Quote:
I want to understand the relationship between the individual hands and totals. For a given node of a tree I copied the weights, EVs, and equities to a spreadsheet.
Unfortunately using weights to calculate total EVs and EQs is not a correct way to do it. The reason is that there is card removal effect coming from opponent's range. If for example the opponent has a lot of top pairs on Axxxx board we have top pair less frequently in comparison to other parts of our range.
I went ahead and constructed a toy example for you:
Code:
#TreeBuilding#V2
#Range0#JJ,AK
#Range1#AJ,A4
#Board#5s Jh 4h 3d 4s
#Pot#100
#EffectiveStacks#100
#AllinThreshold#67
#AddAllinOnlyIfLessThanThisTimesThePot#500
#RiverConfig.BetSize#100
#RiverConfig.DonkBetSize#100
#RiverConfigIP.BetSize#100
(You can copy it and then go to tools->paste treebuilding config to recreate the tree).
In this tree the board is:
Jh 5s 4s 4h 3d
and our range is:
AK, JJ
opponent's range is:
AJ, A4
Let's look at our equity:
AK: 0
JJ: 100
If we use simple weights to calculate averages we would get:
(16combos * 0 + 3combos * 100) / 19combos ~= 15.7894
Now let's think about real probabilities. We could see that JJ is less likely as every time the opponent gets AJ we can only have JJ in one way. The way to calculate real probability of us having a specific hand is to count matchups and thus:
If we have AK (16 combos) the opponent can have:
1)AJ then it's 16 * 9 = 144 matchups (they have 3 aces and 3 jacks left the deck)
2)A4 then it's 16 * 6 = 96 matchups (they have 3 aces and 2 fours left in the deck)
If we have JJ (3 combos) then:
1)AJ then it's 3 * 4 = 12 matchups (they have the last jack and 4 aces left in the deck)
2)A4 then it's 3 * 8 = 24 matchups (4 aces and 2 fours left in the deck)
Overall it's 144 + 96= 240 vs 12 + 24 = 36 matchups.
Now let's calculate weighted average using those relative probabilities:
(240 * 0 + 36 * 100) / (240 + 36) ~= 13.043
and this is what the viewer shows:
https://gyazo.com/6495953ee453c75d2aa8f62218861948
This is possible to verify on a toy river example but unfortunately with wide ranges on the flop it becomes increasingly difficult to do by hand.
Last edited by punter11235; 08-12-2018 at 03:56 AM.