1. Penn Poker Fall Strategy Session Series
Equity and Odds:
Using mathematical 'rules of thumb' to improve your decisions
(adapted from Professional No-Limit Holdem)
by Mike Naughton,
VP of Strategy and Education

2. (First, Penn Poker in 60 seconds)
Fall Strategy Session Series, Tournaments, Other Events
Homegames listserv
The Global Poker Strategic Thinking Society (GPSTS)
Poker is an awesome game, as well as powerfully instructional
Keep in touch: Facebook group, gpsts.org/upenn
Leadership and joining the Board

3. (Also, Some Congratulations)
Current Members:
Tony Zheng – Annual Pottruck Poker Tournament
Josh Eisenberg – won entry to Main Event of the European Poker Tour in London
Penn Poker Alums:
Matt Larriva – Trader, TransMarket Group
Joe Udine – FTOPS 1K - $360,000 prize

4. Goals for this session
Realize that poker is a game of incomplete information - we win when we make better use of that limited information than our opponents do
Learn how to make better decisions than our opponents based on our estimation skills
Learn how to use mathematical processes and “rules of thumb” to make those better decisions and take our opponents’ money
Hi guys I am Mike Naughton and as Daniel said the focus of this strategy session is on equity, odds, and the mathematical background behind poker decisions

5. Intro: Hand Example
Three players limp and we call with the 8h 6h on the button. The blinds call - six players see the flop.
The flop is Qs 7c 5d.
We have an open-ended straight draw (any nine or any four gives us the “nuts”).
The big blind bets, one player calls, all else fold, and the action is on us.
What do we do and why?
We are going to start off more broad before we jump right into odds and equity and get ourselves thinking about poker as this is our first strategy session.
The nuts is the best possible holding on any given board.

6. Hand Example Answer: It depends! It depends on:
Odds and Outs (your probability of winning)
Expected Value
Stack sizes
Bet size
Pot size
Position
Opponents’ Tendencies
Opponents’ ENTIRE range of hands
This session’s focus: ODDS and OUTS
Hopefully by the end of this strategy session series we will be able to hit on a lot of these topics, but today we will focus on one of the most important topics - pot odds

7. Three step process
STEP 1: Calculate pot odds (our “risk-reward measure,” or the “price” the pot is laying us)
STEP 2: Estimate our winning chances (our “equity share in the pot”)
STEP 3: Compare our pot odds to our winning chances
If our winning chances are greater than the pot odds risk-reward measure, we call
If our winning chances are less than the pot odds risk-reward measure, we fold 7

8. Pot Odds
“Pot odds”: A measure that compares what is currently in the pot to what you have left to call
a measure of risk (price of a call) versus reward (what is in the pot)
The price the pot is laying us
(Simplistic) Example: You have a $200 stack in a $1-$2 game. An early position player raises to $10. Two players call, and you just call on the button with pocket jacks. The small blind calls the big blind then reraises all in for a total of $30 (raises $20 more). Everyone folds (unrealistic), and the action is on you.
How do we calculate our pot odds?
Calculating our pot odds is actually the easy part of the calculation - calculating pot odds is the first thing we want to do in almost any poker decision

9. Pot Odds Contd.
First, count up how much is currently in the pot (the reward)
$80
Then, determine how much it costs you to call (the risk)
$20
Since you are risking $20 to win $80, your pot odds are $80-to-$20, or 4-to-1
If you believe your chance of winning the pot is better than 4-to-1 (or 20%), it will be profitable to call (our call will constitute a 20% share of the final pot)
Put this in perspective - if he has ONLY pocket Aces, you will win the pot about 19% of the time. But he probably has many more hands, such as hands like Ace-King.
4-1 means that we should make this call if we believe we will win the hand more than 20% of the time. Intuitively, let’s think this out.
If our hand holds up to win, we will win the $80 plus the $20 we will have to put in to make the call. Therefore, our $20 will make up a 20% share of the final pot of $100. If we expect to win the hand more often than 20% of the time, this is a profitable call
How to convert from pot odds to percentages like this - add one to the right hand side of the ratio, and divide one by that number. For instance, for 9-1 odds, your winning chances need to be 1/(1+9) or 1/10 or ten percent 9

10. Outs How many outs do we have?
Pot Odds are only helpful if you can make good estimates of your winning chances - for this we count our “outs”
An “out” is a card that will improve our hand to the likely winner
Back to our original example: You have 8h 6h and the flop is
Qs 7c 5d. We estimate that either the bettor or the caller has at least a pair of queens.
How many outs do we have?
You can calculate pot odds at any point in the hand - just divide the pot by the cost of a call and you get a ratio. The harder pot is estimating our winning percentages in the hand, and we do this by counting our outs. 10

11. Counting Outs
With an Open-Ended straight draw, 8 cards will complete our straight and give us the nuts (the 4 nines and the 4 fours.)
Other common outs situations (commit these to memory):
Flush draw (Ah 4h on a 9h 6h 3s board): 9 outs (at least)
Gutshot straight draw (Kd Ts on a Qh 9d 3c board): 4 outs (at least)
Overcards (Ad Kc on a 9h 6h 3s board): as many as six outs
Combination (combo) draws:
Flush draw and gutshot (Kh Th on a Qs 9h 3h board): 12 outs (9 hearts, including the Jh, and the 3 other jacks)
Flush draw and open-ended straight draw (Kc Qc on a Jc Ts 2c) 15 outs (9 clubs, including the Ac and 9c and the 3 other aces and 3 other nines)
The definition of an open-ended straight draw is that we have four cards in order, so there are four cards that will give us the higher straight and four cards give us the lower straight
With combo draws, be careful about overlapping and double-counting 11

12. Discounted Outs
Example: You have Ah 4h on a 9h 6h 3s board. You have one opponent and you think has something good - either a set or a hand like pocket jacks (an overpair). You estimate he is just as likely to have pocket jacks as he is to have a set. How many outs do we have?
Any of the 9 hearts will give you the nuts. While the three remaining aces are outs for you if he holds pocket jacks, they are not outs if he has a set. So you need to “discount” these three outs and say they are “worth” 1.5 outs, so you have a “total” of 10.5 outs (9 hearts plus 1.5 aces)
Similar example: you have Kh Jh on a Th 2h 2d board. Why can’t we say we have nine “full” outs? 12

13. Converting outs to our winning probability
We have a flush draw with 6h 5h on the Kh 9h 2c board. What is the chance that the next card will complete our flush?
Count your outs - there are 9 hearts left (13 total hearts - 4 seen hearts = 9 hearts).
Count how many total cards are left in the deck. We have seen a total of 5 cards - the 2 in our hand and the 3 on the flop. That leaves 47 cards left unseen ( = 47).
The chance that we will hit our flush on the turn is 9/47 or 19% (about 4-to-1) 13

14. Conversions using Rules of Thumb
The “Four Times Rule”: It states that on the flop your probability of winning with two cards to come is approximately the number of outs times four.
With a flush draw, 9 outs x 4 = 36% (close - exact chance is about 34% or 1.9-to-1)
The “Two Times Rule”: This will give you the chance of winning on the next card only.
With a flush draw, 9 outs x 2 = 18% (close - exact chance is about 19% or 4.3-to-1)
This is difficult to do in the heat of battle at the poker table, so we give ourselves a rule of thumb to make life easier for us. 14

15. Three-step process in action
Say there is $90 in the pot. You have a flush draw with the 6h 5h on the Kh 9h 2c board. Your opponent goes all in for $30. Should you call?
First, calculate our pot odds. The pot now contains $120, and it costs us $30 to call, so the pot odds are 4-to-1 (so we should call if we will expect to win more than 20% of the time)
Next, calculate our (expected) chances of winning. By the Times Four Rule, we multiply our 9 heart outs by 4 and see that we have about a 36% chance of winning, or better than 2-to-1 (if we discount outs, will be less then this)
Our chances of winning are better than our pot odds price, so we call.
Should we call if our opponent goes all in for $150?
(end) You see people mess up these decisions and make huge mathematical errors all the time - hopefully we won’t make that mistake

16. “Implied” Odds
For pot odds calculations, the “reward” must be certain (the size of the pot)
Rarely in deep-stacked cash games do we encounter odds situations where the reward is certain because there is still money left in the stacks
Implied Odds: an estimate of what you are likely to win by the end of the hand versus what you risk now.
Example: You have a gutshot to the nuts with the 6s 5s on the Qh 4d 2c board (the 4 treys would give you the nut straight). Your opponent bets $10 into the $20 pot, so your pot odds are 3-to-1. You both have $200 left behind. Should you call?
Reward is certain when we are last to act and there are no more betting decisions 16

17. “Implied” Odds contd.
You can’t call based on based on expressed implied odds alone - the Four Times Rule says will hit our straight by the river about 16% of the time (4 outs x 4 = 16%, or close to 6-to-1). Our chances of winning are less than the pot odds price.
However, we will almost certainly win more than the $30 in the pot if we hit our straight. If our opponent has a good hand like a set, he will probably lose his whole stack to us.
If we estimate that we can win $60 MORE (on average) on the turn and river if we hit our straight (because we think he has a good hand), then our implied odds are $90-to-$10, or 9-to-1, whereas our pot odds were only 3-to to-1 pot odds (need to win 10% of time) is a better risk-to-reward ratio than our 6-to-1 (16% chance that we hit our straight), so we could argue calling is correct here 17

18. Again: This depends!
This last analysis depended on a lot of different (possibly-wrong) assumptions:
Our estimation of our opponent’s range. Based on his tendencies we guessed he had a strong hand here that he would lose a lot of money with (he might not have this).
Our estimation of our opponent’s tendencies. We estimate that our opponent would lose a lot of chips to us with a strong overpair like KK or AA. If we estimate that our opponent is in fact a good hand reader, we wouldn’t expect to win as much if we hit, for he would be able to get away from his hand cheaply realizing he is beat. 18

19. Takeaways from this session
We win money at poker by making better estimations and better decisions than our opponents make
For every decision-point in poker,
Calculate your pot odds (and/or implied odds)
Use discounted outs to make sure you aren’t overestimating your chances of winning
Using discounted odds, estimate your winning chances
Compare your pot odds to your winning chances and make your decision 19

20. Thank you.
Penn Poker