Error in Sklansky-Chubukov numbers?

[Jack Fate]

I was trying to compute the SC numbers for some hands by myself and it seems to me that the published numbers are not correct. I searched the forums but couldn't find any discussion them being incorrect.

I will explain how I'm calculating the SC number. If you can find a flaw please point it out to me.

First of all, I am going to assume that the N_Call and P|call columns in this table are correct. So, the probability of getting called, c, is N_Call/1225 and our equity when called, E, is given directly by P|call.

Our E.V. equation that we need to solve (setting E.V. to 0) is

0 = (1-c)*3 + c*[E*(X+3)+(1-E)*(-X)]

Solving for X, this gives

X = 3*(c-cE-1)/(2cE-c)

So, we should be able to derive the SC number directly from the N_call column and P|call column in the table with

c = N_call/1225 and E = P|call.

If you paste that table into an excel spreadsheet starting at column B. Then the following formula will compute the SC number:

=(3*((C5/1225)-1)-3*(C5/1225)*E5)/((C5/1225)*(2*E5-1))

If you do this you will see that the computed numbers are off by a bit compared to the published numbers. For example AKs is published as 554.51, but when computed as above it comes out to 559.9259. Another noteworthy example is deuces. It goes from 48.05412 to 55.25959. Since these differences are too large to be attributed to rounding error, then either the published numbers are wrong OR the SC number cannot be derived from N_call and P|call as I described.

If anyone has any insight to this problem, please let me know. It's driving me crazy for no good reason.

[DarkMagus]

[ QUOTE ]

0 = (1-c)*3 + c*[E*(X+3)+(1-E)*(-X)]


[/ QUOTE ]

I think (X+3) should be changed to (X+2). Assuming that X is stack behind after posting the small blind, your opponent has to call X-1, not X.

As a side note, I wouldn't mind seeing how these numbers change when adjusted for rake. This could be useful dealing with short stacks (e.g. someone sitting with $20 at .5/1) since the full pot will be raked 5% for an all-in.

[Jack Fate]

Excellent. Yes it should be X+2 instead of X+3. This is printed incorrectly on page 216 of NLHT&P. When I make the change to X+2, the numbers come out correct to 2 decimal places.

Thanks for finding the mistake. Now I can sleep [img]/images/graemlins/smile.gif[/img]