Poker Math: Advanced Poker Math

OUTS
-unseen cards in the deck that can improve our hand.
eg. AKs on JT3
-> we can hit A,K or Qs to make top pair+ therefore we have 10 outs

Calculating Equity based on Outs
- 10 outs on the flop => 47 cards remaining in the deck
What is our Equity?
-to improve on the next street: 10/47 = 21%
-to improve by the river: 2*(10/47) = 42%
[USE 2-4-RULE]
- 2 cards to come = outs x 4
- 1 card to come = outs x 2

ODDS
-odds = ratio (eg. 3:1)
- probabilities as odds = unfav:fav
-odds into percentages: right side divided by both sides eg. 3:1 = 1/4 = 25%

Comparing Pot odds and needed equity
-odds show the ratio between the current size of the pot and the bet to be made
-> eg. pot sized bet give us odds of 2:1
Pot = $100, V bets $100 =? we call $100 to win $200 so odds = 2:1 = Equity needed is 33%


Scenario: NFD with  Overs on TURN (TBC)
Pot: $60, Effective stacks: $470
Hero: AhKh on [9h8s3d][2h]
Hero bet $45, villain raise $110, we shove all-in
Villain's range before calling: [99,88,33,98,JhTh,JTo,A5s-A4s]
We estimate villain will call with sets, two pairs and JhTh

What equity does villain need to make the call?
Villain needs to call 360 to win 1000 (360+640) = 36%

What is our equity when called?
14%

What is our EV for the shove?
EV(total)
= EV(Villain calls) =
Total combos: 39
Two pairs and better = 3+3+3+9


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