DaPhunks Second Post In A Row! Warning - Ramblings, don't read!
I can't sleep so I'm posting again. I have 2 Questions.
Question 1)
How come party seems to have starting lagging when i play over 1000 hands in a session and starts to use more processing and memory power than Half-Life 2 does. Surely to render highly detailed environments and handle the dynamic physics engine would take more than simply displaying 16 1 dimensional tables with just a few buttons to click on each. Its ridiculous and frustrating when the lag causes party to take 5 to 10 seconds to bring up the buy-in / rebuy window.
It is really annoying.
Question 2)
Why the hell is it that whenever i see a formula i have to write it down in a different way to learn it/ understand it? Its like i have to reinvent it or something. This even goes for a simple formula like the ± EV one for a push. I am somehow unable to just look it up and use the one provided, i have to "invent" a new one which takes a different aproach.
Pleas note - I do NOT expect Anyone to read this. In fact i would be Amazed if anyone read this. Not just EV formula, these are just ramblings, mathematical dribble, lots of stuff i will miss out and lots of errors too. I'm sure. (gag me with a spoon - get the reference?)
So, without further ado, My EV formula;
EV ≈ A + B (Simple huh?)
A ≈ Mean value of profits from the opponent folding.
B ≈ Mean Profits/Losses from the opponent calling.
So B ≈ % times opponent calls(x) Multiplied by our mean winnings(y) ± mean losses(z).
Now, to work out A and B;
A ≈ Fold Equity x Pot Size
B ≈ (x)(y + z)
x ≈ 1 - FE
y ≈ Equity(multiplied by Pot Size + Our new contribution to it)
so y ≈ Equity(Pot Size + Remaining Stack)
z ≈ (1 - Equity)(Remaining Stack)
From this we can construct Simple Formula Number 1.
EV ≈ (Fe x Pot) + x(y + z)
Now we have that out of the way can examine what FE and Equity are.
Fe ≡ % of hands villain will continue with.
Fe ≈ % of time villain thinks he is not ahead or does not have a strong enough draw to continue with or bluffcall with.
Fe ≈ 1 - [Ø(D + S+B)] D = % Villain has Draw he will play.
S = % villain thinks he has Strongest hand. B = % Villain will Bluffcall.
Ø = % How often we make this push play.
Equity ≡ Chance we will win.
Eq ≡ % chance μ Beats φ.
μ ≈ Our Hand range. Determined by interpretation of image of opponent/ stats of opponent, our adjustment to our opponents image and our propensity to bluff against opponent.
μ ≈ [k + α(shr - ρ)] + [k2 + α2(shr - ρ)]
k = starting hand range played against average opponent
k2 = Hand range we bluff against average opponent
α = % adjustment in terms of hands we play "valuewise"
α2 = % adjustment in terms of hands we play "bluffwise"
ρ = opponents deemed % of played hands
shr = opponents % of played hands
φ ≡ Our opponents Hand range which is determined by the same factors we use to adjust our Hand range to his image except that we replace k with g. He has already invested money into the pot so will have to play with more hands.
g / g2 = opponent handrange.
φ ≈ [g + α(shr - ρ)] + [g2 + α2(shr - ρ)]
please note - for φ [g2 + α2(shr - ρ)] is reffering to bluffcall range rather than bluffing range.
Now we have established what determines some ranges we can compare the difference. Lets see if we can get something to work;
Difference between μ and φ. (μ : φ)/2 This gives us our % of hands played.
Eq ≈ 1 - [(μ : φ)/2]
Assumption; The smaller our handrange the more often we win. The lower the % the closer more often we have the absolute nuts so win. Neither player ever makes a mistake.
Yay! A lovely little formula for Eq! This makes me so happy. Even though its gonna be wrong because of our assumption. Now i have to think through Fe again so i can see if i can draw any comparisons to Eq.
Fe ≈ (1 - φ) = % hands opponent folds with.
Ok, now I'm going to create the not so simple simple little EV formula 2 to and plug in some arbitrary numbers to see what happens, playing around with different variables to help me think. Remember Formula 1;
EV ≈ (Fe X Pot) + x(y - z) x ≈ 1 - FE
y ≈ Equity(Pot Size + Remaining Stack)
z ≈ (1 - Equity)(Remaining Stack)
P = pot R = remaining stack in this formula.
Ev = [(1 -φ) x P] + φ[(1 - [(μ : φ)/2])(P+R) + R[1- [1 - [(μ : φ)/2]]
Ok, i am now going to go to bed, I shall return again and work myself a sample formula for g. It is required for me to test my model which is trying to prove that;
α = % adjustment in terms of hands we play
Is important.
I'm tired now! What wonders a bit of mathematical rambling can do to help you sleep! Especially for people like me who are terrible at math lol. Good luck at the tables everyone!
Enjoy!
powpow
I use FreePHG too
