Quote:
Originally Posted by HappyPixel
Looks good, there's no better strategy in the long run though. Simpler way of looking at it:
EV of 1 spin is $2.
EV of 2 spins is 0.1 x $4 + 0.2 x $3 (win $3 or $4) + 0.7 x $2 (take another spin if not) = $2.4
EV of 3 spins is 0.1 x $4 + 0.2 x $3 (win $3 or $4) + 0.7 x $2.4 (take another 2 spins if not) = $2.68 hence free monies!!!
This would be full credit, but its actually spin 3 is worth $2 (because that is the EV and you would have to take that spin as its no choice, and I think that is what you meant)
Spin 2 is 2.4 and Spin 1 is $2.68
Here is what it looks like
Spin 3 worth $2
Spin 2 and 3 have a combine value of 4*(.1) + 3*(.2) + 2*(.3) +2*(.4)= $2.40 (since if you spin $1, you go to Spin 3 which has an expectation of $2.)
Spin 1 has a value of $4*(.1) + $3*(.2) + $ 2.4*(.3) + $2.4*(.4) = $2.68
So if you play this game 1000 times you make $118.
This is an interesting problem (for a math geek), because it demonstrates how a single event +EV (which by definition you can't do better than), is affective by a decision theory if the single +EV are tied together. If you just look at the +EV of a single spin and base your strategy on that you don't maximize full profits.
Now EV by itself is only valid when its a single player vs. nature in a repeatable decision. Game theory needs to be use when its player vs. player(s), but it gets really complicated when we start having more than two options.
Lets do the batter vs. pitcher game.
So a batter is facing a pitcher that has two pitches Fastball and Curveball.
If the Batter is expecting Fastball and gets a Fastball he hits .300
if he is expecting Fastball and gets a Curveball he hits .200
If he is expecting Curve and gets Fastball he hits .100
If he is expecting Curve and gets Curve he hits .500
What is the EV of his at bat?