Two Keys To Poker
1. Accurate Assumptions
2. Making The Best Decision
1. Accurate Assumptions
Two points, one concerning villains RANGE, other being HOW he will play that range
We improve this mostly by playing i.e. through experience
2. Making The Best Decision
What makes us the most money? We use maths after Key 1 to find this.
We improve this mostly through work away from the table.
For a beginner a large part of our work must be away from the tables DOING MATHS!!
(Owen proves this on page 5)
Measurements
1. Your Surroundings
BB, Stack size, Bankroll, Win rate.
Beginners need a budget - learn the game, don't worry about the money and WR etc!
2. Thinking About Bets
Good players do not think about $ they think about bets in terms of potsize
Minraise is opponents bet x 2 and you can only go smaller if you are short
Pot raise is the amount to call x 2 + the pot size including opponents bet.
e.g. villain bets $50 into $100 - it is $50x2 + $150 = $250.
Or pot raise is the size to call + the size of the pot after we call
e.g villain bets $50 into $100 - it is $5o (the call) + $200 (the pot after our call) = $250
3. Your Expectations
Think in terms of hourly rates & realise micros is the learning place not the earning place!
Results can be very deceptive
Rake can be 10bb/100 at micros
Your thought process is the true way to measure your skills and progress
This will in turn improve your financial results over the long term
Getting Started With Numbers
Fractions, Percentages, Ratios.
5:1 = 1/6 = 16.7%
Expectation Value
The average amount of money you expect to win/lose on any wager
1. Identify each possible outcome and the probability of it happening
2. Multiply the probability of each outcome by the result it has.
3. Add results together from step 2.
e.g coin flip tails we win $15 theads we lose $10
1. Each outcome is 50% or 1/2 or 1:1
2a. Heads is 0.5 x -$10 = -$5
2b. Tails is 0.5 x +$15 = +$7.50
3. (-$5) + $7.5 = +$2.50
Notice we never win $2.50 in one go but this is the average or EV
Hit The Deck
Counting outs
Standard outs = any outs that give you the best hand
Backdoor outs = on flop only as require a combination of outs on turn and riv eg BDFD
3 BDSD = 5% better, 2BDSD = 35, 1BDSD = 2%, BDFD = 4% (so avg is 4%)
BDFD + 3 BDSD can give 8% extra
If seeing both turn and riv (all in otf) then you can add 1 out each for BDFD or BDSD
Hidden outs = we have AQ vil has 33 on TT85 - an 8 or a 5 are hidden outs!
we have 12 outs in this hand ^ 3x8s, 3x5s, 3xA's, 3xQ's
Chopping outs = A2vA7 on AQ63 - 3x2's(clean), 3x6's (hidden), 3x3's (hidden)
The 4/2 Rule
We use our outs to estimate our equity using this rule
On the flop we multiply our outs by 4 and this assumes we get to see turn and river
On the turn we multiply our outs by 2
Remember to add in one out per backdoor draw if we are on the flop and seeing turn and river
Putting It Together
Pot Odds
Villain bets $10 into $10 we need to call $10 to win $20, so its 20:10 or 2:1
We convert this to a fraction which is 1/3 (See above)
We convert this to a percentage which is 33.3% and this is what we need to break even
Implied Odds
This is looking at your risk:reward ration in the light of future betting
Hero has 67, villain has AK, board on turn is AK54
Villain bets $5 into $10 = 3:1 = 1/4 = 25%
We have 8 outs to the nuts = 16% equity
Looking ONLY at this we should fold BUT….
If we know he has money behind on the river we can call
Sometimes it is good to have a disguised draw so SD > FD
The stronger the villains hand the greater our implied odds & vice versa
We need to add the amount we think we will win to our odds when we make the call
(e.g we have 20% i.e 1/5 then it is 4; we have 25% or 1/4 it is 3)
So, villain bets 20$ on turn and we have 15% we need to win 6x$20=$120
BUT we must subtract from that what is already in the pot when we call.
E.g pot is $20, villain bets $10, we have 20% equity
We need to multiply by 4x, his bet is $10 so we need $40
There is already $30 in the pot so we need to make $10 more TO BREAK EVEN
If we call then the pot is $40 on the river so we only need to win a 1/4 pot size bet
World Of The Unknown
Combinations
A pair has 6 combinations (take the no of cards 4 and then add together the numbers below that down to 0, so 3+2+1=6
If there is an Ace on board there are 3 combos of AA he can have (2+1=3)
Unpaired e.g AK is just the number of each multiplied so in this case 4x4=16
If there is an Ace on board vill can only have 3x4=12 combos of AK
So, QQ+, AQ+ has…..
6 combos of QQ, 6 of KK, 6 of AA, 16 AQ, 16 AK = Total 50 combos
And how often does he have a pair?
18 times of 50. So 18/52 = 0.36 so 36% of the time
E.g we have KcQs, villain AQ+, TT.
Board QdTh2s6c2d. Villain bets pot on the river. We are getting 2:1 so we need 33% to break even.
We beat AK but we lose to AQ and TT.
AK = 3x4 = 12 combos
AQ = 2x4 = 8 combos and TT = 3 combos, therefore 11 combos we lose to.
So we win 12 times of 23, or 12/23 which is 0.52 = 52% = EASY CALL.
Equity Versus A Range
We have AA on J65r and bet flop $25 into $25 and villain shoves all in for $100 so do we call the $75?
We are getting 2:1 or 1/3 or 0.33 = 33% pot odds (so we need this equity to break even)
Villains range is 55, 66, 78 (yh, it is narrow but good to start with!)
Let's work out our equity versus his RANGE.
1. Determine equity against each hand
2. Multiply that equity by the combos for that hand
3. Add together the results from 2
4. Divide the total from 3 by the total number of combos in the range
So, versus 78 we have 68% ( he has 8 outs x 4 = 32%), v 55 we have 8% and 66 we have 8%
Then, 78: 16 combos x 0.68 = 10.88, 55: 3 x 0.08 = 0.24, 66: 3 x 0.08 =0.24
Then, 10.88 + 0.24 + 0.24 = 11.36
Then 11.36 / (16 + 3 + 3) = 0.516 = 52% = EASY CALL!!!!
To make this a little easier we can think about his range and realise he has a set ~ 1/4 of the time (6/22)
So 1/4 of time we have 8% and 3/4 of time we have 68%
0.25*8 + 0.75*68 = 0.53 or 53% (remember we said ~ 1/4 time he has set so it is not accurate but close)
Another example?
We have AsKs and raise to $3, tight SB shoves to $18 (forget the BB as rake will have it!!) so pot is $21
Pot odds = 15/(21+15) = 41.67%
Tight range = JJ+, AK.
Use Stove to see versus his 9 combos of AK we have 51.6% so 9 * 0.52 = 4.68
Versus JJ 46% so 6 x 0.46 = 2.76, QQ: 46% so 6x0.46=2.76, KK: 34% x 3 = 1, AA: 12%x3 = 0.36
Total = 4.68+2.76+2.76+1+0.36 = 11.56
11.56 / 27 (his total combos) = 0.43 = 43% SO BREAK EVEN CALL
Owen uses a method he calls the Mental Slider here where he thinks how we fare versus parts of villains range
So, against ~ 25% of his range we have 20% equity and against 75% we have ~ 50% equity
He then mentally tries to get 3/4 of the way between 20 and 50, that being ~ 40 giving the same BE call
Note, if we add TT to his range it gives 6 combos we have 46% against so our equity climbs a little
Also, if we give him AQ that is 12 combinations we have 75% against so our equity climbs substantially.
Which Bucks?
Real Bucks = how much we actually lost or won (over the whole hand) = useless
Sklansky Bucks = the EV (at bet point) against villains hand (so knowing cards) = slightly useless!
G-bucks = an improvement on Sklanksky where we work out the EV versus his range = excellent
Reciprical Bucks = Tommy Angelo's variant where we compare it to if we switched for villains perspective.
Main point here is that we should not be discouraged when we lose to the top of villains range
We analyse, and if we made an EV+ play in G-bucks, then we can feel good about our play
AGGRESSION
Bluffing
The equation to find out how often our villain must fold when we bluff is the same as the equation for calling
x/(x+y) but now x is the size of our bet (before it was our call), y is pot before we bet
Say pot is $10 and we bluff with a $10 bet
So, 10/(10+10) which is 10/20 = 1/2 = 0.5 = 50%
So, our villain must fold over 50% for us to profit, or to have an EV+ bluff
Let's take a look from villains perspective….
For him to BE on the call he does that similar equation but his numbers are….
x = price to call = $10 and y = pot before he calls = $20
So, 10/(10+20) which is 10/30 = 1/3 = 0.33 = 33%
Think about this! It is a basic risk to reward ratio
And the reason it is better for villain is because the pot is bigger when he makes his decision
So, how much do we need to bet? We have to try to define what we are trying to achieve…
Example, we have As4s. Villain has TT, JT, QJ, KJ, AJ, KQ, AK
Board 2s 5s 9h Jd Kc. The pot is $100 and we have $180 effective left
Assuming we are never good here we want to know how much to bluff, let's go for a pot sized bet…
We know we need villain to fold 50% [100/(100+100) is 1/2 = 0.5 = 50%]
Let's also assume to this size bet he folds TT, JT, QJ, AJ but calls KJ, KQ, AK.
What percentage of his range is he folding?
Well he folds 39 combos and continues with 30 combos so he is folding 39/69 = 0.565 = 56%
So our bluff here is EV+
In general as we decrease or increase our betsizing the calling range changes (assumes elasticity).
In this case we are trying to fold out his Jacks and we need to make assumptions about what size he calls at
Then we can just bet over that size (and just over it)
So if he folds them to a $33 bet (1/3 pot) then we would rather do that.
If he folds at $33 and higher let's check the EV of the different betsizes…..
Bet $100: 0.56x100 - 0.44x100 is $56 - $44 = +$12
Bet $33: 0.56x100 - 0.44x33 is $56 - $14.52 = +$41.48
What if he calls those Jacks to a $33 bet?
He now only folds TT which is 6 combos of 69 so 6/69 = 0.087 = 9% of his range.
A 1/3 pot sized bet needs 25% folds [33/(33+100) = 0.248 = 25%]
So the EV of $33: 0.09x100 - 0.91x33 = -$21.03
In summary, we need to think about our opponent's range and what he will do with different parts of it versus different size bluffs
People say "bet enough to get the job done" but this is too narrow.
We must choose the line which makes the most money
Spend time away from the table getting used to this, its hard work but the great players have done it!
Semi-bluffing
The above notes on bluffing were on the river where we have the worst hand
Semi-bluffing is when we bet a hand which we doubt is good but has chances to improve on later streets
Example time……!
NL 100, we hold AdQd, we isolate EP limper to $4, BB has $40 and calls, limper folds.
Flop is 9d7d3h, pot is $9, BB has $36 behind.
We cbet $9 and BB calls, pot is now $27.
Turn is Kc and BB leads out for $12.
Our pot odds - he bets 12 into 27 so we have to call 12 into 39 so roughly ~ 3:1 (we need about 23% equity)
Let's find our equity… If we assume his range (just for sake of it) to be AK, 88, TT, 89s….
Against 88, TT, 89s we have ~ 15 outs on turn so 30%
Against AK we have 9 outs on turn so 18%
So against 15 combos we have 30% and against 9 combos we have 18%
Find 2/3 up the scale from 18 to 30 so about 26%. (Stove gives 28% so we're ok)
Remember we needed 23% to call so we have immediate odds to call his bet, also versus AK specifically we make more in implied.
So we can call here and be very happy about it (even without those implied odds)
HOWEVER! Let's consider all of our options here!
Folding is EV0 so call > fold, but what about raising!?!?!?
We could minraise or shove and all amounts in between.
Let us look at shoving……
If we assume he will call our shove with AK and TT but will fold 88 and 89s, he calls 15 combos and folds 9, so he folds 37% of the time
Effective stacks behind are $15 (remember he was short and he bet $12 of his $27 on turn)
Pot is $39 before our shove and we risk $27 to win it so we need him to fold 27/(27+39) = 41%
But he only folds 37% so is raising EV-? No, we also have our showdown equity to add to this!!!
This following is the detailed look at how to work out how much fold equity we need…
Fold%(pot won when he folds) + Call%(amount we win/lose when he calls), let x be the percentage he folds
x($39) + (1-x)(0.24($54)+0.76(-27)) > 0
39x + (1-x)($12.96-$20.52) > 0
39x + (1-x)(-$7.56) > 0
39x - 7.56 + $7.56x > 0
49.56x > 7.56
x > 0.1624
He has to fold more than 16.24% of the time for our shove to be EV+ ( we can check this by putting 0.1624 in above for x)
He folds 37% of the time so the shove is definitely EV+
Let's work out the EV of the shove……
0.37($39) + 0.63(0.24($54) + 0.76(-$27)) = EV
$14.43 + 0.63(-$7.56) = EV
Shove EV = $9.67
Now the EV of calling….
0.28($39) + 0.72(-$12) = EV
$10.92 - $8.64 = EV
Call EV = $2.28
So, here we see the power of the semi-bluff. We often win the pot uncontested and when we do win on the river we win a bigger pot
There are three key variables to consider when considering a semi-bluff shove.
1. The size of the pot in relation to the money behind. The larger the SPR the more he must fold (it follows as we are risking proportionally more)
2. How often he folds. Normally the smaller the SPR the less often he will fold and vice versa (this follows from villains risk:reward ratio)
3. Your showdown equity. The more showdown equity we have, the less often he needs to fold.
The Shortcut!!
WE need to look at our risk:reward ratio…
Pot is currently $39. We have to shove $27. Also we have equity so shoving isn't actually risking $27 to win $39. We have to find out what we are actually risking…
1. Total pot size x our equity.
2. Subtract result from our bet
3. Examine risk:reward
So, 1. Total pot will be $81 and our equity v his all in range is 24% so we get $19.44
2. Our shove is $27 so we do $27 - $20 = $7
3. So we are risking $7 to win $39 and we do 7/(7+39) = 0.15
So we have come up with 15% which is very close to our original 16%!!
The way to think this through is that when we shove this $27 we get $20 back in SD equity anyway so we are only risking the $7 portion to win $39 as a bluff, which gives us that he needs to fold 15%
Value Betting
One of the most important skills in poker
The term is reserved for betting when we believe we have the best hand (we actually bluff because we think it has more value than not bluffing!!)
Sometimes we maximise value by getting small, steady pay outs
Sometimes we maximise value by getting the infrequent big pay off
Extreme Example…..
We have AdJd on 2c 5d 8d Ah 7d (so we have Ace high flush)
Villain will call up to $8 - A9, A2, AJ, AQ, KdQd
Villain will call all in to $500 with KdQd
Assume villain has $500 left on river and will never raise just call and we can only bet $8 or $500
Villain has 29 combinations and KdQd is only 1 combo so is 2.5% of his range
For the $8 bet, EV = $8 x 100 = +$8
For the $500 bet, EV = $500 x 0.035 = +$17.50
So, in that EXTREME example the $500 is higher EV even though it rarely gets called.
Let's change $500 behind to $100
For $100 bet, EV = $100 x 0.035 = +$3.50
So now the $8 bet has higher EV
We need to practise a lot of this away from the table to get used to situations
Now let's assume villain will always RAISE all in with KdQd and will call $8 with all of his pairs
For the $500 bet, EV = $500 x 0.035 = +$17.50
For the $8 bet, EV = 0.035($500) + 0.965($8) = +$25.22
Obviously even better!
As a general rule we want villains to be calling with over 50% worse hands than better hands to be EV+
Sometimes we have assumptions that do not allow us to bet….
We have TsTc on 2h 3d 8h Jd Ah, villain is conservative, timid.
Once he called the turn we gave him 89,99, FD as a range.
The Ah on the river removes a lot of the flush draw combos we gave him
We give him only suited connectors and a couple of suited one gappers say 10 flush draw combos
So we have 89(12)+99(6) = 18 combinations we beat and 10 have us beat so we have best hand 64%
THIS DOES NOT MEAN WE SHOULD BET!!
Remember our villain is timid and conservative so he will be scared of the flush
So we bet and he folds all that we beat and calls all that beats us! Say we bet $10 on the river
EV = 0.64($0) + 0.36(-$10) = -$3.60
Let's go another step further……
This is a bit daft but assume he calls with 98, fold 99 and still call flushes
89 is 43% of his range, 99 is 21% and flushes are 36% and we still bet $10
EV = 0.43($10) + 0.21($0) + 0.36(-$10) = +$0.70
We have an EV+ bet because he calls more than 50% worse hands than better hands
What else can we consider???
Well what if he raises us on the river as a bluff?
If this is so then we will need him to CALL with more than 50% of hands we beat to make up for us folding to a raise
Following from this sometimes it might be good to make a small bet to INDUCE a bluff raise from an aggro villain
The same is true for when considering whether to bet or check, if a check induces bets from worse then check!
*** Owen refers to an Appendix here. What we have just dealt with is "Evaluative EV" as opposed to "true EV", we have compared the EV of different bet sizings but this does not necessarily say what we would make in true EV (how much richer we will be after the wager) ***
AT THE TABLE
A Bit Of Memory
There are a few situations that come up often enough to be worthy of committing to memory
The unpaired holdings are all offsuit, you can add roughly 4% on for being suited
Remember, if you think you run into different ranges then find the equity versus those and memorize them
Chunking
We are talking about the exponential growth of the pot on each street.
If you open 3.5x and get one caller and bet pot on each street you never have to overbet to stack off.
Whereas if you bet 3x and get one caller and bet pot on each street you would need to overbet the river
Firstly it is important to look at the effective stacks
If you have over 100bb then we will have some very big river decisions to make
Set Mining
A pocket pair flops a set (or better) roughly 12% of the time
In ratio terms it is roughly 8:1
Let us assume everytime we flop a set we get the villain all-in and we called a $1 bet preflop
Breakeven point is when 0.12($x) + 0.88(-$1) = 0
0.12x-0.88=0
0.12x=0.88
x=0.88/0.12 = $7.33
So in order to BE we need to win $6.33 postflop
So, if villain started with 8x more than we called then we THINK we would be ok
HOWEVER, there are a lot of other factors to consider….
That calculation assumes we have 100% SD equity, but if villain wants to get AI he most likely has equity too
For example, if he has a flush draw then we only have 75% equity, maybe they flopped a straight and WE have 35% equity, maybe the over setted us!
Let's assume we get AI with 33 on Q73 flop and villain has KK, villain has 13% equity, $8 stacks, $7 behind otf
EV = 0.87($7) + 0.13(-$7)
EV = $5.18
This is short of what we needed to win postflop to BE and this is a relatively good situation (versus overpair)
Some players will get it in loose and some will be much tighter.
Let's see how much money we need to win to BE is we have 80% equity
BE = 0.80(x) + 0.20(-x) = $6.33
0.8x-0.2x=6.33
0.6x=6.33
x=6.33/0.6 = $10.55
So with an assumption of 80% we need our opponent to stack off 11 times what he had preflop
And it gets worse, say villain holds KK, well an Ace flops 16% of the time so we lose action. It is worse with QQ when an A or a K can flop.
This cuts down our implied odds
Also, when we have 88 on 763tt do we lose money?
Can we extract so well when we are out of position?
A good tip is to set mine when you know your villains range is strong
Owen ends up recommending villain has 15 times the preflop bet size in his stack to set mine
Table conditions and dynamics etc can allow us to tweak this
How Much To Bet?
It is good to consider this, if we do not bet our villain almost always has some SD equity and we are making a mistake to let him realise it
Letting a villain draw for free and the further possibility of paying him off if he hits is horrible!!
We need to look at our bet sizings given our opponent's range when we are on flop and turn
We are ready to move away from "standard" bet sizings (eg many people just bet flop 0.66 etc )
Thinking about making maximum value from your opponent's range takes precedence over chunking
Example, we open AA and tight passive calls in BB
Flop is A72r, villain checks, SPR is 13
We know we need to bet pot on three streets to stack him
But we believe his range to be mostly pocket pairs which will not be likeyl to stack off (if he hit a set stacks go in anyway later usually)
So we might want to make a small bet on this flop to get some action from a weak range, say 0.25 pot
Another example, we have AA, flop is JT6tt, villain in BB is now loose…
His range preflop is BWBW, any two suited and pocket pairs and postflop he is calling any pair and any draw
Now we have good reason to think about chunking and getting stacks in on the river (at least!)
A big part of betsizing is thinking about what odds we are offering to our opponent
We are taking the the idea of pot odds and flipping it round
We want villain to make a mistake so we want him to call when he does not have the pot odds to do so
Remember, if our opponent cannot call profitably WE WANT HIM TO CALL - too many times people bet to make draws fold which is wrong thinking
Example…..
We have AA, villain has 5d6d, turn is KhQh4s3s, pot is $10 we have $10 behind
Villains SD equity is 16%. If we bet 0.25 pot villain has a BE call (neutral EV) and since he's not losing any money we're not making any
Betting 0.25 pot is better than checking though as if we check we are giving up 16% of the pot
If we bet $5 (0.5 pot) villain needs around 25% equity which he does not have so his call is EV-
Villain's EV = 0.16($15) + 0.84(-$5) = -$1.80
So on average he loses $1.80 if he calls (assume zero implied odds if he hits!)
Now, if he calls we own 84% of a $20 pot = $16.80
If he folds we get the $10 pot plus our $5 back = $15.00
So we make more money when he calls - WE ARE NOT TRYING TO BLOW HIM OFF THE POT
Obviously in this example if he will call off the whole $10 we should bet that, when he cannot call profitably we want to bet as much as he will call
Remember that villain's will think they have implied odds too so we can bet a bit bigger sometimes
Also we must keep the make up of a villains range in mind when we bet.
For example if his range has more combinations of pairs that we beat than combo draws then we might need to let him make an EV+ call with the draw part of the range but an EV- call with his paired hands and therefore an EV- call overall
Balance
Game Theory Optimal play is the opposite of exploitive play
Exploitive play is taking advantage of opponents strategy
If he folds too much, we bluff more
If he calls too much, we bluff less
If he bluffs too much, we call more
If he bluffs too little, we call less
Villain bets pot otr so we need 33%, say villain has 100% bluffs - we call (with our bluff catcher) 100% of the time
Same situation but villain is never bluffing - we fold 100%
What is the MAXIMALLY EXPLOITIVE play if our opponent bluffs 50% of the time?
It is NOT to call a bit more frequently - we should call 100% of the time
If villain is bluffing 34% to 100% of the time when giving us ££% pot odds we call 100% as if we fold a bluff catcher we lose EV
Same if he is only bluffing 30% of the time then we fold always
Are we worried about villain noticing and counter exploiting us? Only if the two following things are prevalent…
1. Our opponent must observe the exploitable behaviour
2. Our opponent must act on it in the correct way
We can respond to this by either carrying on and trying to stay one step ahead of our villain
Or by pulling back on our maximally exploitative strategy (so perhaps we call 90% instead of 100%)
The essence of balanced play is a defensive strategy, our villains decisions become EV 0
We might use it if our villain is just a better player than us and can exploit us very well
Also we might use it readless, before we have any information
It is not necessary until we get to much higher stakes!
SUMMARY
ChampionsWe must work away from the table at the situations in this book so they become internalized
All champions have dedication and work hard and practise
Remember, in this book we were given the assumptions regarding opponents range/hand, this was about the 2nd Key To Poker - MAKING THE BEST DECISION!
Read the next book - Hole Card Confessions to learn the first key - MAKING ACCURATE ASSUMPTIONS
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