..

I like it.
OESFD with 1 over

1st situation: A Big Pot on the Flop
6-max NLHE
100BB stacks

UTG calls 1BB
HiJack calls 1BB
CO fold
Button calls 1BB with 86
SB calls 0.5BB
BB raises to 9BB with AK

UTG calls 8BB
HiJack folds
Button calls 8BB
SB folds

The pot is: 29BB
The flop is: K97

BB bets 21BB
UTG folds
Button calls or shove?


EV if shove is called:
Equity 86 56.263%
Equity AK: 43.737%

0.43737 (-91BB) + 0.56263 (50BB + 70BB) = +27.71 BB

Just a detail:
Do you see something?
If no, read this thread: Little work No6: When is that better to take the pot right away
And now?
Spoiler:
When you shove, you are really hoping to take the 50BB pot right now:
EV opponent folds = +50 BB
EV opponent calls = +27.71 BB



Can you make more money by just calling?

When you shove, you are playing for 2 cards: the turn and the river, which gives you an equity of 56.263%
If you only calls a bet, you are playing for only 1 card: the turn, you equity is easy to calculate with your outs:

Your outs: any (9outs), any T (4outs), any 5 (4outs)
=> 15 outs (don't forget to remove the T and 5 counted twice)

Total unseen cards of the remaining deck (considere AK is unseen): 47 cards
=> 15/47 = 31.91%, that's you equity or in odds: (47-15)-to-15 = 32-to-15 = 2.13-to-1 drawing odds

Now, we have to compare our drawing odds to our pot odds:
Pot odds: 50-to-21 = 2.38-to-1
=> Pot odds > Drawing odds => You make an immediate profit, but how much?

EV = 0.68085 (-21BB) + 0.31915 (50BB) = 1.65965 BB

But things don't stop here! You have to considere your implied odds if you hit on the turn.
Remaining stacks: 70BB
Pot on the turn: 71BB
Remember, an uncalled shove is EV = +50BB and a called shove is EV = +27.71 BB

Now, assume that when we hit on the turn, the opponent lose his stack, thus your implied odds are 70BB and the EV is:

EV = 0.68085 (-21BB) + 0.31915 (50BB + 70BB) = 24 BB

But that's an ideal scenario, our opponent is not going to stack off everytime and your implied odds are probably 30BB or less on average.

EV = 0.68085 (-21BB) + 0.31915 (50BB + 30BB) = +11.23 BB

Therefore you see that even with an ideal scenario, the call is the worst option.



Summary:

You shove and he folds:
EV = +50 BB

You shove and he calls:
EV = +27.71 BB

You call:
EV = +11.23 BB

Thus, the last thing we want to do is to call.

What can we conclude?

When the pot is large in comparison to the remaining stacks and you have a favorite draw to the showdown (and your opponent is on a good hand or less), your best move is to go all-in everytime.

2nd situation: A Small-Medium Pot on the Flop
6-max NLHE
100BB stacks

UTG raises to 4BB with AK
HiJack calls 4BB
CO folds
Button calls 4BB with 86
SB folds
BB folds

The pot is: 13.5BB
The flop is: K97

UTG bets 11BB
HiJack folds
Current pot: 24.5BB
Opponent's remaining stack: 85BB
Your stack: 96BB
Button calls or raise or shove?


EV if shove is called:

EV = 0.43737 (-96BB) + 0.56263 (24.5BB + 85BB) = +19.62 BB

EV if shove is not called:

EV = +24.5BB (the current pot) or if you prefere 0.00 (-96BB) + 1.00 (24.5) = 24.5BB

Here also you prefere a fold when you shove than a call.

Now what happends if you call?

Immediate profit (which means without implied odds):
EV = 0.6429 (-11BB) + 0.3571 (+24.5BB) = +1.67705 BB

But you have to add implied odds in cases you hit.
Turn pot if you call: 35.5 BB
It's ok to assume you can make at least 15BB more on average I think:

EV = 0.6429 (-11BB) + 0.3571 (+24.5BB + 15BB) = +7.03 BB

Not very much on average, but what happens when you win the max implied odds, which means the opponent's remaining stack, it happens when you are against a donk which overplay TPTK or overpairs or something like that, and yu can be sure that this guy will call your shove on the turn:

EV = 0.6429 (-11BB) + 0.3571 (+24.5BB + 85BB) = +32.03 BB

Last question: How much implied odds you need to equals the called shove result???
EV = 0.6429 (-11BB) + 0.3571 (+24.5BB + XBB) = +19.62 BB (Isolate XBB)

=> XBB = 50.25BB = implied odds needed
Considering the turn pot is 35.5BB, it's a little hard to extract this amount against a good player, on average it's probably not possible.



Summary:

You shove and he folds:
EV = +24.5 BB

You shove and he calls:
EV = +19.62 BB

You call:
EV = +7.03BB on average against good player, the more the player is a calling station or is unable to fold TPTK or overpairs, the more you win, 7.03BB is a minimum I think.

EV = +32.03BB if you can stack off your opponent when you hit

What can we conclude at this point?

-If you are against a donk which overplay his TPTK/overs, you have a better EV if you call and take a better equity on the next street to put the rest of your money.

-If you are against a good/great player, you implied odds are very small thus your EV is poor and way behind the EV's shove situations, thus it's better to shove and even if you are called your EV is a lot higher than the calling method, of course if you pick up the pot, that's a very nice result (against a good player, it will happens a lot of the time).

Now the big part: the Raise
Reminder:
6-max NLHE
100BB stacks

UTG raises to 4BB with AK
HiJack calls 4BB
CO folds
Button calls 4BB with 86
SB folds
BB folds

The pot is: 13.5BB
The flop is: K97

UTG bets 11BB
HiJack folds
Current pot: 24.5BB
Opponent's remaining stack: 85BB
Your stack: 96BB

Imagine, you decide to raise to 35BB, a correct amount I think.
If your opponent shove
That's a no-brainer, you CALL!
And you win EV = +19.62 BB (precision, that's not for the last move (your all in call), but for the totality of flop moves which is like when your opponent calls your shove)

If your opponent folds:
You win the current pot: EV = +24.5BB

If your opponent calls:
Immediate profit (which means without implied odds):

EV = 0.6429 (-35BB) + 0.3571 (+24.5BB + 24BB) = -5.18BB

You are EV-. But you have to include your implied odds.
Pot turn: 83.5BB
Remaining stacks: 61BB
It's ok to assme that you can extract 35BB (implied odds) on average I think.

EV = 0.6429 (-35BB) + 0.3571 (+24.5BB + 24BB + 35BB) = +7.32BB That's similar result that in the case where you just called.

And now, what is the maximum amount possible? (= opponent remaining stack win or max implied odds)

EV = 0.6429 (-35BB) + 0.3571 (+24.5BB + 24BB + 61BB) = +16.6BB That absolutely not a similar result that in the case you just called. Here it's twice worst in EV term.


Now we put all reactions for the Raise toghether, shove%, fold% and call%.
Thus you have to estimate a percentage for each scenario, for example:

Very High fold%
shove% = 15%, fold% = 60% => call% = 25%
EV = 0.8 (24.5 BB) + 0.05 (7.32 BB) + 0.15 (+19.62) = +22.91 BB against strong player
EV = 0.8 (24.5 BB) + 0.05 (16.6 BB) + 0.15 (+19.62) = +23.37 BB against a donk

High fold%
shove% = 15%, fold% = 60% => call% = 25%
EV = 0.6 (24.5 BB) + 0.25 (7.32 BB) + 0.15 (+19.62) = +19.47 BB against strong player
EV = 0.6 (24.5 BB) + 0.25 (16.6 BB) + 0.15 (+19.62) = +21.79 BB against a donk

Medium fold%
shove% = 15%, fold% = 40% => call% = 45%
EV = 0.4 (24.5 BB) + 0.45 (7.32 BB) + 0.15 (+19.62) = +16.04 BB against strong player
EV = 0.4 (24.5 BB) + 0.45 (16.6 BB) + 0.15 (+19.62) = +20.21 BB against a donk

Low fold%
shove% = 15%, fold% = 20% => call% = 65%%
EV = 0.2 (24.5 BB) + 0.65 (7.32 BB) + 0.15 (+19.62) = +12.60 BB against strong player
EV = 0.2 (24.5 BB) + 0.65 (16.6 BB) + 0.15 (+19.62) = +18.63 BB against a donk

Zero fold%
shove% = 15%, fold% = 20% => call% = 65%%
EV = 0.0 (24.5 BB) + 0.85 (7.32 BB) + 0.15 (+19.62) = +9.17 BB against strong player
EV = 0.0 (24.5 BB) + 0.85 (16.6 BB) + 0.15 (+19.62) = +17.05 BB against a donk

Discussion:
When you raise, the last thing you want with those draws is a CALL. Especially if the opponent is strong.
A shove from your opponent is a good deal, don't be affraid about that. A fold is the better result.

General Summary for 2nd situation

You shove
Opponent folds
EV = +24.5 BB
Opponent calls
EV = +19.62 BB

You call
EV = +7.03BB on average
EV = +32.03BB against a donk

You Raise: 3 possible reactions
1st Opponent shove and you call:
EV = +19.62 BB

2nd Opponent folds:
EV = +24.5BB, you win the current pot

3rd Opponent calls:
EV = +7.32BB on average
EV = +16.6BB against donk

Combination of those 3 reaction to find the real EV in different situation:

Very High fold%
fold% = 80% / call% = 5% / shove% = 15%
EV = 0.8 (24.5 BB) + 0.05 (7.32 BB) + 0.15 (+19.62) = +22.91 BB against strong player
EV = 0.8 (24.5 BB) + 0.05 (16.6 BB) + 0.15 (+19.62) = +23.37 BB against a donk

High fold%
fold% = 60% / call% = 25% / shove% = 15%
EV = 0.6 (24.5 BB) + 0.25 (7.32 BB) + 0.15 (+19.62) = +19.47 BB against strong player
EV = 0.6 (24.5 BB) + 0.25 (16.6 BB) + 0.15 (+19.62) = +21.79 BB against a donk

Medium fold%
fold% = 40% / call% = 45% / shove% = 15%
EV = 0.4 (24.5 BB) + 0.45 (7.32 BB) + 0.15 (+19.62) = +16.04 BB against strong player
EV = 0.4 (24.5 BB) + 0.45 (16.6 BB) + 0.15 (+19.62) = +20.21 BB against a donk

Low fold%
fold% = 20% / call% = 65% / shove% = 15%
EV = 0.2 (24.5 BB) + 0.65 (7.32 BB) + 0.15 (+19.62) = +12.60 BB against strong player
EV = 0.2 (24.5 BB) + 0.65 (16.6 BB) + 0.15 (+19.62) = +18.63 BB against a donk

Zero fold%
fold% = 0% / call% = 85% / shove% = 15%
EV = 0.0 (24.5 BB) + 0.85 (7.32 BB) + 0.15 (+19.62) = +9.17 BB against strong player
EV = 0.0 (24.5 BB) + 0.85 (16.6 BB) + 0.15 (+19.62) = +17.05 BB against a donk

Conclusion:

By shoving, you guarantee a 19.62BB at least.

By raising, in every situation we have a maximum EV close to the minimum you win by shoving. Thus it's probably better to shove instead of raising.

By calling, there is 2 different situations. It is a very bad move to call against a strong player.
But it is THE BEST IDEA to call against a super donk who stack off light, you will win more money if you do that than when you win the flop pot.

Finally:

Shove everytime in those situations except if you are against a donk who stack off light, here just call and put the money later when you hit.

What do you think about this conclusion?

my cats name is mittens

nice post

In a small pot, your shoving range is small, pretty much only draws. Your raising range is larger, and includes more made hands. Therefor, a raise has more fold equity then a shove versus thinking players, and lets you increase your raising range beyond value / air, and add a bit of draws.

hi can you link to the first 6 ones in this thread too? would help a lot thx

Little work No1: protection, equity, EV

Little work No2: betting or raising for an immediate profit

Little work No3: 3-bet pot, don't fight to much

Little work No4: Introduction to Combos for Dummies

Little work No5: Combos, Hand Ranges, Fold %, EV

Little work No6: When is that better to take the pot right away

One important point about the raise for 2nd situation:
If you are OOP, a raise is more dangerous than IP if you suspect your opponent to call. Because in the next round, you generally can't take a free card OOP by checking behind. In position, even if you are called, you have the luxury to check behind on the turn (because your opponent checks to you the vast majority of the time after your raise), which is like if you had put your money on the flop with a 56.263% equity (because you can see the river for free) and not with the 31.91% (one card shot).
Thus, raising with position is strongly recommanded.

Of course, when you raise all in on the flop, position is irrelvant, there is no more action to do.
And if you are in a close decision between raising or shoving OOP, it's perhaps better to shove to avoid to be paralyzed on the turn OOP if called on the flop.

great work! I didnt know you made a series I def check them out.

Hi, ty very much!

This work is not finishied, there is the Small Pot on the Flop situation which will comes in several hours

Yes, I have made a serie and try to connect every works between them also, some works are very basic, others a little more complex, but I think even simple thing are good to reorganize your ideas sometimes.

Hope you will like it!

Al1

3rd situation: A Small Pot on the Flop
6-max NLHE
100BB stacks

UTG calls 1BB
HiJack calls 1BB
CO folds
Button calls 1BB with 86
SB calls 0.5BB
BB checks

The pot is: 5BB
The flop is: K97

UTG bets 3.5BB
HiJack folds
CO folds
The current pot is 8.5BB
Button calls or raise or shove?

Before anything, be sure you understand why in case the pot is big, you prefere a fold than a call if you shove: When is that better to take the pot right away

You shove:

We assume here that you have a similar equity than against the previous AK hand: 56.263%. And that SB and BB fold to the shove.

...and you are called
EV = 0.43737 (-99BB) + 0.56263 (8.5BB + 95.5BB) = +15.21BB

...and everybody folds

EV = +8.5BB

It's clear that when you shove, you prefere a call now, because you make more money. If you have understood the link I give to you above, you know why.
It's because this time the pot is small in relation to the stack size, thus you can protect you hand, what is not possible in previous shove situation because the pot is too large.

But you can be sure that the vast majority of your shove will be folds, perhaps 85% or more: thus your EV for shove is

EV = 0.85 (+8.5BB) + 0.15 (+15.21BB) = +9.51BB, which means something close to the "everbody folds". Not very good... (Precision, this EV is probably too high, because when you are called in this situation, you are more often than normal against a set, but even in this case, you only a small underdog, 42.121% equity against a set of 999)

Thus, even if you prefere a call in this case, the shove is perhaps not the best move.

You call:

If you call, you play for one street, thus you equity is 31.91% and you immediate profit is:

EV = 0.6809 (-3.5BB) + 0.3191 (+8.5BB) = +0.3292 BB

But of course you have to add you implied odds, and this time you can perhaps extract value both from the turn and the river because your opponent will probably call with TP.
Imagine you can extract on average 10BB more (flop pot is 12BB):

EV = 0.6809 (-3.5BB) + 0.3191 (+8.5BB + 10BB) = +3.52 BB, not a lot

And even if we considere that the opponent is very generous on average (25BB):

EV = 0.6809 (-3.5BB) + 0.3191 (+8.5BB + 25BB) = +8.31 BB, which means something similar to the shove situation...

Even against a calling station, it's hard to hope he will stack on the turn or river when we hit, because the pot is so small.

Thus, first thing to notice: calling is not an option, because shoving make more money.

You raise:

[This case is perhaps the most interessting in this little work but also the more complex]

Imagine you raise to 11BB. What happens?

Sometimes, you opponent folds, sometimes he calls, sometimes he reraises and sometimes he shove.

1) If he folds, you take the pot: EV = +8.5BB
2) If he shove => you call, you are the favorite EV = +15.21BB (globally for the flop)
3) If he reraises, the raise-size will be something like 25-45BB, perhaps 30BB in average. And the pot will contain 44BB, this is a big pot like in the 1st situation, and the solution was to shove:
-if he folds, that's great EV = +34BB (globally for the flop), doable for example against a super-aggro on the flop but tight to call a shove
-if he calls, EV = +15.21BB (globally for the flop)
4) If he calls:

This case is the most complex. There is more factors to take in consideration, but the most important is your position I think.

Immediate Profit:
EV = 0.6809 (-11BB) + 0.3191 (+16BB) = -2.38 BB (without implied odds)
With implied odds:
Flop pot: 27BB, it ok to imagine 15BB for implied odds I think.
EV = 0.6809 (-11BB) + 0.3191 (+16BB + 15BB) = +2.4 BB

If you have the maximum implieds?
EV = 0.6809 (-11BB) + 0.3191 (+16BB + 88BB) = +25.7 BB
This can happens if your opponent is a big calling station.

Globally, that's not very good, but what happens if you check behind on the turn when you miss?

Immediate Profit:
EV = 0.43737 (-11BB) + 0.56263 (+16BB) = +4.19 BB (without implied and IP, you already EV+, that's good to know )
With implied odds:
Your implieds will be smaller I think if you can only value bet the river, for example your opponent if more likely to fold if he was on a draw, but would have called on the turn to draw. Thus I have put 12BB instead of 16BB.
EV = 0.43737 (-11BB) + 0.56263 (+16BB + 12BB) = +10.94 BB
That's a good result, better than the shove, thus it's perhaps a good way to raise/check behind. But considering that, what happens if we decide to make bigger raise than usual to increase our EV:
Say we raise 15BB instead of 11BB:
EV = 0.43737 (-15BB) + 0.56263 (+20BB + 18BB) = +14.82 BB (implied odds are proportionnaly bigger because the pot is also a little bigger)

Have you see something?



The check/behind option is generally only avaible if you are in position, thus you can see how position is important here.

Just to have an idea: If you have the maximum implieds?
EV = 0.43737 (-11BB) + 0.56263 (+16BB + 88BB) = +53.7 BB
This can happens if your opponent is a big calling station.

It's time to assign some % to each opponent's reaction to discover if the raise is better than the shove.
fold% = 30%
call% = 55%
reraise + call shove = 7%
reraise + fold shove = 3%
shove = 5%

Of course that's just an estimation, it will be very good if you can say me if those numbers are ok, thx.

Out of Position:

EV = 0.3 (+8.5BB) + 0.55 (+2.4BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +6.71BB
(and by modify the fold/call%)
EV = 0.4 (+8.5BB) + 0.45 (+2.4BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +7.32BB
EV = 0.5 (+8.5BB) + 0.35 (+2.4BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +7.94BB
EV = 0.6 (+8.5BB) + 0.25 (+2.4BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +8.55BB
EV = 0.7 (+8.5BB) + 0.15 (+2.4BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +9.16BB

It seems that even with a monster fold%, it's hard to do better than the shove...

In Position if you use the big raise/check behind:

EV = 0.3 (+8.5BB) + 0.55 (+14.82 BB) + 0.07 (+15.21BB) + 0.03 (+34BB) + 0.05 (+15.21BB) = +13.55BB

Discussion:
It seems that calling is not an option with a draw like this in a little pot.
Shoving is strangely not so bad OOP, unless you are against a big calling station (the raise is better here)
Raising is the best play IP.
When you raise, the best result against good opponent is to induce a shove, especially OOP (IP it's close).
Your position is essential
Two moves are interressant
-the big raise in position on the flop
-the raise+shove to induce a reraise+fold, and you win the reraise (this is a weapon you can use both IP or OOP)

Your moves are strongly opponent dependant and you can radicaly change the "default play" (raise if big fold% or shove OOP, raise big/check behind IP), for example
*Against a monster calling station (you are fairly sure he will stack off), you can raise OOP, not in the hope to take the pot right now but to build an enough larger pot to have the possibility to make big bets if you hit.
*Against a flop-hyper-aggro but tight player, you can try the "the raise+shove to induce a reraise+fold", not to steal the bet but to steal the reraise (take care about the raise size for the reasons I mentionned).

Al1

Please say me if you see some errors, or don't like the numbers I choose.

Thx