Maths and Odds Oracle that is.

Myself and Kreatief did some work using leakbuster and odds oracle. In leakbuster we filtered for straight free disconnected boards and decided to run some analysis.

Hero (SB): $25 (100 bb)
BB: $30.10 (120.4 bb)
UTG: $10 (40 bb)
MP: $35.25 (141 bb)
CO: $36.26 (145 bb)
BTN: $38.79 (155.2 bb)

Preflop: Hero is SB with
UTG folds, MP calls $0.25, CO raises to $0.75, BTN folds, Hero raises to $2.75, 2 folds, CO calls $2

Flop: ($6) (2 players)
Hero bets $3.20, CO calls $3.20

Turn: ($12.40) (2 players)

In this hand V is 50/16 and we make the assumption that he calls 100% to 3b.

We assigned a range of:

(16%$np$ds, 16%$np$ss, AA, KK$ss, QQ$ds, QQ$R$R$ss, $R$R$R$R$ss, 5678+$ss, 5789+$ss, 679T+$ss, 9TJK+$ss, 69TJ+$ss, 67TJ+$ss, A[K-9][K-9][K-9]$ss, RROO, A[567+]:Aww, [JJ-TT][78+]$ss, A$R$R:Aww, [99-77][5-8][5-8]$ss$nt, [99-77][8-J][8-J]$ss$nt)

Which we saved as a macro and called it MP for Middle Position. We used 16%$np$ds and 16%$np$ss to account for random SS and DS hands that are in a typical opening range as everything else only constitutes ~11% of starting hands.

On a board of AcQh4d we have ~14% equity. If we assume V calls:

(A, AQ, A4, Q4, KQJ, KJT, A23, A35, A25, QQ, 44)

and folds everything else V folds ~ 38% of the time meaning that with fold equity alone our cb should show a profit in the long run which is obviously a great result for us.

On the turn we pick up a tonne of outs and vs his turn call range (Add, AQ, A4, AQ, A6, Q6, Q4)$np we have ~32% equity.

Now we need to figure out how profitable a turn barrel is. If we assume V raises (QQ, 44 and AQd, 66) this accounts for 14% of the hands that made it to the turn.

His turn call range (Add, AQ, A4, AQ, A6, Q6, Q4!44)$np makes up 43% and we assume he folds everything else 43%. Lets assume we bet $8

So:
14% V raises and we fold and lose our bet of $8
43% V calls and we go to the river with ~33% equity
43% V folds and we win a pot of $12.4

Therefore:

%fold*(pot size) + %raise(-betsize) + %call * [EQ*(pot+betsize) + (1-EQ)*(-betsize)] = EV

.43*(12.4) + .14*(- + .43*[.33*(20.4) + .67*(-] = EV

5.33 - 1.12 + .43(6.73 - 5.36) = EV

5.33 - 1.12 + .43*1.37 =EV

5.33 - 1.12 + .589 = EV

= $4.799

= 19.1bb

As you can see we have a very proitable turn bet. This is of course assuming our ranges are correct. Some V will raise QQ, 44 and AQ on the flop. Regardless of whether the ranges are correct or not I learned a huge amount of both the maths and Odds Oracle. This is something I will be using a lot more of in future.

((turn_call_range),(turn_raise_range)) : ((flop_call_range) : (preflop_call_range))


Kreatief was very patient explaining everything and I am very happy with my progress so far.

Anyway....in other news....I have moved half my roll back to iPoker. I have been having a horrible time at Stars and a change will do me good. Firing up the Stars client already has me halfway to tilting. I hope I can return soon.

Anyway folks. Hope you all run better than me

Pt