[fnord_too]

Wow, I am getting some strange results. Here is a table of expectations for various raise numbers.

Raise Number Expectation
0 0.1250000
0.1 0.2164059
0.2 0.2756923
0.3 0.3081655
0.39 0.317645741
0.4 0.3176441
0.41 0.317440559
0.5 0.3068750
0.6 0.2878182
0.7 0.2718444
0.8 0.2598767
0.9 0.2524926
1 0.2500000


The maximum seems to fall right around 1/e (which is not too surprising, that number shows up all over the place in probability and statistics).

What does surprise me though is, apparently, raising all the time is a winning strategy, if A calls with every .25 or higher, he wins about 55% of the time and looses about 45% of the time, meaning that he is actually giving up too much by folding his < .25 numbers!!

If anyone wants the spreadsheet I whipped up to check it for errors I'll be happy to send it to you, I am having a hard time believing these numbers. The only thing I can think of is that how I am calculating the winning chances of calling the raise are wrong. I have assumed that if the average raising hand is X and the average calling hand is Y, then the raiser will win X /(X+Y) percent of the time and the caller will win Y /(X+Y) percent of the time.

Any thoughts on this? If I am getting a number between 0 and 1 and you are getting a number between .25 and 1, how often do you win? For reference, computing it my way the split is .44 repeating to .55 repeating (5 to four in favor of the .25 to 1 number. Think I will go monte carlo that to see what what develops.