Mathematics of NL. holdem notes
Episode 1: Why is math important? Math gives us a basis for making decisions.
Math is not a replacement for physical tells, timing tells, our gut reads. Math is a tool we can use to combine with the information gathered through tells.
Basic probability and odds
Probability: Is the likelihood that some condition will occur or that some condition is currently the case.
Probability can be expressed as a ratio or as a percentage. The ratio and the percentage give us a mathmatical basis for how likely something is to happen.
Converting a ratio to a percentage
Convert 2:1 into a percentage. 2:1 means you expect to win 2 times for every 1 time you lose. That means your winning 2 out of 3 or 2/3 of the time. To find the percentage you divide the times you expect to win by the total number of outcomes, so 2 wins 1 lose thats 3 outcomes. our 2 wins divided bytotal number of outcomes 3.
2/3= .66666666 Therefore we have a 66% chance to win.
"Shortcut"
Add the left side to the right side
(left side + right side) 2+1=3
Divide the number of wins by the total added
(wins / total added) 2/3= .666666666
Converting a ratio to a percentage when we're a dog
So if we're a 4:1 dog are wins are now on the right side and our losses are on the left. So remember when converting this ratio to a percentage to move our wins to the left side
(1 + 4) =5 (1 / 5) =0.2 or 20%
Converting a percentage back to a ratio
If we're a 75% to win that means out of 100 tries, we win 75 times.
With a ratio we put wins on the left and losses on the right.
75%= 75 wins, 25 losses = 75:25= 3:1
"Shortcut"
Find the largest common divisor or LCD.
This is done by finding the largest number that can be divided into both sides.
The (LCD) is 25 so 25/75=3 and 25/25=1 or 3:1
Variance: Refers to the degree of different outcomes for a situation and how far those outcomes are from the expected result.
What is a "High variance play"? That means that there can be many trials with a lot of outcomes. In poker terms it means playing a certain hand many times and expecting different outcomes before the end result evens out.
Rules of 2 and 4
Rule of 4: On the flop you can multiply your outs by 4 to figure out your percentage chance to win.
Rule of 2: On the turn you can multiply your outs by 2 to figure out your percentage chance to win.
"Reminder" These rules start to lose affectiveness when you have more than 13 outs. Hand ranges
Handranges: A hand range is the collection of every 2 card starting hand that you can have based on the actions that have taken place throughout the hand.
Why do we use hand ranges? Because we can narrow our opponents hands down based on the actions thus far, what position the're in ect. By doing this we can eliminate hands they most likely dont have and focus on the hands they likely have.
Pot equity
Pot equity: Is our stake in the pot ($ or %) if the hand is played out to showdown.
Pot equity = (our % chance of winning) x (the pot)
Example: 25% to win $500 pot .25 x 500 = 125
Equity can only be calculated exactly when we know our opponent's hand or have an idea of his range of hands.
By using pot equity we can determine our "Expected return" either positive or negative on a givin hand.
Expected Value (EV)
Expected Value: Is the determination of what our long term expected outcome is on a givin hand in profit or loss. Also known as Sklansky bucks.
