There is a prop bet thread in BBV where allegations of collusion have been raised. Any probability experts able to take a look at it and give an opinion as to the odds of the situation arising?

http://forumserver.twoplustwo.com/54...op-bet-736624/

Basically two microstakes cash/sng players, with no history of taking shots, jumped several stakes on March 19, the day of the prop bet, and lost a significant amount of cash in suspicious hands to the guy doing the prop bet, gary_neville. It turns out these players are connected to gary_neville and are friends/students/stakees of gary's long time friend Roseeker who was posting in gary's defence in the the thread under two accounts.

Here's how I see it. Out of say 700 days that ptr has been tracking hands these players BOTH decide to make this unprecedented huge jump in stakes on the March 19. Odds of one of them making this jump are 700-1. Therefore odds on both of them doing it are 490000-1. Of all the opponents they played on that day, they both lost the most to gary. I speculated that if the first player, breeezzz, played 8 opponents on that day, it was and 8-1 chance that he would lose the most to gary. I speculated that the other player, stoppedclock played 25 opponents so it was 25-1 that he would lose the most to garry. Taken together, those hypothetical figures mean that it was 200-1 that they would both happen to lost the most to gary.

What do you make of these figures, am I way off, or is this whole incident way too big a coincidence to explain away as pure chance.

Edit: Gary also made his only two 3bets with unsuited junk from the SB/BB out of 30K hands against these two players. One of these hands was what led to the allegations of chip dumping. So from a probability point of view do you reckon these two hands are significant?

Here's a way to test your theory. Without knowing what'll happen tomorrow, look for all such occurences of any two players jumping stakes and losing the most to the same person.

If it only happens once a day then with other evidence this might be suspicious. If it happens all the time then you're paranoid!

But he isn't talking about random players, he said the 3 players have a prior connection to each other. If true, that makes it virtually certain there is more going on here than coincidence, regardless of whether the allegation is true.

One essential missing piece of information is the history of these two playing together or not. It's possible they both decided to jump in because of the prop bet, having no arrangement made with the 3rd player. But either way, it isn't coincidence.

if they both knew about the prop bet and wanted to take a shot at him, then there you go. hard to prove collusion in a situation like that, unless losing was much more profitable and you can connect the money.

It could be coincidence *if* the information about previous contact was only found out and looked up because of this other suspicious activity. There needs to be some kind of control. It could be that even entirely honest people quite often have prior connections without necessarily knowing it.

It's important to have some kind of control and some kind of measure of the chances of it all being coincidence vs people actually trying to rip others off.

While this is true, it is not true that 3 random players with a prior connection just show up in the same game on the largest poker site, at a common stake, on a specific day where a bet is taking place, and in a game that two of them do not normally play. This is all beside any play analysis that the OP refers to. Just the showing up on that table isn't coincidence. As I mentioned before, it could be that the two players just wanted to take a shot at the bettor because they knew who he was, and they failed.

Isn't this really more of a 'smell test' than a probabability question.

When you talk about two who know each other 'moving up' on the same day, the problem is that we're not talking about independent variables.

The very fact that they moved up has nothing to do with collusion, per se.

Example, if my best friend and I sit down at the same table, would one say that since the odds of this occurring randomly are slim, it must be collusion. Of course not. We sat down at the same table because we like to play together -- but we don't soft play each other. Much more fun to brag over beers when I kick his assets.

Similarly, the fact that they both moved up and played at the same table with a third friend. I'd say again, this is probably not a random occurence, but does not in and of itself mean collusion. And the fact that two of them lost and the third won. Again, no proof of anything.

Now -- getting two friends to move up on the day of your prop bet and lose to you, is one way to collude on the prop. But this really isn't a statistical question.