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05-09-2019 , 01:36 AM

Bob148

Carpal \'Tunnel

Join Date: May 2012 Posts: 11,972

a no limit holdem situation, multiway or heads up, where the bettor/raiser's range has an average ev of (pot). The trick is that we can't miss any chance to make the most profitable play at every opportunity, nor can our opponents.

in before thread fail

ok go

Spoiler:

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05-09-2019 , 04:42 AM

plexiq

veteran

Join Date: Apr 2007 Posts: 2,554

Seems trivial as asked?

Any river spot where our bettor/raiser always holds the nuts and blocks any other nut hands would qualify. (e.g. bettors range being only AsXs on something like 2s3s9sKxQx)

If you mean profitable play at every opportunity even BEFORE the spot occurs, that's less obvious but should still occur even in GTO play. Basically you just need to hit a jackpot board runout where your opponent's range is capped and you have enough strong hands to force them out of the pot 100% of the time.

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05-09-2019 , 06:16 AM

jkak

centurion

Join Date: Dec 2018 Posts: 140

im sure theres such a spot in the great game of no limit super texas holdem.

i reckon that game will eventually take over since you can use three cards.

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05-09-2019 , 05:04 PM

browni3141

Pooh-Bah

Join Date: Aug 2015 Posts: 5,678

I don't understand. When you bet a properly balanced polarized range on the river, the EV of the betting range is POT. When you have enough value hands that you can range bet then the average EV of your entire river range is POT.

I am certain you'd be aware of this scenario, so why doesn't it apply?

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05-10-2019 , 09:54 AM

Bob148

Carpal \'Tunnel

Join Date: May 2012 Posts: 11,972

I think that if the ev of my range is zero, this indicates a flaw in my strategy on previous streets.

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05-10-2019 , 09:57 AM

plexiq

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Join Date: Apr 2007 Posts: 2,554

If you end up with zero EV on the worst possible 5-card run-outs, that doesn't necessarily mean that the strategy was flawed. You don't get any extra points for making sure you protect those super rare worst cases, they can be rare enough to not matter for your overall EV.

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05-10-2019 , 10:02 AM

Bob148

Carpal \'Tunnel

Join Date: May 2012 Posts: 11,972

Wouldn’t the value of slow play be quite high for me in such a situation?

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05-10-2019 , 10:19 AM

plexiq

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Join Date: Apr 2007 Posts: 2,554

Sometimes, sure. But we are only interested if there exists at least one spot where that isn't the case, right?

You are essentially claiming that playing GTO will prevent us from ever hitting 0EV with our range on any possible board or action sequence. This certainly doesn't trivially follow directly from the Nash Equilibrium definition, so the onus is on you to prove your hypothesis.

It would be straightforward to show that such 0EV spots can be part of the NE in smaller toy games, idk how you'd show that for real poker games though.

Last edited by plexiq; 05-10-2019 at 10:30 AM.

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05-10-2019 , 12:01 PM

Bob148

Carpal \'Tunnel

Join Date: May 2012 Posts: 11,972

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the onus is on you to prove your hypothesis.

bummer. Proving that a negative statement is true (no such situation exists) is usually quite difficult.

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05-10-2019 , 12:07 PM

#10

plexiq

veteran

Join Date: Apr 2007 Posts: 2,554

Same for the positive statement in this case, unless you make the game small enough to make it solvable.

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