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Professor Plotkin ep 1

This chart is a great way for us to visually spot where we can open up our 3-betting range or open up or defending range to avoid being exploited. Before we go into breaking down the numbers, I need to explain how this chart works.

The Open % is an assigned range a player will raise from the varying positions around the table. As you can see, the range gets looser as we approach the BTN and Ls BTN stands for Loose BTN. Combos is the combination of hands a player will have given the Open %. The 4 categories after Combos is a players 3-bet defend range. The bottom chart is a breakdown of the hands that correspond to a players defending range. The output in the 4 categories is how often a player is defending given their position/open % and 3-bet defend range. So for example, if a player opens UTG with 16% of his hands and is super tight versus 3-bets, he will be defending versus a 3-bet 16% of the time. Mathematically, it would be 2.6/16 = .1625 or 16%.

The chart basically states that the looser a player's open range is and the tighter they defend versus 3-bets the more liberally you can 3-bet them. This is the case up until your opponents or you start defending with a Loose range. We should always be looking out for players who defend too tightly because they are basically free money to 3-bets, but not the case versus a Loose defender because we are going to have to play pots post-flop and lose the benefit of scoring an immediate profit. Conversely the chart tells us that if we are opening wide, we must widen our defending range otherwise we will become exploitable.

Couple of things the chart has emphasized for me is:

• Take advantage of the nits who fold to 3-bets too much
• Be aware of my steal range and whether it is exploitable by another solid player
• Adjust versus opponent's 3-bet by either opening up my defend range or lowering my steal range which proportionately increases my defend range because I will have more strong hands with respect to my overall range.
• Depolarize my 3-bet range versus players who do not fold by significantly increasing my 3-bet value hands.
• Attempt to 3-bet more because it can be very profitable if done correctly, especially IP.

Mathematics of NLHE Ep 4

Covered in this episode:

• EV calculations
• EV calculations
• and more EV calculations

Expected Value (EV) is the long term expected outcome of a given hand or situation, either positive (+EV), negative (-EV), or neutral (0EV).

EV Calculations 101

Basic EV calculation setup:

• EV = [result of win] - [result of loss]
• To expand a bit:
• EV = [Our Equity] * [what we win] - [Villain's Equity] * [what we lose]

• Basic Example:
• We're in the big blind w/ AsAc. The UTG player shoves w/ KhKd and folds to you. It's $990 to call to win $1015 (stack + blinds) 5/10nl, $1000 stacks.
• EV = (.81 * 1015) - (.19*990)
• EV = 822.15 - 188.1 = +$634.05

• Alternative Method:
• EV = [our equity] * [total pot] - cost of our call
• EV = (.81 * 2005) - 990 = +$634.05

Example 1 - 89o on 7T24 vs AA. We need to call 650 to win 700, what is our EV for calling?

• EV = .18 * [650+700] - .82 * 650
• EV = 243 - 533 = -$290

Example 2 - Vil opens from the to Co to 35, we 3bet him again OTB to 125, Vil thinks for about 2 seconds and calls.

• First let's put him on a range: Mostly, pairs, AQ (he would 4bet AK a lot), occasionally a suited connector or AXs type hands.
• On the flop Kc 9c 8d, Vil checks, we bet $200 into $265, he checkraises all in for $875 meaning it costs us another $675 to call. Do we call or fold?
• Let's evaluate his range now that we have more information: He always has 8 outs+ if drawing (OESD, FD or better), and let's assume he 4bets AK 100%, but he could call AA/KK planning to trap.
• Based on our preflop and flop range, we now get a narrowed down range of: KK+,99,88,AQcc,AJcc,ATcc,A8cc,QJcc,QTcc,JTcc,98s,87cc,JTs,67s. Against this range, how is our hand doing?
• Against the range above, our hand has about 35% equity

• EV(call) = .35 *(875+200+265) - .65 * 675
• EV(call) = 469 - 438.75 = +$30.25

WoT's TUPAC method

• Following these 4 steps will help guide you to mentally calculate your equity against a hand range while at the table:
1. Tally Up the hand combinations
2. Pair combos to known equities
3. Analyze unpaired combos
4. Combine the analysis to estimate

Cont. on Example 2 using TUPAC method

1. Tally Up the hand combinations
• Let's break apart his range into the 3 main categories of hands: Those that crush us, those we're flipping with, and those we're decent favorite over.
• Crush us: AA, KK, 99, 88, 98s (5 hands, 13 combos)
• Flipping with us: AQcc, AJcc, ATcc, A8cc, QJcc, QTcc, JTcc, 87cc, 67cc (9 hands, 9 combos)
• Decent favorites against: 67s, JTs (2 hands, 6 combos)

2. Pair combos to known equities
• Start matching up hands that crush us and the flips, those should even out between 25 to 35% equity depending on how badly we're crushed. A set has us drawing much thinner than overpairs.
• There are 13 combos of hands that crush us and 9 combos of hands that flip. If we match those, we will have 9 pairs with about 25-30% equity (not quite because of the sets) and 4 left over unpaired combos that crush us. We can guesstimate that we have about 30% equity before the 4 unpaired combos and after adding in the left over combos, our equity is going go down and be between 25 to 30%

3. Analyze unpaired combos
• There are 5 combos of OESDs and against those hands, we are a 2:1 favorite or 66%
• Thinking a little deeper though, we have a Q and that removes one out from the JTs hands which moves us closer to a 3:1 favorite.
• Our JTs can average out with the left over combos of 98s from the "crush us" category which will boost our between 25 to 30% lets say 27% a percent or 2 to about 28% or so.
• That leaves us with the 3 unaccounted combos of 76s where we are about a 2:1 favorite. 76s makes up about: 3/(13+9+5) or 10.7% and we have 66% equity so .66*.107 = 7%.

4. Combine the analysis to estimate:
• Our base is about 27% after pairing the combos of crush and flips
• Pairing JTs and 98s bumps our equity up a little
• Our decent favorites add about 7%
• The total is 27+1+7 = 35%
• This is very close to the 34% equity that pokerstove gives us. This method is by no means 100% accurate and at times, it will be incorrect but this is a good way to start calculating equities and as you get better with pokerstove and estimating equities, this will all become easier and second nature to you.
• Finally when our decision at the table is so close, where our estimated equity calculation is close but not 100% in line with our mathematical requirements, it is best to rely on the gut reads/intuition to tip the scales on whether to call or fold, depending on how frustrated we perceive our opponent to be.

Alternate Method

1. Tally up combinations
• Crush us: 13 combos w/ about 13% equity
• Flipping: 9 combos w/ about 50% equity
• Decent favorites: 6 combos w/ about 66% equity

2. Multiply range by equity
• (13/28) * .13 = .06
• (9/28) * .5 = .161
• (6/28) * .66 = .141
• You can fudge these numbers to make it easier
• Ex. (13/28) is close to 50% so .5 * .13 = .075. (9/28) is close to 30% so .3 * .5 = .15. (6/28) is close to 20% so .2 * .66 = .132

3. Add up the equities
• .06+.161+.141 = 36%
• Fudge: .075+.15+.132 = 36%

Table Estimations Thought Process

• WoT's thought process at the table when using his TUPAC method:
• As soon as I get checked raised all in, I think: ok, I doubt he ever does this as a pure bluff and right there I am talking about his hand range. I figure him to do this with big draws, sets, pocket aces, and the two OESD, 67s and JTs. He never has AK here because he will 4bet it 100% preflop. There are about 10 or so big draws he can have depending on how many Axcc combos and suited club broadways he is calling with preflop to a 3bet. I know I have been hammering on him so I know he may call with a lot of those combinations. So the more he is calling with those combinations the more draw combos there will be. As for sets, it's hard for him to have KK because I have one and the board has one. He could have AA and the smaller sets. He has aces and smaller sets about as often as he has big draws so if that's true, my equity against that part of his range is between 25-30%. he could have the 98s for two pair and the OESD as well. I am doing bad against the two pair but I am ahead of his OESD so that sort of balances out and gives me some equity. I am actually a 3:1 favorite against JTs since I have one of the Qs removing an out for him, giving me more equity. Over all I'd estimate that I am about 30-35% or about a 2:1 dog. I am getting about 2:1 on my money which makes it close. This leaves it down to reading my opponent. The more frustrated he is, the more apt I am to call. The less frustrated he is, the more I will fold.

Mathematics of NLHE Ep 3

Covered in this episode:

• Revisiting Pot Odds
• Implied Odds and Reverse Implied odds math
• Tools to help us determine Pot Equity
• Mental shortcuts

Pot Odds let us determine whether or not we can profitably continue in the hand based on the amount of money we stand to win vs the amount of money we must risk. So basically a risk to reward ratio, risk:reward.

Reverse Implied Odds is the term used to describe the amount you may lose by hitting your hand and still not having it be the best (and subsequently losing more money).

• Ex. UTG opens to 35 and you call w/ 98s OTB at 1000nl. Flop comes 7T4r and our assumption is that the villain is TAG and if he has a good hand, we are going to stack him. UTG cbets 60 into 80 and we call due to implied odds. Turn is 4x and UTG fires 140 into 200. Do we have the odds to call if he is stacking w/ a range of only TT-AA?
• If our plan is to get all in when we hit our straight against this player. There are 6 ways to make AA-JJ (24 combos) and only 3 ways to make TT which makes 27 combos, 3/27 giving him a set of tens or 11%.
• JJ being 6/27 or 22% of his range, now we only have 6 cards to improve to a straight... which means we need 6.7:1 to call however we only have 4 clean outs as the 2 jacks give him a boat. We'll hit those 2 outs about 4.5% of the time.
• (TT) 11% of the time we'll be drawing dead and "improve our hand 18.2% of the time
• (JJ) 22% of the time he'll make 2 of our outs dirty and we'll hit one of those 4.5% of the time
• (QQ-AA) 66% of the time we'll hit our draw 18.2% of the time and win the pot, 81.8% of the time we'll lose our $140
• EV(TT) = 11%[18.2%(-140+(-765)) + 81.8%(-140)] = -$30.73
• EV(JJ) = 22%[8.75%(140+200+765) + 4.5%(-140+(-765)) + 86.75%(-140)] = -$14.41
• EV(QQ-AA) = 66%[18.2%(140+200+765) + 81.7%(-140)] = +$57.15
• EV(TT-AA) = $12.01. This is barely positive considering this tight range, if we add 77 and 44 into UTG's range, this will become -EV and even more so if we take out QQ or JJ since he will not always stack with those.
• EV(TT), (-140+(-765)) is what we lose if we hit our hand
• EV(JJ), 8.75% is how often we will hit our 4 clean straight outs. 4.5% is how often we will hit our dirty straight outs and lose our call + stack. 86.75% is how often we miss

Multiway Pots

• Multiway pots can affect pot odds and implied odds decisions in a few ways
• When making a pot odds decision in a multiway pot, our position will matter greatly whether or not we can continue in a hand even if we're getting good immediate odds and implied odds

More on Implied Odds

• Don't fall into the trap of overestimating implied odds
• Implied odds vs a good LAG player is often bad and implied odds vs a TAG is often good but what about vs a 40/10 calling station? Our implied odds stands to be pretty good vs a station, especially one that plays 40/10. He has a tight preflop raising range and often is not willing to give up w/ weak one pair hands or draws.
• If your implied odds is not good but you have a hand that you want to play, it is better to 3bet the hand and take control.
• Board texture can greatly affect implied odds and thats why straight draws play better than flush draws and 1 gappers have a lot of implied odds

Mental Shortcuts

• Fudge the numbers so that it is easier to calculate it in your head
• Ex. 1 - We have 30% equity. Vil bets 265 into 490. Call or Fold?
• 30% equity is close to 33% equity which we know is 2:1 so we need slightly better than 2:1
• pot odds = 265+490:265. This can be fudged so we can do it quicker. 265 is close to 250 and 490 is close to 500 so we are getting 250+500:250 odds which is 3:1. much easier

• Ex. 2 - We have 20% equity. pot is 725 and Vil bets 365. do we have pot odds?
• 725 is close to 700 and 365 can be round down to 300. 300+700 = 100 and 25+65 = 90 or roughly 100. So we know our odds are 1100:365. We need 20% or 4:1. 4x300 = 1200 and we only have 1100. So no.

Mathematics of NLHE Ep 2

Covered in this episode:

• Pot Odds
• Implied odds
• Fold Equity
• Hand Combinations
• G-Bucks

Pot Odds

• Definition: Ratio between the value of the pot and the value that must be called to continue.
• Ex. The pot has $40 in the middle and there is a $10 bet. It's your turn to act, what are your pot odds?
• $40 +$10 = pot = $50
• To continue with the hand we would have to call the $10 bet to win $50 so the ratio is 50:10 or 5:1 which also means we have to win the hand 1 in 6 times in order to call

• To correctly continue in a hand, in terms of Pot Odds, your price to continue in the hand must be better than the odds against you making your hand (or having the best hand).
• Ex. If you are a 2:1 dog, as you know that means you'll lose twice foe each time you win. To continue you'd need at least 2:1 on your money to break even. Any better than that and you'll make money over the long haul. Any worse, you'll lose.

• If we know our odds of winning the hand, we can determine what odds we need to call a bet profitably
• Ex. 1 - Let's say you have 6h8h and the board is 9723r and you're playing against a tight player who bets $40 into a $50 pot on the turn. You suspect, at worst, this player has a pair of nines and the only way you can win is to hit one of your straight outs. Do you have pot odds to call?
• OESD has 8 outs to improve
• We are roughly a 5:1 dog (4.7:1 exactly) to improve on the river
• He bet $40 into $50 pot so total = $90 and it costs us $40 to win it
• We are risking 40 to win 90, getting 90:40 or 2.25:1 odds on our call
• We need 4.7:1 to make the call, we can't profitably continue in this hand based on pot odds alone.
• Ex. 1 continued - Let's say we've got the same 6h8h again and the same 972r board but this time we're on the flop and we're playing against a loose passive player who goes too far with his hands and calls to much but generally won't put money in postflop without top pair or better. The pot is $100 and we've got %950 behind in our stack. He makes a pot bet, $100 into $100 pot. Based on our pot odds, call or fold?
• We've got 8 outs to the straight, that means we need 2.2:1 on a call based on pot odds alone. We're getting 200:100 or 2:1 on a call so we fold right?
• WRONG! Our flop odds assume we get to see both the turn and the river but often in NLHE that's not the case. Therefore it is better to calculate based on the odds you'll hit on the next street.
• So do we still fold because we need 4.7:1 and we are getting 2:1?
• No. Why?
• We have a read that this player calls much too liberally postflop and that he rarely puts money in the pot without at least top pair. He's willing to pay us off whenever he has a decent pair and he usually has a hand when he bets so he'll have something to pay us off with often. Another piece of good news is that the stacks are deep. We have $950 left to play with and we have reason to believe he will put a lot of $ in with marginal holdings.

Implied Odds

• Ratio of the total amount of money to be won from the pot + from stacks behind to value of the current bet
• Ex. 1 continued - What are our implied odds?
• We are calling $100 bet to win the 4200 in the pot plus potetinally the $950 left to play with.
• We could be looking at as much as 950+200 = 1150:100 or 11.5:1. Since we need roughly 5:1, we are getting over double what is required.

Fold Equity

• FE is essentially the estimated % chance that a bet or raise will induce our opponent to fold.
• FE is often used in estimating how successful semi-bluffing (bluffing with outs to improve) is in a specific situation, but it applies to pure bluffs as well.
• FE is measured by which hands in our opponent's hand range he/she will fold to a bet or a raise.
• Ex. We have AsTs and the flop is 8s9s7h with $100 in the pot. The stacks are $950. Opponent bets $100 into $100. Call, fold or raise?
• In this hand if our opponent has something like K9, we could have a ton of outs: 9 spades, 3 Jacks, and 3 sixes (remember not to double count the Js and 6s), 3 tens and 3 aces = 21 outs.
• With our big draw, we are actually a 68% favorite over top pair so folding is obviously out of the question. Raise or call?
• We are getting 2:1 on a call si if we were guaranteed to see both cards, we'd only need 33% equity. We have 68% equity with 2 cards to come, but even with only 1 card to come we have over 45% equity so calling would be ok.
• Raising is the best option as we have a lot of FE and Pot Equity. We don't have much if any implied odds as the board is so coordinated nor do we have a made hand.

• Some hands and situations get a big part of their profitability from the use of FE
• Ex. 5/10 NL $1000 stacks. You have an aggressive image and the other players at the table are similarly aggressive. You open AKs from the CO to $35, the BTN calls and the SB who you've seen play small pairs very aggressively makes it $160 to go. Folds to you and you have a decision to make.
• In this spot based on our read, we know the SB can be 3betting (or making a "squeeze play" as its known) with hands such as 22+, AQ+. That's the range we give him and we're a slight underdog to that range. So do we fold? Call and hope to hit taking our pot odds?
• No, the best play is to 4bet him. The reason is FE. Our AK doesn't mind getting all in preflop against most of his range, but we'll force him to incorrectly fold hands that hes a slight favorite in.

Hand Combinations

• Hand combinations refers to the number of ways a particular 2 card hand can be made given the known and unknown cards in the deck.
• Knowing the number of combos possible for a given hand can help us determine the likelihood of that hand in a given range of possible holdings.
• Ex. You hold AsAc and the board is Kc5d9h and your "gut" says our opponent either has a set or AK. How many hand combos are there of AK?
• You hold AsAc so he cannot have those in his hand. The Kc is out on the flop so he cannot have that either. The possible cards left to make AK are: Ah, Ad, Kh, Kd, Ks. How many ways can we make AK from these cards?
• There are 6 combos of AK. 2 Aces x 3 Kings = 6 combos
• AhKh
• AhKd
• AhKs
• AdKd
• AdKs
• AdKh
• How many combos of sets? Let's start with a set of fives.
• 5d is on the board so we need to make a 2 card hand out of: 5h, 5c, 5s
• There are 3 combos of a set of fives.
• 5h5c
• 5c5s
• 5h5s
• Same for set of 9s
• So if his range is really {AK, sets} then how likely is it that he has a set?
• 6 combos of AK. 3+3+3 = 9 combos of sets. so of 15 combos, 9 are sets. 9/15 = 60% chance that he has a set if our hand range is correct.

• Hand Combos to Memorize:
• Any exact two card hand: ex AsKs - 1 combo
• Specific suited starting hand: ex 98s - 4 suits = 4 combos
• Unpaired hand with no other info: ex AK preflop - 4 aces * 4 kings = 16 combos
• Pocket pair with no other info: ex QQ preflop - 4 suits, 2 cards = 6 combos
• Pair + Kicker with no other info: ex AK on K95 - 4 aces * 3 kings = 12 combos (note: you do not know villain has AK, you only think he has a pair and kicker)
• Two pair hand with no other info: ex AK on AK5 - 3 aces * 3 kings = 9 combos (note: same as above except you think he has two pair)
• Set with no other info: ex 55 on K95 - 3 suits, 2 cards = 3 combos
• When thinking about it at the table, realize you can use straight multiplication only when you're dealing with two separate cards such as aces matched with kings.

G-Bucks

• The term "G-Bucks" coined after Phil Galfond is the next level of complexity in EV calculations
• G-Bucks calculations determine your expected value based not on our actual holding against your opponents holding, but instead your range of hands against his actual holding.
• Over the long haul in a given situation, we're not playing the exact hand we have, we're playing a range of hands that our opponent has to react to. Therefore we see how his actual hand stacks up against our range.
• We can determine our range based on:
• the betting sequence
• board texture
• our overall read on how our opponent plays
• and often what we believe his read is on us

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