data success rate starts at 50% influences the log trend line to infer the bottom left hand part of the learning and give only the top part as I make progress toward the ceiling?

Any thoughts on how to interpret my half-essed learning curves?

I could post a picture if that would help.

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@dubina,

You can't randomly pick a curve type and expect it to fit your data. The slope of the log function decreases as x increases, so it will rise steeply when x is small and gradually when x is large. The slope of the exponential function is the opposite. It will rise slowly when x is small, then steeply for large x. Neither will give you the S curve you're seeking. If you're using Excel, then I think (not positive) that your best bet from the limited choices will be a polynomial function.

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@markr,

@ markr

Thanks for that. I wasn't sure how to choose the right function to trend the data and show a classic S-shaped learning curve. I tried the linear trend line and that was easy to understand in terms of the data and resulting graph. Apart from the linear trend, OpenOffice also affords log, exponential and power functions. OO gives an exponential trend line that is almost the same as the linear trend line...I did not expect that...and the log and power trend lines were somewhat similar, but not like the linear and exponential trend lines.

I can see a flattened S curve in the graphed data from 50% success rate initially to something around 90% recently. I know where I began to implement different play strategies, and I marked some of them in the data. I see those inflection points in the data and on the chart.

OpenOffice affords no polynomial trend line format.

All in all, I see no classic S-shaped learning curve, but I think probably I should.

I read something about b-spline functions being applicable to learning curves. Have not explored that possibility either.

I could post the chart with four different trend lines if that would help and this forum allows it.

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@dubina,

The data is what the data is. If you don't see an S curve when you look at the plotted data, you're not going to be able to manufacture a valid one via any type of trend line. It may be that that initial upward bend happened so quickly that it's essentially linear until it flattens out at 90%.

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