Quote:
Originally Posted by Husker
I was discussing 2 seperate things:
1) To show how much AK's raw equity drops even when we add a random range. I'd previously pointed this out though
2) The point about two optimal players with the same range was to explain that the player in position will have a higher EV (quite a bit in percentage terms)
Your example is ineffective, though. Our absolute equity drops with any hand as we add players. Our pot share in dollars based on equity goes up with AK against random hands. Our true EV may or may not go down, but you showing the difference in equity is an argument that it should go up, not that it should go down. If you think the EV should go down, you should argue it a different way.
Of course all else equal, the IP player will have an edge when considering range vs. range and not specific hands. No one is arguing that position is not an advantage.
Quote:
Also, the player with AK won't necessarily have a very large equity edge over the other ranges. I think you're also assuming raw equity = best chance of winning the hand, which unless you're all in preflop isn't the case. EV, where it can be calculated, is a better indicator.
AK still has a very large equity edge against typical cold-calling ranges in most situations.
Quote:
Even if we just use raw equity as an indicator of where the money is going, the majority of it is going to your opponents when it's multiway. It's possible you'll have a higher equity than them individually but not collectively.
We're not playing against two hands collectively when each player bets independently of each other. Using raw equity to calculate EV, our EV goes up with AK as players are added with a range of any two cards.
Ignoring any dead money such as blinds:
Code:
Two players:
| AK | random
--------------------------
Equity | .6575 | .3425
EV | .3150 | -.3150
Three players:
| AK | random | random
-----------------------------------
Equity | .4886 | .2557 | .255
EV | .4658 | -.2329 | -.2329
When a second player cold calls, our EV and the first cold caller's EV go up. The third player's EV is being distributed to the others because he's making a losing call. Based on equity and ignoring factors such as post-flop playability and position, AK is happy to see the third player call.
Quote:
I am not talking about playing ability, although that could be a factor contributing to edge. Edge = EV/bet. If our edge is positive and constant, which it is roughly when ranges are insensitive to bet sizing, we would like the pot to be bigger.
Quote:
I don't understand what you mean by much of this. Can you explain it in more detail?
I can try. Maybe you're not used to considering edge as a quantifiable term. Edge is the fraction of our bet we expect to gain/lose by having placed the bet. For example, for every dollar bet at single zero roullete, our expected value is -$.027, and our edge is -.027. If we bet $2, our EV is -$.054, and our edge is still -.027. Having a positive edge is the same as being +EV, but EV describes an amount, and edge describes a ratio.
Edge remains constant as we scale our bet sizing in roulette. Edge does not scale this way in poker, because an opponent still has the ability to make a decision after us. However, if you pre-determine that our opponent will call with his entire range. Our edge will be roughly insensitive to bet sizing.
In case it's not clear. I'm not arguing for limping AK or any other hand. I think it has no place in GTO play outside of the SB (although some place in exploitative play). I'm just arguing that thinning the field is not a very good reason to raise AK.
I do not consider thinning the field as the same as equity denial. Thinning the field implies we have a hand that would not like to go multiway. Equity denial is a different concept. Arty is right that a lot of hands don't like to go multi-way, but I'd counter that by mentioning that most hands prefer to go zero-way
. Certainly our very best hands want to go multi-way. AA should absolutely be happy to get as many callers as possible. AKs probably is happy to get as many callers as possible. AKo probably wants to be heads up or win the blinds against optimal opponents. Against atc fish I'm happy to get everyone to call.