Playing like a maniac (or continuing with the semi-bluff)

[King Yao]

nice post ncray. Is it possible for you to re-do it given that he only donkbets with middle pair 25% of the time?

[imported_ncray]

[ QUOTE ]
nice post ncray. Is it possible for you to re-do it given that he only donkbets with middle pair 25% of the time?

[/ QUOTE ]

In order to calculate the immediate EV of the flop raise? Or, say on the turn? I'm sure that even with a small chance of a free turn card, the flop raise is necessary, especially so if he only donkbets pairs 25% of the time.

Which street(s) did you want the numbers for?

[King Yao]

If you could do it for the Flop, that would be great.

[imported_ncray]

[ QUOTE ]
If you could do it for the Flop, that would be great.

[/ QUOTE ]
Assumptions:
1.He has either a draw (open ended or gutshot) or middle or bottom pair
2.He will call with these hands in the BB (liberal blind defense), so we can assume they are weighted equally
3.When he donkbets, he has middle pair 25% of the time

From before, he will have middle pair 114/360 = 31.7% of the time
Let's come up with some numbers to fit your criterion when he donkbets, he is donkbetting with middle pair 25% of the time

P(donk betting) = P(DB with draw)*36.7% + P(DB with middle pair)*31.7% + P(DB with bottom pair)*31.7%

We see that he has to be donkbetting with middle pair less often if we want the percentage to be 25%. Let's just say that he is more inclined to donkbet draws than he is to donkbet middle pairs than he is to donkbet bottom pair.

Assume he donks draws 100% of the time, middle pair 55% of the time and bottom pair 50% of the time.

36.7 + 17.435 + 15.85 = 69.985
So, the percentage of time that he is donkbetting with middle pair is 17.435/69.985 = 24.91% of the time, approximately 25%

You could tweak the numbers to work out the same by making him donk bottom pair more often than middle pair if you want.

So now, to repeat the EV calculation:
He has a draw 36.7/69.985 = 52.4% of the time he donks
Middle pair 24.91%
Bottom pair 22.65%

Immediate EV of a flop raise: %he has a draw * %you stay ahead * 1SB - %he has a pair * %you stay ahead * 1SB

52.4% * 76.3% * 1SB - 47.6% * 85.1% * 1SB = -.005SB

Wow, neutral EV. If I didn't make an extra assumption about his donkbetting frequencies with different hands, I'd say you already worked out the numbers beforehand.

In sum,
if his donkbet means he has middle pair 25% of the time
if he is more inclined to donkbet a draw (100%) than middle pair (55%) than bottom pair (50%)

Then the immediate EV of a flop raise would be -.005SB. With the possibility of a free card and "taking control of the pot" it's a clear, clear raise. Cheers.

[King Yao]

Thanks for the work. I need to look carefully over your formulas to make sure I agree, but assuming its correct (I have no reason to believe otherwise, but its always useful to make sure for onself), this is an interesting result. I chose 25% because that's what feels like the right number, but I don't have any evidence to say it is. I think its arguable if he would donkbet with made hands more often or less often. Its also arguable if he donkbets with draws or nothing.

But at least now we have a number to work with and we can isolate the argument to that one specific number. 25% is the breakeven point to raising on the Flop (again, pending double-checking the work). If you think he donkbets more than that, then its a bad raise on the Flop.

[imported_ncray]

No problem. Could you let me know if you find any mistakes? I didn't really go over them too carefully. Also, the 25% depends on the tendencies of the bettor, of course.

I'd like to know what your stance is on a numerical approach to poker. It is fairly easy to reduce almost every decision in poker to probabilities (that he has a certain hand or will choose a specific action). However, it's not always easy to estimate what these numbers will be, and we could end up with fairly convoluted equations when isolating variables, especially with multiple people involved in a pot. As it stands, though, maybe such numerical analysis is best used for illustrating broad concepts, such as your book's explanation of the EV of a semi-bluff raise.

[King Yao]

[ QUOTE ]
I'd like to know what your stance is on a numerical approach to poker. It is fairly easy to reduce almost every decision in poker to probabilities (that he has a certain hand or will choose a specific action). However, it's not always easy to estimate what these numbers will be, and we could end up with fairly convoluted equations when isolating variables, especially with multiple people involved in a pot. As it stands, though, maybe such numerical analysis is best used for illustrating broad concepts, such as your book's explanation of the EV of a semi-bluff raise.

[/ QUOTE ]

I only like to do EV analysis on situations that come up often and I think it is most interesting when the EV can be negative or positive based on the opponent's style of play. Since it is impossible for most (me included) to do EV analysis at the table, it is useful to think about situations that occur over and over while not at the table. A common example of this is using a shortcut method to figure out pot odds at the table.

I think it is most useful to look at EV analysis when the EV of a play differs based on the opponent. Maybe the same play would be positive EV against one type of player while negative EV against another type of player. In shorthanded games, the donkbet situation comes up fairly frequently, so it seems worthwhile to do the EV analysis and think about it. Assuming 25% is the breakeven point, it is possible for us to say that raising against some players is correct, while others it is incorrect. To me, that's what makes the EV analysis interesting - when it can be applied to real game situations that come up often, and when the EV varies from negative to positive based on the opponent.