[ShaneP]

How exactly are you guys taking into account the random actions of other players at the table? This will affect the VPIP and PFR of these 4 suspected bot accounts. I don't see how the random behaviour of the other players at a table can be incorporated into your standard deviation formulas.

For example, assume the bot or robotic human player has the following actions with KQ in middle position.

if (hand = KQ and posn = MP)
{
if ( opponents_action = raise )
fold;
else if ( opponents_action = reraise )
fold;
else if ( opponents_action = call )
call;
else if ( opponents_action = all_fold )
raise;
}

Now there would be a similar case for every hand and position. If one player followed these actions at a LAG table with average stats of 25% VPIP and 15% PFR for 100K hands then his personal VPIP and PFR stats would be drastically different than someone who played with these actions at a rocky table with average stats of 15% VPIP and 4% PFR.

I don't understand how your STD formulas could be incorporating the effect of other players' random actions on the VPIP and PFR stats of the suspected bots. Don't you think that these variations would affect these guys VPIP stats by at least fractions of a percent even if they were following a rigid system?

I agree that if the bots had programmed actions regardless of their opponents actions then you could expect the stats to be nearly identical after 100K hands though. But if this was the case then the bot would be a huge losing player, so this can't be the case. But isn't this the assumption that you're making with these STD calculations?

[/ QUOTE ]

I just want to be clear in what I've said...using the naive calculation of SD, the largest deviation from the mean that *I* calculated for VPiP was 2.6 or so. However, this estimation of SD is the smallest it could possibly be. I've given one reason (changing the underlying VPiP halfway through play, to generate the draws from two different distributions), and you have another very valid way to pick from two distributions which would also mean the naive calculations underestimate SD. Thus a SD of 2.6 doesn't show me anything.

Thus, the VPiP doesn't prove they're not bots (doesn't prove they are either). Someone could just be following some author's PF guidelines extremely rigidly or something. Now (not statistically talking yet) the postflop numbers...

I hope this wasn't cleared up in the next 100+ posts before I post this [img]/images/graemlins/smile.gif[/img].