my thoughts on everything

What I learned from Poker Math 101 by Noah SD...

• Math is very important, and you should become very comfortable with the numbers
• Estimate at all times, estimation is your best friend
• Play with WinCalc open during sessions
• Think about villains likely stacking combos when working out calcs
• Do math alot out of the table against a variety of villains
• Its important to get to a very thorough understanding of HAND COMBOS!

COMBOS

You hold 9h 8c:

 on board of Ah Tc 9c  - lets look at possible combos:

QJ: 4 Q;s x 4 J's = 16 combos
AK: 3 A's x 4 K's = 12 combos
T9: 3 T's x 2 9's = 6 combos
QJs: d,c,s,h = 4 combos
T9s: d,s = 2 combos
KK = 6 combos
TT = 3 combos
99 = 1 combos

PURE BLUFFING

You Hold Ah 5h in the bb and three bet a loose BTN opener to $22 who calls

on board of Jd Tc 8c

Pot Size: $45 ($22 raise + $22 call + $1 sb)

Bet Size: $30

- The general rule for considering a pure bluff:

for x time the pot is that you need villain to fold x times as often as he calls to break even.

-Here we're betting $30 into $45 so we neeed villain to fold 2/3 as often as he calls
-Math check: $45 * 2 - $30 * 3 = 0

to b/e we need villain to fold 2/3 as often as he calls, any thing more than this = profit

Lets take a look at the combos..

Number of hands Villain folds:
22-77 = 33 combos (22-77 =  6 combos each - 3 combos for the blocked 5 he hold)
78s = 3 combos (usually 4 but the 8c is blocking 1 combo)
total = 36 combos

Number of Hands Villain Calls/Raises>(remember we are pure bluffing so if we get called we are c/f as default on turn, therefore getting called or raised is essentially the same for our hand):

88-AA (99,QQ,KK = 18 combos + 88,TT,JJ,AA = 12 combos (we hold an Ace, and the board blocks some combos =  30 combos
AJs = 2combos (AJhh is blocked by us, AJdd is blocked by the board, therefore only clubs and spades are available)
JTs =  2 combos again (JTd is blocked by the board as is JTc so only hearts and spades are left)
QJs, T9s, 89s = 9 combos (remember each suit combo is blocked by the board once)
KQs = 4combos
AQs= 3combos (we hold an ace)
total= 50 combos

so we have 36 combos where villain folds and 50 combos where villain continues
we need to get 2/3 folds to B/even so lets run the math: 36/50 is the same as 72/100.
72/100 = 72% - This play is profitable since we only need 66% (2/3) to break even.

SEMI BLUFFING

200NL, eff stacks $340

You hold JcTc and get 3bet to $22 and call.

Board is AhQs8d2c

Villain cbets $30 and you call, and are facing a $70 turn bet and you shove for $288.

PotSize: $174
BetSize:$288

For a pure bluff to be good we need him to fold about 5/3 as often as he calls

Number of hands Villain Folds:

KJ, JT, 45s, 9T =  12 combos of KJ (we hold a J), 9 combos of JT (we hold a JandT), 4 combos of 45s, 12 combos of 9T (we hold a T) = total 37 combos

Number of hands Villain Calls:

AK, AQ, A8s, AA, QQ, 88, 22 = 12 combos of AK (1 A on board, means 3 Aces x 4 Kings), 9 combos of AQ (A and Q on board, means 3 A x 3 Q), 2 combos of A8s (Ah and 8d on board (meaning only A8 spades and A8 clubs), 3 combos of AA (Ah on board meaning Ad,Ac,As available meaning only AdAc, AdAs, AsAc), 3 combos of QQ (Q on board, same as Ace example) 3 combos of 88 (8d on board, ibid), 3 combos of 22 (2c on board, ibid) = total 35 combos

So there is obviously a clear problem here. 37 combos villain folds is only slightly better than 35 combos villain calls. 

How do we resolve this when we know we need to win as a pure bluff 5/3 of the time?

We need to remember that we are Semi Bluffing. So we are not PURE BLUFFING.

We need to factor in our pot equity when called into the equation. So what is that?

So let's go grab poker stove and plug in JTcc Vs villains calling hands:

1,540  games     0.010 secs   154,000  games/sec

Board: Ah Qs 8d 2c
Dead: 

    equity     win     tie           pots won     pots tied   
Hand 0:     17.403%      17.40%     00.00%                268             0.00   { JcTc }
Hand 1:     82.597%      82.60%     00.00%               1272             0.00   { AA, QQ, 88, 22, AQs+, A8s, AQo+ }

So we have 17.40% Equity, lets run the $ in the pot that is "ours" when we get called

Pot size when called  = $681
% in pot that we can say is "ours" (our equity share) = 17.4% of  $681

.174*$681 = $111.53~

$ in pot "ours" when called  ($ equity share) = $111.53~

Still here? Ok, good. But you may be asking yourself, what is the relevance of this?

We have to go back to the fact that we are Semi-Bluffing, so when we bet our $288 on the turn, we don't lose 100% of the bet of $288. Because we still have $111.53 equity in the pot. Therefore, our NET EQUITY LOST when called is $288-$111.53= $176.46

The lesson here is this:
When Semi-Bluffing, instead of working out a calculation of our needed fold equity as money lost when / money in pot we can win ($288/$174 or roughly need villain to fold 5/3 of the time or as a deciman 1.655xxxxx).
What we have to do is subtract the NET EQUITY LOST when called from the money we bet as a semi bluff, THEN work out our needed fold equity.
This would be $176.46/174 or very close to need villain to fold around 50% of the time or as a decimal 1.014xxx.
Now we go back to our hand combos. Villain folds 37 combos and Calls 35 combos = therefore villain folds 1.05714 or just slighlty more than 50%. Hence making the semi bluff +EV (although only slightly).

Estimating Equity without PokerStove

Same example as above.

Number of hands villain calls:

AA, AK, AQ, A8S, QQ, 88, 22 = 35 combos

We work out our outs vs each part of his range.

AK = 12 combos, we have 7 outs
AA, AQ, A8s, QQ, 88, 22 = 33 combos, we have 8 outs

So we have 8 outs 2/3 of the time vs his range and 7 outs 1/3 of the time vs his range, so an average of 7.67 outs vs entire range.

In each case, we know 8 cards, 2 in our hand, 2 in villains hand, 4 on board. so there are 44 cards left in the deck (52-8 lol)  therefore we win 7.67/44 = 17.4%
Its important to get to a very thorough understanding of HAND COMBOS

VALUE BETTING AND WEIGHTING RANGES

Value bets are simple, all you need to be profitable is to be ahead of villains calling range.

You Hold Ac 4c

Board Ah Tc Jc 4d 9s
(note: totally ignore hands that will fold, only think about hands that will CALL, dont waste time on hands you beat)

Hands we beat that call:

AK, 8 combos
AQ, 8 combos
JT, 9 combos
total 25 combos

Hands that that beat us:

KQ, 16 combos
ATs, 2 combos
AJ, 6 combos
A9s, 1 combo
TT,JJ, 6combos
AA, 1 combo
78cc, 1combo
total 37 combos

So how do we WEIGHT RANGES? Meaning, how often are they getting into this spot with these hands given the action! Ie. does villain ever have AA or AK pre and just flat pre? How often? Thats weighting ranges.. we have to consider how they play strangely.

So, we have to take the list of combos, then discount a certain number of them to match the likely play of the hand. Again, estimation is your friend. Your numbers will not be accurate, but the results you get from following this system will be much better than a pure guess, or not attempting to do anything whatsoever.

So lets take the above combos we listed, and adjust them slightly so that they are weighted, its ok to be rough:

Hands we beat that call:

AK, 2 combos (means 25% of the time he will play his 8 combos AK this way)
AQ, 6 combos (means 75% of the time he will play his 8 combos this way)
JT, 2 combos
total 10 combos

Hands that that beat us:

KQ, 3 combos
ATs, 1 combos
AJ, 1 combos
A9s, 1 combo
TT,JJ, 1.5combos
AA, 1 combo
78cc, .5 combos
total 9 combos

So, we get called by 10 combos and are ahead, and get called and are behind by 9 combos, making this a pretty thin value bet, but a good valuebet. but remember, if villain is capable of folding say AQ on this river more, the value bet becomes much much thinner, sometimes to the point of it being bad.

WHY BLOCKING BETS SUCK

Worst case scenario example:

The pot on river is $100. Villain is ahead x% of the time, and when he is not ahead he has air. He will always value bet when checked to and will bluff with an unexploitable frequency, betting $y. He will never bluff raise us if we bet at least 1/2 pot.
So should we bet 1/2 pot as a blocking bet? NO OF COURSE, but why?

Blocking Bet Equity:

We're called x% and lose 1/2 pot/ 100-x% of the time, we win the pot.

Net equity is $100-$x-$x/2 = $100-$300x/2

Checking Equity:

Villain is betting y$ offering us y=100:y odds. Unexploitable opponent will bluff y/(y+100) times as often as he value bets. So he bets X + y*x/(y+100) = (100+2y)x/(y+100) % of the time.

Translation = calling or folding vs his unexpolitable bluff strategy and his value bets is breakeven for us.
simplyfied: y=$100

therefore $100 is the breakeven point for his inexploitable bluffs and value bets combined when we call. Thus, when he bets less than pot (b/even point), checking is better than block betting.
PUNCHLINE: So long as villain is never betting over pot, block betting is always worse than checking. A half pot bet is ONLY better than checking IF villain is betting at least full pot.

This depends upon a few very basic assumptions, we are making villain play perfectly in this example and this is the worst case scenario you can face. An unexploitable bluffing frequency coupled with valuebetting hands better than ours. If we adjust these assumptions so that the villain bluffs less than an unexploitable frequency, the argument against block betting becomes even stronger.

Lets see why:

1. Villains rarely bet pot on the river as either a bluff or a valuebet, unlike example
2. The more you have to bet as a blocking bet, the worse it is
3. Villains are not perfect (infact, they suck lol) unlike example
4. In order to be a poker player, you must ESTIMATE
5. Villains WILL bluff raise your blocking bets, unlike the example
6. Blockbets ruin your metagame. If on the river, and you use the "blocking betting strategy" and you check, its face up as always air. This is because you valuebet your made hands, bluff occassionally and blocking bet your marginal hands. If you are using a blocking bet strategy, they now know your check is extreme weakness.
7. In conclusion - Blocking bets SUCK. Amen