Harrington V2, SHAL Calculation Error?

[AZnuts]

Structured hand analysis (SHAL), Page 166 at the bottom.

Harrington is calculating the probability of no one calling your all in move. His probabilty math is not technically correct; it may just be a simplification, as opposed to an error, but he usually states any simplifying assumptions.

Chance of being called by players A, B, C, D is 2.8%, 5.3%, 11.1%, 2.8%. He calculates probability of no one calling as 78.0% (or simply 100% - 2.8 - 5.3 - 11.1 - 2.8).

The actual total probality of successive events like that is the product of each individual event (using prob. of not being called): Total Prob = .972 x .947 x .889 x .972 = .795, or 79.5%

Now, I realize in his specific case the amount of error is very small (1.5%) because the probilities of each individual caller are small.

However, if you use this approach yourself for a different situation, such as the very late stages of a tourney where all stacks are very small versus the blinds, and the chance of being called by each player is higher like 25%, then the error is significant:

True probability of not being called by any of the four = .75 x .75 x.75 x .75 = 31.6%

Harringtons method would yield a 0.0% chance of being called (100% - 25 - 25 - 25 - 25).

So, be VERY careful when you apply the same overall method to a different scenario.

[cwsiggy]

There is no way that someone can calculate this on the fly in a tourney, and I think even Dan implied as much. Didn't he say this was for at home analysis???

[AZnuts]

Yes, Harrington does state this is for detailed at home analysis.

I'm in no way implying anything different, and the post stands as appropriate anyway; What is your point?

[Jbrochu]

I believe that Harrington says something like, "we have to make an assumption that is slightly wrong but makes calculating easier, we assume we will only be called by one player."

In light of this, it makes sense to me how he proceeds with his calculations.

[AZnuts]

[ QUOTE ]
I believe that Harrington says something like, "we have to make an assumption that is slightly wrong but makes calculating easier, we assume we will only be called by one player."

In light of this, it makes sense to me how he proceeds with his calculations.

[/ QUOTE ]

Maybe his comment is directly related, but the assumption seems unnecassary at this point in the process, and I still don't see how it affects calculation of that first number. The 79.5% number for getting ZERO callers is exact and just as easy to calculate.

His stated one-caller assumption seems much more relevant later in the process when you have to calculate how your hand will showdown versus only one other, and multiply that result by their individual probability of calling. That part is significantly simplified with the "one caller" assumption.

I don't know, the 78.0% number is still a mystery to me, and a similar calculation like I show in the original post shows the method would produce an erroneous answer if the calling probabilities were more like 25%.

Anyone else have some more ideas on this?

[Jbrochu]

[ QUOTE ]
His stated one-caller assumption seems much more relevant later in the process when you have to calculate how your hand will showdown versus only one other, and multiply that result by their individual probability of calling. That part is significantly simplified with the "one caller" assumption.

[/ QUOTE ]

If you use the technically more correct 79.5% figure as the chance of not getting called, when you get to the part of the problem where you are adjusting for each of the respective callers range of hands and how your hand holds up against his range, the total percent will exceed 100% when you put it all together for your EV calc.

79.5 + 2.8 + 5.3 + 11.1 + 2.8 = 101.5%


I'm sure this can be solved for but not as easily as living with being "slightly wrong." That's my take on it anyway.

[AZnuts]

I see what you're saying about the end EV calculation. It would either be slighty off up front, or at the end. I acknowledge that in his specific example, it makes no real difference.

However, in thinking of using this approach, I do not know how to handle a case like I described, where you assign a much higher calling percentage to players like 25% such as late in a tourney. Seems like the math breaks down.