When you bet the flop, you reduced their range to mostly Jx, 6x and 2x. When the turn pairs, the aggressor should generally slow down, as the defender will often have a higher proportion of trips.
You then proceeded to overbet shove 3x pot on the turn for some reason. That's a huge mistake.
May 25, 2021 | 6:44 a.m.
The vast majority of BTN's range are pocket pairs and overcards. They have a lot of medium and not that much air, so you aim to make their pairs indifferent, which requires more fire power.
25% of your range (overpairs+) beats like 90% of their range (99-), so you can definitely polarize the flop. If you were deeper than your reverse implied odds from running into trips becomes more of a problem.
May 18, 2021 | 6:50 a.m.
Solve the flop for two bet sizes, then see which size is preferred on what flop and resolve for 1 size, simplifying each flop as necessary.
It's a ton of work, but it's also good training for knowing when a (Small-wide) bet is good and when (Big-polar) bet is good.
May 18, 2021 | 2:48 a.m.
More rake means less EV means every hand from move one gets dragged down.
There is an extra dollar in the blinds which incentivizes you to play wider, but the extra rake incentivizes you to play tighter. Hard to say which one has the greater effect on your opening strategy, but it will probably be the rake
A lot of preflop theory is geared towards no-flop no-drop. It's why you're supposed to 3bet huge preflop oop. It's why 3b/fold is so common. Without the incentive to take down the pot pre, you're less incentivized to play hyper-aggressive pre. There will still be raises of course, but I imagine a lot of hands shift from raises to calls.
May 12, 2021 | 2:30 a.m.
Large bets on dry paired boards are generally rare. If BB is betting everything it must have a huge range & nut advantage.
There aren't enough details in this post to verify the claim. What are the exact ranges, SPR, and rake structure being used here?
May 4, 2021 | 1:41 a.m.
How does fish making polarization errors, betting with weak/medium made hands affect this concept?
The mistake is that they are inefficient and exploitable.
They won't get much showdown value with medium because these hands either fold you out or narrow you down to a range that has medium crushed.
Meanwhile, their passive ranges are so capped that they don't get to realize equity with half their range..
You can overfold bluff-catchers because they aren't bluffing. You need to be able to beat a bluff (or cleanly outdraw value). If their weakest bluff is 2nd pair, then you're not making a mistake folding 3rd pair.
April 28, 2021 | 6:16 a.m.
MDF is so easy to misuse.
1) MDF is 1 - 58.3% = 41.6% on the river. Villain needs you to fold 58% to break even on a pure bluff.
2) if their river bluffs have equity then you defend less than MDF. Your goal is to make their bluffs indifferent between betting and checking. If their bluffs have value as a check, and you call exactly MDF, then the EV of checking becomes higher than bluffing. Thus you compensate by overfolding a bit to make them indifferent between checking and betting
3) You only call hands that have enough equity to meet pot odds on the river. That's true in theory, and in practice. Solvers don't always adhere to MDF, but they 100% adhere to pot odds on the final bet.
April 28, 2021 | 5:44 a.m.
Y is exploitable and does not play perfect GTO. It doesn't matter which suboptimal strategy Y adopts, he will always lose to X.
Not always true. GTO doesn't punish mixing mistakes.
Player A, B, and C all play a GTO strategy, with one twist-
Player A always folds any hand that is indifferent/mixed between folding and another action.
Player B always calls any hand that is indifferent/mixed between calling and another action.
Player C always raises any hand that is indifferent/mixed between raising and another action.
Player A, B and C would all have the exact same EV vs a fixed GTO player. At the same time Player A, B and C would all be exploitable.
It is impossible for perfect GTO to be the highest EV strategy against an opponent who does not play perfect GTO.
GTO can be equal to or lower than the most exploitative strategy.
GTO is the best strategy against an adjusting opponent who will punish mistakes. Exploitative is just a fancy word for a strategy that is specifically optimized to destroy some fixed strategy. Obviously the solution to the general strategy will not be as razor sharp as the solution against a specific strategy.
As soon as X deviates from GTO to exploit Y, he in turn becomes exploitable and exposes himself to the risk of actually being a losing player against Y if Y adopts the correct counter strategy
Usually yes, but there can be multile nash equilibria in certain situations. They could change from one equilibrium strategy to another, which Y plays worse against, without becoming exploitable themselves.
April 28, 2021 | 5:17 a.m.
QJs has more equity than A8o against a range of any two cards.
Avoid hand vs hand equity comparisons because they lead to rock-paper-scissors situations.
e.g. A8o > QJs > 22 > A8o > QJs > 22 > A8o > QJs > 22 > etc etc
The value of drawing increases as stacks get deeper. You don't want to play for 100bb stacks with top pair no kicker, you want to play these big pots with hands that can draw to the nuts.
If you want to read more about this, google "equity realization".
April 28, 2021 | 4:32 a.m.
Start by defining your "continue" range, then shift the entire line of indifference tighter. Marginal calls become bluffs, marginal 3b bluffs become folds, thin value 3bets become calls.
There are two lines of indifference:
Value line- hands which are thin value 3bets or strong calls.
Continue line - Hands that are almost too weak to play. EV of continuing very close to folding.
The easiest way to implement this is to use preflop charts that are specific to every position. Then just pretend you're playing an earlier position.
Would you 3bet an OMC nit UTG with the same range you'd use against an 80%VPIP whale in the SB? Of course not.
I don't think 3betting ranges change that much vs tighter ranges
They change significantly. Compare a SB/BB 3bet vs UTG to vs BTN.
For example, a hand that has x ev when called but has x+0.01 when 3bet
0.01 is usually within dEV so just treat that as solver noise.
If X is 0, this is an indifferent continue against a GTO range, and a losing continue against a stronger range (not considering explo factors).
April 28, 2021 | 4:12 a.m.
Stop limping altogether.
Just always raise KK+ at the microstakes. You really don't have to get that fancy.
You trap with the nuts when you think the value of trapping is greater than the value of raising. Maybe they bet a lot against your flatting range, but overfold to your raising range. The other side of that reasoning is that trapping helps defends the rest of your flatting range to prevent being run over.
April 17, 2021 | 4:36 a.m.
You've learned how to use the tools, the next step is to learn why.
Take one node in one spot and figure out everything there is to know about it. Reverse the positions, change the rake, nodelock them to barrel too many flush draws, add and remove bet sizes, make predictions, and repeat.
Drill down into the complexity and try to understand not just what the strategy looks like, but WHY it looks that way.
April 14, 2021 | 1:44 a.m.
Your line looks fine. Sizing seems okay. You set it up for a nice river shove which is ultimately what's important.
I think it's a call. Calling only Tx is playable as an exploit against extreme value, but there's no way you have enough straights here to only call the nuts and not be exploitable to overbluffers.
April 14, 2021 | 1:39 a.m.
live abc regs likely aren’t opening things like K8s from the HJ
Fair point! You can always plug in their assumed range and do some combinatorics. It's a good exercise tbh.
Something else I didn't consider is that all non-Kx combos have proportionately more outs. For example, Ax would be more likely to flop top pair. Maybe something to consider.
I think the main takeaway here is that Kx and 5x hands will simply be less valuable when K5o is exposed.
April 8, 2021 | 12:19 a.m.
All Kx and 5x combos lose value because they have fewer outs. So I would lean the opposite direction and start folding more Kx.
With the folded K5o, there are only 3 combos left of KK. You holding K7s reduces that to 1. So you block 2 combos of KK. This is largely irrelevant.
You unblock everything else, meaning they are significantly more likely to have Ax. Let's examine the combinatorics for a simple HJ opening range.
HJ Opening range:
HJ Opening range after removing K5o
HJ opening range after removing K5o and K7s:
Ax before removal: 102/298 = 34.2%
Ax after removal: 92/243 = 37.8%
JJ+ before removal: 24/298 = 8.0%
JJ+ after removal: 19/243 = 7.8%
So you're more likely to run into an ace, yet your chances of running into JJ+ doesn't actually change much. You could do a full analysis by plugging in their exact folding range and figuring out how that frequency changes with card removal.
To recap, you have fewer outs, less value, are equally likely to run into JJ+, and more likely to run into an ace. The combinatorics and EV are not in your favor, so I don't like the 3bet.
April 7, 2021 | 3 a.m.
True, but you can modify it for bluffs with equity. Alpha/MDF is just a primative EV calculation.
Here's what a normal alpha calculation looks like where bluffs have no equity. To find alpha, set EV to zero and solve for fold% needed to break even.
EV = (fold% * reward) - (call% * risk)
Here's a more complicated version that assumes bluffs have equity:
EV = (fold% * pot) + call%(win% * (pot+risk) - lose% * risk)
Plug in bluff equity and solve for the fold% needed to break even. Then MDF is just 1- above.
April 7, 2021 | 1:21 a.m.
MP is risking 2.9 to win 1.2, but yes that's the correct calculation.
One could argue that EP shares the MDF with everyone after MP, after all MP has to get a pure bluff through CO-BTN-SB-BB-EP. Though EP absorbs most of the responsibility of defense as the PFA.
April 5, 2021 | 12:16 a.m.
The easiest way to to calculate alpha. Alpha is (1-MDF) and represents how much fold equity is needed for a 0-equity bluff to be profitable.
BTN opens 2.5bb, SB folds, BB 3bets to 11bb, BTN 4bets to 24bb. What is BB's MDF?
Alpha = risk/(risk+reward)
BTN is risking = 24bb - 2.5bb = 21.5
BTN's reward = (0.5bb + 2.5bb + 11bb) = 14bb
Alpha = 21.5 / (21.5 + 14) = 60%
BB's MDF = 40%
Or more intuitively:
If BTN is bluff-4betting, they are risking 21.5 to win 14, therefore, they need to get that bluff through at least 60% of the time to be profitable. Therefore, BB should defend at least 40%.
(60.56% * 14bb) - (39.44% * 21.5bb) = 0
April 4, 2021 | 9:26 p.m.
You need them to be folding a better hand more than 2/3 of the time vs your overbet for bluffing to be better than checking. Pick lower equity bluffs with better blockers. Or just don't bluff the station. AK seems like a standard check either way.
I think you overestimated your range and nut advantage. Their wide preflop calling range does much better than your iso range on this runout.
March 21, 2021 | 7:28 a.m.
Making a hand indifferent is very simple. Calculate their equity against your range, and use a size that gives them exactly pot odds to call.
If they block your value range, then you'll need to bluff less, or target a worse hand type for indifference. It's also a good idea to pick bluffs that block the hands that call you.
Before you go implementing this, we should discuss 2 practical issues:
1) It's not usually practical to try and make top pair indifferent on the flop. Target hands that are naturally very close between continuing and folding.
2) Your ability to bet on later streets and repolarize changes these equations. If you're not all in on the flop bet, then the math gets exponentially more complicated.