[arw]

Also, you are aggressive, active, and raising every hand. They think you’re bluffing and you have a made hand. Time to act like it.

[arw]

Thank you. The point of this question was to get a discussion going and talk about adjusting strategy based on stack size for Pre-Flop spots.

For most of my hands, I work from the big picture and narrow it down. I try not to incorporate any “tells” until the end. I use them as a way of shift my vote, not as a foundation for my decisions.

In other words, I would analyze the board the same way whether it was Gus Hanson or Action Dan. I have High confidence that combinatorics will give me a better guess than any live reads I have post-flop. When I think about the action, the range I build may be adjusted to fit my opponents tendencies and flow of the game.

[arw]

Apes suggests a bet of $300.

The strong hands likely won’t fold the flop and they will want to see future cards. Apes says charge them for their curiosity.

[arw]

The 9 bb, 21 bb, and 26 bb stacks have 16%, 37%, and 46% of the chips in play respectively. When the prize pool is $425, $305, and $175, this next hand has a pay-ladder of $130.

According to ICM,

• The 9 bb stack is worth ~ $245
• The 21 bb stack is worth ~ $320
• Th 26 bb stack is worth ~ $339

The action:

• The flop is As Qh 8s
• You have Qc8c for bottom two pair.
• On the flop, you lead for 2.5 bb into 4.5 bb and the big stack shoves.

With bottom two pair, you lose to:

• sets (AA, QQ, 88) — where combos are (3 + 1 + 1)
• two pairs (AQ, A8, Q8) — where combos are (6 + 6 + 4)

<div>
</div>

With bottom pair, you’re ahead of:

<div>

• one-pair aces (AK, AJ, AT, A9, A7) — 12 combos each
• gut-shots (KJ, KT, JT) — 16 combos each
• flush draws (KQss, JTss) — 1 combo each

After looking at these ranges, the value range has ~21 combos and the bluffing range has ~ 110 combos. To me, this makes it very very difficult for me to lay down Q8 on this flop. This seems like a cooler that I just won’t get away from very often. There is some merit in folding because Q8 two pair is the absolute bottom of the value range on this board and if you’re beat, you likely have few outs. The drawing hands have between 4 – 12 outs to beat you on the turn and river.

• Q8 vs AA is drawing dead
• Q8 vs QQ is drawing dead
• Q8 vs AQ is drawing to an 8
• Q8 vs A8 is drawing to a Q

Last comment,

If the big stack is competent and playing for the win, he/she may be using “leverage” to force extra folds because he/she understands ICM and how to push people around. The idea is to apply pressure and force opponents to make a decision for all their chips. With lots of money on the line and time invested, most people don’t take marginal spots. The big stack may be raising wider and because he/she knows that mind is on the $$$. If my opponent is making this play, this might impact whether I shift to a call or fold.

This is a great hand to take a look at. After thinking about it…I’m confident that you would see me at the WSOP Main Event tanking at least 5 minutes and then eventually laying it down. The big stack applies pressure well and it makes Ideally, I would want to conserve chips, stay in 2nd position, and apply pressure in a better spot.

</div>

[arw]

Tournaments are very different from cash games. In a tournament, chasing a flush draw is risky because you only have X number of chips. In cash, you can rebuy so people tend to gamble more.

On monotone boards,

• when should you get to showdown cheaply? (play passively)
• when should you try to raise and take it down? (play aggressively)

• The answer to both of these questions highly depends on:

• how many players are in the pot?

• fewer players ~ aggressive

[arw]

Note:

With this range, AJ is only beating 53 combos of two-pair, chopping in the rare case they have one of the other 4 combos of AJ, and losing to the rest of the range of 70 combos.

[arw]

Questions:

• Would this player make this river bet with a worse two pair?
• Would this player make this river bet with only a flush or straight?

<u style=””>Combinatorics

On the board (As 8d 4c Jc 6c)

• Sets:

• AA — 1 combo
• 88 — 3 combos
• 44 — 3 combos
• JJ — 1 combo
• 66 — 3 combos

[arw]

@rabman50

What is poker FPS? — I’m thinking about (frames per second)

[arw]

Hero has 77 in the big blind and 85 bb effective.

After the pre-flop action, there is 9 bb in the pot and it’s 3 ways.

The flop is (9d 8d 5s)

The small blind leads 9 bb and gets two callers. (VERY INTERESTING)

The turn is (9d 8d 5s 2s)

The small blind bets 36 bb. Both players fold.

___________________________________________

This board is very connected and draw heavy. Your opponents could have a wide range pre-flop since they got in cheaply until you spoiled the party with your squeeze to 3 bb. The flop action tells us a lot.

• The small blind bet full pot into two people who have better position. We can assume this isn’t a complete bluff.
• The big blind (you) flat called a full size bet with another player behind who could potentially (fold, call, raise).
• The button called a full size bet and is willing to play the turn against two players, the button didn’t raise the flop.

This flop isn’t ideal for 77. It’s painful to fold 77 on this flop because you have a draw to the nuts but here is why I would fold and not call 9 bb :

• The # of safe cards on the turn and river. What cards do you want to see where you think your pair of 77 is the best hand? You don’t want to see any diamonds, you don’t love it when the board pairs, you might not want to see another 7, and you don’t want to see any broadway cards like an A, K, Q, J, T.
• The Pot Odds. You opponent led 9 bb into 9 bb. This means you have 1:1 odds and need to win 50% to break even.

• Pocket 7’s is 62% to win against (3d2d) for a flush draw.
• Pocket 7’s is 60% to win against (6d2d) for a flush draw and straight draw.
• Pocket 7’s is 46% to win against (AdKd) for a flush draw w/ over-cards.
• Pocket 7’s is 23% to win against (9s8s) for top two pair.
• Pocket 7’s is 23% to win against (5c5h) for bottom set.

[arw]

Hero has Kd9d has 25 bb at the start of the hand

Villain has him covered with 57 bb.

Pre-Flop

Villain raises to about 3 bb

Another player calls 3 bb

Hero raises to about 10 bb

One caller

Pot Size is (30 * 9 + 125 + 250 + 2000 + 2000 + 625) = 5270 or 21 bb.

Flop

The flop is K62 rainbow.

The hero has invested 10 bb and has ~14 bb remaining.

Action goes check check.

Pot Size = 21 bb

Turn

The board reads K627 rainbow.

The villain checks, hero bets 1000 or 4 bb, villain calls to see the river.

Pot Size = 29 bb

River

The board reads K627A.

Action goes check check.

Pot size = 29 bb

_______________________________________________________________

K9 suited is not the best hand to make this play when you only have 25 bb to start the hand. If the villain is loose like a goose, then yes, this seems correct. Against most opponents, I think it is a losing play to 3-bet K9 suited against the opening range of a pre-flop raiser. They would need to have the tendency to raise/fold under pressure and I would need some leverage with my stack size. You only have 25 bb and this limits your post-flop options. Especially, when the pot size has been bloated to 21 bb pre-flop by your 3-bet and a call.

On the flop,

• the pot is huge (21 bb)
• you have top pair + nine kicker
• you have 11 bb left in your stack

By 3-betting pre-flop, you would be representing a stronger range:

• Big Pairs (AA, KK, QQ, JJ, TT)
• Big Aces (AK, AQ, AJ, AT)
• Big Kings (KQ, KJ, KT, K9

If these hands are in your 3-bet range, then c-betting them might be good for balance.

• Broadways (QJ, JT)
• Connectors (T9, 98, 54)

On the turn,

• the pot is 21 bb
• you bet 4 bb with only 7 bb behind
• your opponent calls

It’s safe to say that the villain is calling with something. But What??

• if they have a set, why aren’t they raising?
• if they have two pair, why aren’t they raising?
• if they have a better king, why aren’t they raising?

On the river

• the pot is 29 bb
• both players check when the Ace hits

The ace on the river is not good for your hand but it is good for your range. You should be holding a lot stronger aces than he/she has in their raise/calling range. The ace helps your range. Especially after your (forgive me), fishy 1000 bet on the turn to “reel them in”.

Shove the Flop!!!

Taking down the 21 bb pot w/o showdown is a huge win.

[arw]

<div>You have AK on a A63 rainbow flop.</div>

Before the flop, the small blind 3-bets your min-raise to 8 bb.

You call with AK

Pot Size is about 18 bb.

On the flop of A63 rainbow, the villain has 36 bb and he decides to lead out 4.5 bb. You have about 77 bb left in your stack and you have 3 options:

• Fold

• before you fold, you need to consider the pre-flop range of the opponent. They just 3-bet you from the small blind and c-bet on an ace high flop. Maybe it’s something like (AA, KK, QQ, JJ, TT, 99, 88, 77, AK, AQ, AJ, KQ, QJ, JT) where you can also add some bluffy hands like weak aces, small pairs, and other suited connectors. The villain has enough chips to still play a wider range and isn’t in push/fold mode yet.

• Does this opponent c-bet 100% of the range on ace high flops?

[arw]

Use this applet to play with the numbers for Poker EV.

[arw]

What % win is needed to break-even when our opponent calls only 25% of the time?

Fold EV + Call EV = 0

Fold EV

= (0.75)(300)

Call EV

= (0.25)[(W)(925) + (L)(-625)] where L = 1 – W

= (0.25)[(W)(925) – (1 – W)(625)]

= (0.25)[(W)(925) – (625 – 625W)

= (0.25)(925W + 625W – 625)

= (0.25)(1550W – 625)

Total EV

(0.75)(300) + (0.25)(1550W – 625) = 0

225 + 387.5W – 156.25 = 0

387.5W = 68.75

W = 0.1774 or 17.7% win is needed

When they fold more often, we need to win less often.

[arw]

If we raise, our opponent might call with a variety of hands and I want to know my equity against the made hands (straight, set, flush, two pair) and the bluffing range (flush draws, gut-shots).

— AK vs JhTc — 17% vs.82%

• our opponent has a flopped straight with the nut flush draw. We have 4 outs.

— AK vs QQ — 17% vs 77%

• our opponent has bottom set of queens. Neither hand has a flush draw. We have 4 outs. There is a ~6% chance of a tie due to running hearts.

— AK vs 3h2h — 17% vs 80%

• our opponent has the worst possible flush. We have 4 outs.

— AK vs KQ — 86% vs 8%

• our opponent has a weaker two-pair. They have only 2 outs to suck out. There is a ~6% chance of a tie due to running hearts.

— AK vs Jh2c — 57% vs 42%

• our opponent has the nut flush draw and a gut-shot. They have 12 outs to win. The 9 remaining hearts to hit the flush and the 3 remaining Tens to hit the gut-shot straight.

Expected Value

<div>
</div>

Fold EV

= (% opponent folds)*($300)

Call EV

= (% opponent calls) * [(% hero win)($300 + $625) + (% hero lose)(-$625)]

Total EV

= Fold EV + Call EV

_________________________________________________________________

To do an example, let’s make assumptions:

• our opponent will call the raise 25% of the time and fold 75% of the time
• If we win ~20% of the time, what is our expected value?

Fold EV

= (75%)($300)

= $225

Call EV

= (25%)[(20%)($925) + (80%)(-$625)]

= (0.25)[(0.20)(925) – (0.80)(625)]

= (0.25)[185 – 500]

= $-78.75

Total EV

= 225 – 78.75 = $146.25

For the price of calling $625 more, our opponent would need to call us more often (higher than 25%) to reduce our fold equity. We are making a lot of $$$ every time our raise forces a fold. To do this, our opponent will need to start calling with a slightly weaker range of hands (drawing hands).

Let’s adjust our assumptions:

• our opponent will now call 50% of the time and fold 50% of the time
• since they are drawing more often, I estimate that we win ~30% of the time and lose 70% of the time, what is our expected value?

Fold EV

= (50%)($300)

= $150

Call EV

= (50%)[(30%)($925) + (70%)(-$625)]

= (0.50)[(0.30)(925) – (0.70)(625)]

= (0.50)[277.5 – 437.5]

= -$58.75

Total EV

= $150 – $58.75 = $91.25

By calling more often, our opponent has changed the EV in their favor. Our expected value decreased from $146 to $91.

Now, let’s get fancy.

What % win is needed to break-even when our opponent calls 50% of the time?

Fold EV + Call EV = 0

Fold EV

= (0.50)(300)

Call EV

= (0.50)[(W)(925) + (L)(-625)] where L = 1 – W

= (0.50)[(W)(925) – (1 – W)(625)]

= (0.50)[(W)(925) – (625 – 625W)

= (0.50)(925W + 625W – 625)

= (0.50)(1550W – 625)

Total EV

(0.50)(300) + (0.50)(1550W – 625) = 0

150 + 775W – 312.5 = 0

775W = 162.5

W = 0.209677 or 20.9% win is needed

This means, if our opponent calls us 50% of the time, we only need to win 20.9% of the time to break-even.

• If we win more than 20.9%, our EV increases.
• If our opponent calls less often than 50%, our EV increases.

[arw]

Analysis

16% to win against 6.78% of range when opponent has a made flush.

64% to win against 42.98% of range when the opponent has a flush draw.

??% to win against calling range, assuming he doesn’t re-raise the flop

100% to win against folding range

Should you raise, call, or fold AK?

Let’s put some numbers to this hand,

You both start the hand with $750 after pre-flop action. You have AK on an AhKhQh flop, your opponent checks, you bet $25 into a pre-flop pot of $50, and your opponent raises to $100 more.

• You can fold. Stack size would be $725. Losing a bet of $25.

• You can call. You’ve invested $125 with 2 more streets to go and only $625 left in your stack. The Pot Size would be $300.

• You can raise. You would be raising an additional $625 and offering pot odds of ((625 + 300)/(625)) or about 1.5 to 1.0. This has a break-even of 40% win needed for them to call the raise and profit from you.

• Which of the villains hands will call our raise?

• made flushes

• this is only 6.78% of the starting hand range
• we win 16% against this range. Bad Shape 🙁

[arw]

Typo — 169 starting hands, not 69.

Also, I want to add this

Flop Textures:

• Monotone flops occur about 5% of the time
• Two-Suited flops occur about 55% of the time
• Rainbow flops occur about 39% of the time
• Flops w/ No Pairs occur about 82% of the time
• Flops w/ One Pair occur about 17% of the time
• Flops w/ Trips occur about < 1% of the time

[arw]

1) The book is a Gem

2) My vote (fold > jam > never call).

With TT and a large stack, I don’t want to take this risk pre-flop against two players. Instead, use my stack to stab for smaller pots in better spots. I completely agree that these are steal spots but I hate flipping with AK, AQ, or worse being against JJ+. Other players, take this risk thinking that it is a sure way to win the tournament if you win this HUGE POT. With 30 left, having the Jamie Gold super stack doesn’t guarantee victory.

Statistics like this scare me about getting it in.

52 cards

16 cards are A, K, Q, J

Odds that an A, K, Q, J don’t hit the community cards (assuming no blockers)

36/52 * 35/51 * 34/50 * 33/49 * 32/48 = 14.5%

[arw]

<b style=”font-family: inherit; font-size: inherit;”>what portion of this process do you have internalized?

• Most of the math is done in my head. I’m estimating and mapping it out. I try not to make assumptions early. Good assumptions are based on making good observations and watching the action.
• In Limit poker, or “no foldem holdem” as some say, combinatorics has helped me quickly evaluate my hand to find (good cards, bad cards) on the turn and river. I play a lot of multi-way hands, I see a lot of flops, I need to be aggressive to win, and most importantly, I need to have the best hand on the river when I always get called.

what portion do you use aids to recall in real time?

• In my spare time, I write code and phone apps. When I step away from the table, I occasionally use a custom phone app to double check a hand or look something up.

what portion do you typically abandon for real-time play and instead apply during pre- or post- play study or review sessions?

• At this point, I don’t really calculate pot odds anymore except on paper because I’ve played enough hands to have a decent estimate in real-time.
• After playing a hand, I try to think it through with an analytical lens and try to avoid thinking about how the result was bad.

[arw]

Very True,

Learning about combinatorics will help you bluff more effectively, pick off bluffs, and simply make better decisions post-flop.

If you study hard enough, you may catch @SteveFredlund bluffing on the Jack high dry flops with Q9 when he has position and the betting lead. I didn’t forget Steve. Keep trying though, I love the hunt!!!

[arw]

Taking down 21 bb on the flop is a huge victory.

Thank you @Jim for the kind words.

🙂