APerfect10 wrote:The flaw is not in your calculations but your viewpoint.
I agree. I'm glad that you understand that the flaw is created by incomplete information about what the dead cards are, not the players' actions in multi-way pots.
Which players in this hand care about their All-In Equity or EV calculations? The two players that went all-in (SB & BB) are the ones that care -- not the player that folded on the turn (BTN). You calculated the SB & BB's EV from the viewpoint of the BTN which would be incorrect.
The only player with complete information of this hand is the player that folded (BTN) since they know their two holecards as well as the other players cards because they went all-in and to showdown. Therefore from the BTN's perspective, you are absolutely correct that we can accurately calculate the SB & BB's All-In Equity but that is worthless because the BTN does not care about the SB or BB's All-In Equity.
From the two players whom actually care about the stat (the SB & BB), they are unaware that the BTN held J3
Please do me a favor and take this hand from the SB & BB's perspective, where the BTN's holecards are unknown, and run it through HM and tell me what EV numbers you get. Since we know the correct EV numbers for both the SB & BB, we can compare the real result from HM vs the correct result and see how skewed the data is.
There's no need for me to do that. It really wouldn't prove anything and I've already shown you that I am aware that the All-In Equity value can vary significantly from its true value without complete information on dead cards. In an example hand earlier I showed that the probabilities of winning for AQo vs 66 can range from 44% to 55% in the PT4 database depending on what information is available to us.
MY GUESS: PT3, HM1 & HM2 are not going to have the intelligence to put the BTN on an accurate range therefore the real result will be negatively skewed.
The results would not have perfect accuracy, but looking at the SB's database it is very difficult to say who is favored by the EV calculation in the long run in this scenario.
Yes, in the example I gave you in the SB's database the 6
5 would have a higher EV against AK
than he has really because there are two dead hearts which prevent him from getting a flush. But you need to look at the bigger picture. While sometimes the BTN would have J3, at other times he would have folded K
T or QQ. If his range was 100% of all hands, the EV calculation in SB's database would be perfect. The key is that his range would only systematically favor one player by a negligible amount. So what we'd see is that in one case, the EV calculation might be $0.24 too high and in another it would be $0.22 too low. It would end up that the average is so close to the actual numbers that we want to use it.I guess that we will find out soon enough to determine how accurate the real vs actual results are. Of course its accurate when you have the complete information of a theoretical hand; however, if we use a real-world example where the information is incomplete then the real vs actual results are not going to be "accurate enough" as you put it.
You are opposed to the idea of using All-In Equity calculations in the hand I described due to the lack of complete information about dead cards. This raises the question: why is PT4 doing an All-In Equity calculations in the AQo vs 66 hand when it does not know what the button folded (66)? Since you are opposed the idea of calculating All-In Equity in the hand I described due to a lack of knowledge about dead cards, you must surely be opposed to the idea of calculating the All-In Equity in the AQo hand since it incorrectly says the All-In Equity is 55% when it is actually 44%.
