Where is my math wrong?
Was taking a look at some preflop stuff earlier and i realised my calculations and solver solutions didn't add up. What am I overlooking? The spot presented is CO 2.5x BTN 8x BB 21.5x BTN? GG Rush and Cash rake structure (3BB cap)
So obviously we must pure jam KK for equity denial purposes, Therefore we need to base a strategy around making his pocket pairs indifferent. The equation to describe this is
%Kings(.2) +%Aces (.2) + %AK (.5) = 80/200 =.4
6(.2) + Aces (.2) +AK (.5) = .4 (6 + Aces +AK) where we let % be combos over total combos.
1.2 + (.2)AA + .5 (AK) = 2.4 + (.4) AA +(.4)AK
(.1) AK - (.2) AA =1.2
The other equation is obtained by the calling range. However when we look at the GtoW range we find this equation does not hold. As BTN jams 2 combos AA,1 QQ and 10 combos AK giving the left hand of the equation a value of 1- .6 =.4 which is very far off from my calculution
4 Replies
Hi Tombos, thanks for the response, This is basically what I did however I didn't assume the solver frequencies to be correct. My attempt was to create two simultaneous equations, one from the raising strategy and one from the calling strategy the latter of which is obviously quite tricky but also less important imo. However the first equation I obtained states that (.1)(Combos of AK)- (.2)( combos of AA/QQ)=1.2, This assumes villain needs 40% to call and that we are required to jam KK at 100% frequency. Also in game I will pure call QQ so the latter part of the equation is virtually just AA. Based on solver solutions there are 3 combos AA/QQ and 11 combos AK ( I assumed 10 in my initial calculation). this yields 1.1-.6= .5 which is definitely not equal to 1.2. So my equation must be incorrect however I am confused as of why.
%Kings(.2) +%Aces (.2) + %AK (.5) = .4 [Equity calculation for villain. He needs 40% (right side), and left side is standard equity calculation. AA is basically AA+QQ]
6(.2) + Aces (.2) +AK (.5) = .4 (6 + Aces +AK) [I change percentages to fractions and multiply across by denominator being total combos]
1.2 + (.2)AA + .5 (AK) = 2.4 + (.4) AA +(.4)AK [The rest is algebra. ]
(.1) AK - (.2) AA =1.2
Your math is fine. The problem is that your equation is extremely sensitive to equity estimates, and you're using pretty rough estimates.
For example, if you use a more accurate estimate for equity vs AK, say 56% rather than 50%, then you end up with this:
0.16 (AK) - 0.2(AA) = 1.2
Plugging in 11 combos of AK and 3 combos of AA yields 1.16 ≈ 1.2
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I recommend calculating the equity vs the shoving range directly.
Assuming you have 20% vs overs and 56% vs AK, you end up with about 39.8% EQ, very close to the required 40%
The reason I actually made the equation is that I assumed villains would play better preflop than postflop in 4bet pots OOP. So my strategy was to pure call AA and AKs and jam AKo and KK. Using the more accurate value of .16 we need to bet 7.5 combos AKo so I guess like 75%. Is this strategy good in you opinion. To just ignore the equation obtained postflop as an exploit while still keeping an unexploitable jamming strategy preflop?
Seems tricky to default to this jamming range in all spots because
1) Pot odds laid when shoving change a lot depending on preflop action, thus altering the ratio of AK to KK
2) Assumptions about how they play pre and postflop are kind of nebulous
3) No room for exploitative maneuvers
