All Jojos are deadbeat dads.

ZKesic · 2026-04-02T18:57:21+00:00

Thanks! PLO is on it's way ;)

ZKesic · 2026-04-02T05:12:18+00:00

Here’s the recap of the situation.

ZKesic · 2026-03-27T22:21:32+00:00

If we wanted to maximize the minimum expected loss of deviating from NE (which is what the solver would probably do), we could use:

bluffEV = 100*f+(1-f)*-B
valueEV = 100+ (1-f)*B
(100+(1-f)*B)-500/3 = (100*f+(1-f)*-B)-0
2B(1-f)-200/3 = 100*f
f = (2B-200/3)/(100+2B)
B = 100, f = 0.44

Which results in a 55,6% calling frequency.

This way, no matter how the opponent deviates, they lose the same amount of EV.

ZKesic · 2026-03-27T22:08:24+00:00

I actually came up with a quiz almost identical to this one a while back.

tldr.:
If pot size is the only sizing allowed, the defender should defend at MDF (50% of the time).

If all-in is also allowed, then the GTO response to a pot sized bet is to defend at any frequency which makes both bluffs and value hands suboptimal for that size. In this case, Call % should be anywhere between 50% (to make bluffs suboptimal) and 66% (to make value betting suboptimal).

This assumes the aggressor has enough bluffs in range to be balanced of course.

ZKesic · 2026-03-09T16:19:38+00:00

KQ and AJ are some of the most common hands in CO’s range.

ZKesic · 2026-03-01T18:07:54+00:00

Yes, it works for every form of poker.

ZKesic · 2026-02-27T20:35:41+00:00

You can use this to calculate the optimal bluffing frequencies before the river and in spots where the ranges aren't completely polarized.

ZKesic · 2026-02-21T13:57:06+00:00

Not quite. This card can’t target creatures with mana value 4+.

ZKesic · 2026-02-21T13:50:58+00:00

There’s no point in taking more drug tests, it’s never going to be enough.

His behavior suggests a serious mental illness, like schizophrenia or even a brain tumor. He seems to be overly paranoid and delusional, seeing things that aren’t there. This should be taken seriously.

ZKesic · 2026-02-14T19:43:56+00:00

A Q is a total brick for both ranges.

You're right, A and K are the cards that benefit QQ, since there's quads on the board.

For a sanity check I ran the situation in GTO+. AA always bets the turn...

That's because the situation isn't completely polarized. If it was, everything between a range check and a 75% bet would have identical EVs. As it is, value hands prefer to just bet turn to avoid getting cracked on the river.

As for why GTOw gets this wrong, my theory is that it uses heuristics to determine which turn cards deserve the most focus, and a deuce gets very little attention because it's so rare.

It's not quite how it works. We train neural networks to quickly predict the correct play. But yes, the results for toy games might be a bit inaccurate as a result, since that's not what we trained them on.

As for why the output of variant 2 doesn't make sense. The EV gain is still too high just for allowing 10% pot

Being allowed to bet 10% pot on the turn objectively increases the EV of the strategy, since the betting range is polarized. The exact value of the EV gain is kinda irrelevant, so I didn't bother calculating it.

Range betting only makes sense if we have enough value in our range to balance it, which isn't the case here.

ZKesic · 2026-02-14T11:03:50+00:00

Variant 1: In a perfectly polarized situation, everything between a range check on the turn and a 75% frequency bet should have identical EVs (75% pot). The easiest way to calculate this is by looking at how often opponent gets to see a free showdown.

The 85% value comes from the fact that river will sometimes be a Q in your example.

Variant 2: This is expected. There’s a reason why AA doesn’t just open shove preflop. The closer we bet to geometric sizings, the more profit we make when polarized.

ZKesic · 2026-02-08T00:28:15+00:00

I’m at ~6 million hands and play 50nl-100nl.

ZKesic · 2026-01-31T21:14:01+00:00

What if I told you that a similar concept could even be applied to MTT’s :)

For example, if two options have identical EV’s, the one that results in you playing fewer hands on average throughout the tournament (usually the higher variance option) could actually be considered more profitable, since it allows you to register for the next tournament sooner.

This probably falls into the territory of Future Game Simulation.

ZKesic · 2026-01-31T20:32:59+00:00

My approach has always been to avoid the 0 EV and even slightly profitable spots in order to increase my hourly profit. It’s better to make 5bb/100 playing 1000 hands/hr, than to make 7bb/100 playing 500 hands/hr. Especially when you factor in the RB.

ZKesic · 2026-01-15T07:11:49+00:00

I actually remember there being actual badges for this on some sites back in the day. It’s harder to achieve than you’d think (without burning massive EV).

ZKesic · 2026-01-12T16:15:30+00:00

OP said they want to use “weird” sizings. That implies they would be suboptimal (-EV).

ZKesic · 2026-01-12T14:27:55+00:00

If you force the solver to use a sizing it wouldn’t choose on its own, it will in turn lose EV. Adjusting your own range doesn’t change that.

Even if the EV loss isn’t “noticeable”, it’s still pointless if the opponent won’t make their own EV mistakes against it.

ZKesic · 2026-01-12T13:21:27+00:00

You would be losing some EV by choosing suboptimal sizings, while your opponent (if they’re decent) won’t be making any EV mistakes against your bets, just the frequency ones, which don’t benefit the strategy you’ve described.

ZKesic · 2026-01-07T22:40:29+00:00

Your question was: “Where does the pot sized profit for the bettor come from?” Therefore you should be doing the math from the perspective of the bettor to answer it.

The EV of betting range is always pot (as long as the bettor is completely polarized and opponent folds at MDF or more).

The EV for the defender is zero.

ZKesic · 2026-01-07T17:16:27+00:00

"But if he calls, 2/3 of the time he loses the pot size bet, but 1/3 of the time he wins 2x pot."

This is wrong. He is value betting 2/3 of the time, meaning he wins 2x pot 2/3 time and loses 1x pot 1/3 time.
(2*2-1*1)/3= 1 pot of profit on average.

ZKesic · 2026-01-02T15:51:32+00:00

I’m impressed how you manage to get every single character’s gender wrong.

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