Wrong formula in Play Optimal Poker?
On page 55 in Play Optimal Poker Brokos' states that
[...] you want a bluff-to-value ratio equal to the size of the bet divided by the bet plus the pot, or Bet/(Bet+Pot).
He then goes on to use another formula for calculating the required bluffing frequency in a table, adding the same bet again to the denominator. I'm familiar with this formula, it's for calculating the pot odds when calling.
Can someone give me an example of how one would use the formula he gave (shown in quote block)?
12 Replies
In a perfectly polarized situation and specifically on the river, the aggressor will have a bluffing frequency equal to the pot odds given to villain because at that price point and bluffing frequency his calls will be 0 EV. This results in the most EV for the aggressor.
That would be = bet/(bet+bet+pot)
Example: River scenario that is perfectly polarized at 1SPR. Hero goes all-in for 1pot on the river. The OOP player has to call 1 pot to win (1 pot + 1 pot + 1 pot) and has pot odds of 1/3 or 33%. This means IP should have an overall bluffing frequency of 33% if we're to ignore all blocker effects and it's a perfectly polarized situation.
In a perfectly polarized situation and specifically on the river, the aggressor will have a bluffing frequency equal to the pot odds given to villain because at that price point and bluffing frequency his calls will be 0 EV. This results in the most EV for the aggressor.
That would be = bet/(bet+bet+pot)
Example: River scenario that is perfectly polarized at 1SPR. Hero goes all-in for 1pot on the river. The OOP player has to call 1 pot to win (1 pot + 1 pot + 1 pot) and has pot odds of 1/3 or 33%
Yes, and I'm familiar with that equation. However, I'm not sure what his "bet/(bet+pot)" represents.
Is it that he actually means bet: (bet+pot)? Note the colon instead of the forward slash.
I don't have the book, but if he is talking about bluffing frequency, then it's possible it is a typo and it's missing a 2 in front of "bet"
bet/(2*bet+pot)
The equation bet/(bet+pot) will equal the required folding frequency you need for a profitable bluff with 0 equity and no future +EV nodes.
Example same as before:
Hero is on river with perfectly polarized range and at 1 SPR in position. We jam our range on the river. Our bluffing frequency is exactly 33%, but the required folding frequency of our opponent to have +EV bluffs is 50% (bet/(bet+pot)). If you run a sim for this situation you will see all of villains bluff catchers will call at a 50% frequency and be 0 EV. This makes IP bluffs 0 EV and is part of the equilibrium output.
If you can take a picture of the page(s) you're referencing and post them here I'd have more information to guide you to the correct answer.
I was drawing the same conclusion, and it being the requiring folding frequency seems appropriate! It's just that we don't normally talk about required folding frequency, so I became a bit confused.
Here's some context I maybe should have added in the beginning:
Does anything pop into your mind?
It's ratio.
If you bet pot you get 1/2, if you bet half pot you get 1/3, this means you have one bluff for every 2 value combos if you bet pot or 1 bluff for 3 value combos in the case of 1/2 bet.
He specifically says ratio. He should have used a colon. I find that way of thinking about it and explaining concepts less intuitive, so I'm not particularly a fan of how he presented it.
Right! But then again, he does say 'ratio equal to the size of the bet *divided* by the bet plus the pot' so he also seems to really want a quotient, not a ratio. However, a ratio, using a colon, would make it make sense.
I suppose the paragraph has been partly cleared up now, and we're agreeing that it's just a bit confusing.
I'd just like to add that the book is *fantastic* overall. Super great read. I've already bought the second one, and am planning on re-reading this one.
Dang, maybe I should write a book.
There are only 2 poker books you need to read
Mathematics of poker
If that's too much
Expert in HU poker by Tipton
Second one is a bit more practical.
^ both good, but not approachable by most people tbh.
Yeah I've also bought Mathematics of Poker, and am looking forward to approach it like any other math textbook!
the question seems to be solved, but ratios can be expressed with a colon or as a fraction. they have equivalent meanings.