weak one card OESD?

[Sushiglutton]

For readability I put the stoves in the bottom. If u have comments on the ranges and/or math,
please respond by making ur own analaysis. I will not make any changes if anyone asks.
By that I don't mean that this analysis is the truth (in fact it is obviously very rough).
I'm sure there are plenty to debate. Just do so by posting ur own work.




SB range: X = {TT-77,AcTc,A9s,Ac6c,KcTc,Kc9c,QcTc,Qc9c,JTs,Jc9c,T8s+ ,T6s,97s+,87s,65s,A9o,JTo,T9o,97o+,87o,65o}

The other twos ranges pf: Y1(14.8% of all hands) = {99-22,AJs-A4s,K9s+,Q9s+,J9s+,T9s,98s,AJo-A9o,KJo+,QJo}

What they call a raise with (assuming they overcall entire range): Y2 = {99-66,ATs-A9s,Ac8c,Ac7c,Ac6c,Ac5c,Ac4c,KcQc,KcJc,KTs-K9s,QcJc,QTs-Q9s,J9s+,T9s,98s,ATo-A9o}

What they fold vs a raise: Y3(6.9% of all hands) = {55-22,AcJc,Ad8d,Ah8h,As8s,Ad7d,Ah7h,As7s,Ad6d,Ah6h,As 6s,Ad5d,Ah5h,As5s,Ad4d,Ah4h,As4s,KcQc,KcJc,QcJc,AJ o,KJo+,QJo}


Our equity vs X and 2*Y3 is 21.148% (ST1).
Our equity vs X and Y3 and Y1 is 18.857% (ST2).
Our equity vs X and Y1 is 20.661% (ST3).
Our equity vs X is 26.274% (ST4).



So by raising we chew up:

(6.9/14.8)^2 * (26.274-21.148) + 2* (6.9/14.8)*(1-6.9)/14.8 * (20.661-18.857) ~= <font color="red"> 0.44% equity </font>

(%both of them have a hand in range Y3)* (the equity we then gain) +
(% one of them in Y1 other one in Y3)* (the equity we then gain)



The conclussion is that the equity we gain by raising is too small compared to the extra bet we put in.

=&gt; Calling is the best play.







ST1
788,202,860 games 23.922 secs 32,948,869 games/sec

Board: 7c 8c 9d
Dead:

equity win tie pots won pots tied
Hand 0: 18.857% 14.64% 04.22% 115361749 33271095.50 { AhTd }
Hand 1: 54.583% 51.02% 03.56% 402146635 28077882.67 { TT-77, AcTc, A9s, Ac6c, KcTc, Kc9c, QcTc, Qc9c, JTs, Jc9c, T8s+, T6s, 97s+, 87s, 65s, A9o, JTo, T9o, 97o+, 87o, 65o }
Hand 2: 16.956% 14.95% 02.00% 117874935 15770259.33 { 99-22, AJs-A4s, K9s+, Q9s+, J9s+, T9s, 98s, AJo-A9o, KJo+, QJo }
Hand 3: 09.604% 08.99% 00.61% 70881776 4818527.50 { 55-22, AcJc, Ad8d, Ah8h, As8s, Ad7d, Ah7h, As7s, Ad6d, Ah6h, As6s, Ad5d, Ah5h, As5s, Ad4d, Ah4h, As4s, KcQc, KcJc, QcJc, AJo, KJo+, QJo }



ST2
788,202,860 games 23.922 secs 32,948,869 games/sec

Board: 7c 8c 9d
Dead:

equity win tie pots won pots tied
Hand 0: 18.857% 14.64% 04.22% 115361749 33271095.50 { AhTd }
Hand 1: 54.583% 51.02% 03.56% 402146635 28077882.67 { TT-77, AcTc, A9s, Ac6c, KcTc, Kc9c, QcTc, Qc9c, JTs, Jc9c, T8s+, T6s, 97s+, 87s, 65s, A9o, JTo, T9o, 97o+, 87o, 65o }
Hand 2: 16.956% 14.95% 02.00% 117874935 15770259.33 { 99-22, AJs-A4s, K9s+, Q9s+, J9s+, T9s, 98s, AJo-A9o, KJo+, QJo }
Hand 3: 09.604% 08.99% 00.61% 70881776 4818527.50 { 55-22, AcJc, Ad8d, Ah8h, As8s, Ad7d, Ah7h, As7s, Ad6d, Ah6h, As6s, Ad5d, Ah5h, As5s, Ad4d, Ah4h, As4s, KcQc, KcJc, QcJc, AJo, KJo+, QJo }




ST3
12,237,456 games 0.297 secs 41,203,555 games/sec

Board: 7c 8c 9d
Dead:

equity win tie pots won pots tied
Hand 0: 20.661% 16.07% 04.59% 1966113 562277.67 { AhTd }
Hand 1: 60.592% 56.72% 03.87% 6940726 474184.67 { TT-77, AcTc, A9s, Ac6c, KcTc, Kc9c, QcTc, Qc9c, JTs, Jc9c, T8s+, T6s, 97s+, 87s, 65s, A9o, JTo, T9o, 97o+, 87o, 65o }
Hand 2: 18.747% 16.78% 01.97% 2052881 241273.67 { 99-22, AJs-A4s, K9s+, Q9s+, J9s+, T9s, 98s, AJo-A9o, KJo+, QJo }





ST4
96,030 games 0.016 secs 6,001,875 games/sec

Board: 7c 8c 9d
Dead:

equity win tie pots won pots tied
Hand 0: 26.274% 21.64% 04.64% 20778 4452.50 { AhTd }
Hand 1: 73.726% 69.09% 04.64% 66347 4452.50 { TT-77, AcTc, A9s, Ac6c, KcTc, Kc9c, QcTc, Qc9c, JTs, Jc9c, T8s+, T6s, 97s+, 87s, 65s, A9o, JTo, T9o, 97o+, 87o, 65o }


---

[JJack]

wow so deep analysis
(too compex for me :P)
Is there any book to cover how we can use both math + pokerstove?

[Sushiglutton]

[ QUOTE ]
wow so deep analysis
(too compex for me :P)
Is there any book to cover how we can use both math + pokerstove?

[/ QUOTE ]

You can also say in word what is wrong with raising. Since SB is a LP player he has a tight range betting out. That means our pair outs are too dirty to be worth protecting.

[Sushiglutton]

Maybe I should give some more explinations so people can repeat.

Step 1:
Put all villains on ranges before our action.

=&gt; X, Y1

Step 2:
Decide which part of their ranges the two guys behind us will give up if we raise but will continue with if we just call.

=&gt; Y3

Step3:
Compute the equity for our hand depending on the ranges we are facing.


Step 4:

Calculate how much our winning chances improve if we raise (that is making hands in range Y3 fold, we remove them). This is the most tricky step. I use this formula:

(6.9/14.8)^2 * (26.274-21.148) + 2* (6.9/14.8)*(1-6.9)/14.8 * (20.661-18.857)


Let me explain the different parts.

(6.9/14.8)^2 = (6.9/14.8)(6.9/14.8) = Probability(MP3 holds a hand he will fold) * Probability(BTN holds a hand he will fold)

Why is that 6.9/14.8? It's the ratio of the hands in the folding range and he ones in the entire range. I here make the simplifying assumption that these two events are independent.


(26.274-21.148): The difference in equity if both calls compare to if they both folds.


(6.9/14.8)^2 * (26.274-21.148): Together we get how much equity we get extra if they both holds Y3 hands and fold them times how often this event will occur.


Now we do the same thing for the event that one of them holds a hand in Y3 (and folds it) and the other one in Y1.

[Sushiglutton]

[ QUOTE ]
(6.9/14.8)^2 * (26.274-21.148) + 2* (6.9/14.8)*(1-6.9)/14.8 * (20.661-18.857) ~= <font color="red"> 0.44% equity </font>

[/ QUOTE ]

Oooops some trouble wih paranthesis. Should be

(6.9/14.8)^2 * (26.274-21.148) + 2* (6.9/14.8)*(1-6.9/14.8 ) * (20.661-18.857) ~= <font color="red"> 2.01% equity </font>

The conclusion i still valid though.