Maths Question: River bet sizing when equities know - Beginning Poker Questions

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Maths Question: River bet sizing when equities know

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08-01-2024 , 04:03 PM

MagicalAubergine

stranger

Join Date: Jul 2024 Posts: 14

Potentially a simple question, but I've tried googling and not found anything clear.

So I understand calculating the required equity to make a call, base on a perceived range.

If I knew my equity, against a range on the river, how would this influence my bet sizing?

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08-01-2024 , 04:52 PM

Brokenstars

Verified Coach NLHE

Join Date: Jul 2012 Posts: 16,306

As equities get closer and closer to a purely polarized situation --- nuts vs. bluff catcher situation, then the optimal bet size increases. In reality, different portions of your range can choose various sizings, but again, as it gets closer to the more purely polarized situation the optimal bet size will increase.

Some other general statements:

IP on the river will rarely ever go <50% pot

OOP on the river can basically use any size. You can also think of an infinitely small OOP bet size as equivalent to a check.

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08-01-2024 , 05:14 PM

MagicalAubergine

stranger

Join Date: Jul 2024 Posts: 14

Quote:

Originally Posted by Brokenstars

Thank you, so in a theoretical situation where you have 30% equity would you only bet 30% of the pot? Or is there another mathematical concept that one should refer to?

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08-01-2024 , 06:37 PM

Brokenstars

Verified Coach NLHE

Join Date: Jul 2012 Posts: 16,306

Quote:

Originally Posted by MagicalAubergine

Thank you, so in a theoretical situation where you have 30% equity would you only bet 30% of the pot? Or is there another mathematical concept that one should refer to?

No, if you have 30% equity you wouldn't really be betting.

EV of bet if no raises allowed would be:

EV = (frequency of fold)*(pot in middle) + (1 - frequency of fold)*(your bet + pot in middle)*(equity when called) - (1 - frequency of fold)*(1 - equity when called)*(your bet)

Or roughly = how often they fold * what is in middle + how often they call and you win - how often they call and you lose

It isn't necessarily true to say that you want >50% equity when called, but that is going to be a rough approximation...

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08-02-2024 , 01:18 PM

MagicalAubergine

stranger

Join Date: Jul 2024 Posts: 14

Quote:

Originally Posted by Brokenstars

Hmmm yes this makes sense. I assume the general theory is that if we are betting for value, we want to win more times than not when called (hence the >50% point) and if your equity is less, you have showdown value and would rather check down, unless you think they have enough folds such that equity + fold equity > 50%.

Its all slowly coming back.

Thanks!

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08-02-2024 , 01:43 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 5,038

The following are bet size criteria based solely on EV math assuming villain either calls or folds and you have a good estimate of your equity..

If hero’s equity is >50%, you want a call; a fold has EV = Pot. The minimum bet to assure EV >= Pot is Pot*(1-eq) / (2eq-1). The size chosen should be the maximum that villain is likely to call.

Example: Pot = 10: eq = 60% For EV >=10, Bet >= 10* 0.4/0.2= 20

If your equity is less than 50% you want EV >= 0. The maximum bet to assure EV >= 0 is Pot*eq /( 1-2*eq)

Example: Pot = 10: eq = 30%. For EV >= 0, Bet <= 10*0.3/.4 = 7.5

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