Strong Short Stack Players vs Weak Short Stack Players

[C8H10N4O2]

Taken from a quote on another forum.

"Short Stack Shoves

You can also glean a good deal of information from seemingly trivial cards that you do get to see. Suppose that the player in the above example moved in, got called, and showed down Ace-King offsuit. This may not seem significant. After all, virtually any player, even those who don't know what an M is, would move all in with AK and an M of 4.

The thing to understand is that AK is a much smaller part of the range of a good short stack player than it is for an overly tight short stack player. Suppose that a strong player would move in with any two cards, but a weak player would only move in with the top 33% of his hands in this spot. Before the hand, you thought there was a 50% chance that this opponent was strong and a 50% chance that he was weak.

Both players will move all in 100% of the time that they have AK offsuit. However, because the strong player is moving in three times as often as the weak player, he will have AK three times less often when he does move in. Thus, when you actually see the AK, there is now a 75% chance that this is a weak player and only a 25% chance that he is strong. In other words, the fact that this previously unknown player showed up with AK the first time that you saw him move all in makes it more likely that he is a weak player, as a weak player will have AK when he moves all in far more often than a strong player will."


What is "M"? And can anyone explain this to me?

[phaul]

Your M is how many orbits you can survive before being pushed all in blind (roughly speaking). It can be worked out by dividing your stack by the total pot preflop before any action is taken. So if there are no antes and yuour stack is 9BBs, you have an M of 6 (9/1.5).

Say blinds are 500/1000 with an ante of 100 and you are 8-handed, the total pot is 2300 so if your stack is 11500 you have an M of 5.

The post is just saying that stronger players will have a much wider shoving range than weaker players, so if they show AK then it's a much larger part of the range of a weak player than that of a strong player, so the player is more likely to be weak (it's the same as saying that if they show QTo after shoving from the button with an M of 5 it's more likely to be a strong player).

[thegrizz1111]

editing to fix my post

[thegrizz1111]

this post uses bayes theorem to determine if the player is stong. The probablity we are interested in is the probability the player is weak given we see AK. this is equal to the probabilty the we see AK given he is weak multiplied by the prior probability he is weak divided by the probablity we see Ak.
P(weak|see AK)= P( see ak|weak)*P(weak)/P(see AK)

there are 169 possible starting combinations. the weak player moves in with 33% of these so probability we see ak is 1/(169/3) which eauals (3/169) = P(see Ak|weak)

since the strong player always moves in the probilty we see ak given stong is (1/169) =P(see AK|strong).

since the player is originally equally likely to be weak or strong the orgianl probablity we see ak is .5*(1/169) +.5*(3/169) = (2/169) = P(see AK)


so therefore
P(weak|see AK)= P( see ak|weak)*P(weak)/P(see AK)

P(weak|see AK)=(3/169)*.5/(2/169)= 0.75


P(strong|see AK)=P(see ak|strong)*P(strong)/P(see AK)
P(strong|see Ak)= (1/169)*.5/(2/169)=0.25

[C8H10N4O2]

Thanks for the replies. I understood stuff about orbits, I just didn't realize it was common to use "M" as the abbreviation for orbit. I figured it had something to do with chip stack in relation to something else, just wasn't sure exactly what "M" was. That makes sense, so I appreciate the explanation.

Thegrizz1111, I'm a bit confused by your post, but I'll re-read it a few times and try to absorb it.