Mathematics of NLHE Ep 1

Covered in this episode:

• Probability and Odds
• Variance
• Rule of 2 / Rule of 4
• Pot Equity
• Expected Value (EV)

Math is not a replacement for physical tells, timing tells, our gut feelings, and our hand reading. Math is the tool we use to determine what the best course of action is based on the information we gathered through the tells, our gut, and our logical hand reading deductions.

Converting a Ratio to a Percentage

• Convert 2:1 to percentage
• English: If you are a 2:1 favorite, that means you expect to win 2 times for every 1 time you lose. That means you are winning 2 out of 3 or 2/3 of the time 2 divided by 3 is .666666666 therefore you haave a 66% chance of winning.
• Math: Add both the "left side" and the "right side" together and divide it by the number of our "wins".
• (wins)/(left side + right side)
• Ex 1. - 2:1 favorite, you expect to win 2 times for every 1 time you lose
• 2/(1+2)
• 2/3 = .666666666 or 66%
• Ex 2. - 3:2 favorite, you expect to win 3 times for every 2 times you lose
• 3/(3+2)
• 3/5 = .6 or 60%
• Ex 3. - 4:1 dog, you expect to win 1 time for every 4 times you lose
• 1/(1+4)
• 1/5 = .2 or 20%

Converting a Percentage to a Ratio

• With a ratio, we put "wins" on the left side and "losses" on the right
• Ex 1. - If we're 75% to win that means out of 100 tries, we win 75 and lose the other 25.
• 75% = 75:25 or 3:1 favorite

• Ex 2. - 33%
• 33:67 or 2:1 dog

• Ex 3. - 83%
• 83:17 or 4.9:1 favorite

Variance

• Mathematical Definition: Variance is a measure of statistical dispersion
• Example of a "High Variance Play"
• You have QJo and Board is AK95r, pot is $110. Opponent bets $10.
• As we'll find out, you are getting the correct odds to call here, however, you will only hit your gutshot straight draw about 1 time in 11. You could miss that draw many, many times in a row before you finally hit and get paid off for all the calls.

Odds to Memorize

• Preflop AI matches:
• Pair over pair (AA vs TT) - 4:1 or 80%
• Pair vs two overcards (88 vs AK) - 1.2:1 or 55%
• Pair vs two undercards (KK vs 98) - 4.9:1 or 83%
• Pair vs higher card/lower card (QQ vs KT) - 2.3:1 or 70%
• Two higher cards vs two lower cards (KQ vs 98) - 1.9:1 or 65%
• High card/low card vs non pair (AT vs KQ) - 1.2:1 or 55%

• Postflop:
• Hand - Outs - Flop - Turn
• Pocket pair (postflop) - 2 - 10.9:1 or 8.4% - 22.3:1 or 4.3%
• Gutshot straight draw - 4 - 5.1:1 or 16.5% - 10.5:1 or 8.7%
• Overcards - 6 - 3.1:1 or 24% - 6.7:1 or 13%
• OESD - 8 - 2.2:1 or 31.5% - 4.7:1 or 17.4%
• FD - 9 - 1.9:1 or 35% - 4.1:1 or 19.6%
• FD + overcard - 12 - 1.2:1 or 45% - 2.8:1 or 26.1%
• FD + OESD - 15 - 1:.95 fav or 51.2% - 2.3:1 or 30.4%
• FD + overs - 15 - 1:.95 fav or 51.2% - 2.3:1 or 30.4%

Rules of 2 and 4

• Rule of 4: on the flop, you can multiply your outs by 4 and that will give you the approximate percentage chance you'll draw to the best hand.
• Rule of 2: on the turn, you can multiply your outs by 2 and that will give you the approximate percentage chance you'll draw to the best hand.
• These rules are very rough estimates and it tends to work better the fewer outs you have.
• Rule of 4, Solomon: (# of outs)(4) - (# of outs - 8) for outs more than 8.
• Ex. 12 outs. 12 x 4 = 48. 12 - 8 = 4. 48 - 4 = 44%

Hand Ranges

• Definition: A hand range is the collection of every 2 card starting hand that you can have based on the actions taken place throughout a hand.

Pot Equity

• Pot equity = (out % chance of winning) x (the pot)
• Equity can only be calculated when we know the opponent's hand or have an idea about his hand range.
• Ex. There is $500 in the pot and we have 25% "equity". $500 x .25 = $125

Expected Value (EV)

• Definition: EV is the determination of what our long term expected outcome is on a given hand in profit or loss.
• EV is also known as "Sklansky Bucks," named after renowned 2+2 poker author David Sklansky
• Ex. 1
• We have AcKc and $1000 effective stacks. Our opponent holds 8s7s on a AhQs2s flop. We bet $175 into a pot of $250 and our opponent shoves for his remaining $875. What is the EV of our call?
• Our equity in the pot or our chance to win this hand is about 63%
• total pot = (250+175+875) = 1300 and it is 700 for us to call
• EV = .63(1300) - .37(700)
• EV = $560