Originally Posted by Stu_Ungar
I'm not sure thats correct FP.
You have a graph of y= profit and x = bet size.
Surely you should have instead a graph of y= frequency of call x = bet size and the area of the rectangle under the intersection point the graph represents profit.
The thing is that for your profit to be higher betting less than the amout his average hand would call, the shape of this graph would have to have a distinct kink in it at the point of the average call.
I think the elastisity of calls does change above a certain threshold because when you bet large you create a potsize that so few hands can comfortably call but for you to justify betting less tan the average call amount, the shape of the graph preceding this point would have to be extremely steep.
Well, uh... I could have measured the frequency, too, of course, but instead of having to measure or calculate the profit from x*y, I just let the program return the profit from each bet size. I mean, you have the same data in the graph, effectively, since Y doesn't actually show average profit but total profit (a minor lie that doesn't affect the point since all bet-sizes had the same number of tries; dividing each value by 1000 just changes the scale not the shape) so it's just a matter of what I choose to graph. As profit was what I was interested in, I went with profit.
I'm not sure what you mean by distinct kink.
But just to clarify what the simulation did:
1. Start with a bet-size of 80.
2. Create a random number between 80 and 120.
3. If the number is greater than the current bet-size, add the current bet-size to the current profit tally.
4. Loop from step 2 1000 times.
5. Print the profit.
6. Go back to 1 and increase the bet-size by 1.
Step 2 is the key; this is where I invent a random opponent with a certain "calling treshold". Because it's random, I don't expect to see any distinct kinks anywhere. Why would there be?