Hi guys,

I am looking for a general rule of thumbs to help me estimate the additionnal EV I might get on later streets if I hit (when holding a draw).

Let's make clear that ITT, we don't include the Fold Equity or the direct EV of the move at the current street.

Let's say we hold a good draw like :
-either an OPESD
-or nut FD
-or good FD (K-Q-J high)
-or low FD

Here are 4 different spots :
1. you face a bet on the Flop and have to decided wether or not you call
2. you may bet on the Flop and have to decided wether or not you bet
3. you face a bet on the Turn and have to decided wether or not you call
2. you may bet on the Turn and have to decided wether or not you bet

Let's say that :
-S2PR is infinite
-Numbers of Villains still in the hand on next street = N
-betsize at the current street = X (% of the pot)

How would you estimate the implied EV you might get on later streets?

Here is what I suggest, but maybe I am very very wrong :

1. you face a bet on the Flop and have to decided wether or not you call
Additional EV = (Frequency I hit) * 1.5*turn pot size*N*50%
Here, basically, I think that when I hit, there's 50% chance that I can extract 1.5* the pot size after my Flop call from any Villain.

and I guess we might change the 1.5 number depending on the type of draw :
-either an OPESD : 1.8?
-or nut FD : 1.8
-or good FD (K-Q-J high) : 1.3
-or low FD : 1

2. you may bet on the Flop and have to decided wether or not you bet
More or less the same as in previous spot.
Maybe a bit more than 1.5 because I am the aggressor, so Villain(s) will be more suspicious when I bet (my range is wider when I bet than when I call).
So let's say the average number would be 1.8

3. you face a bet on the Turn and have to decided wether or not you call
Additional EV = (Frequency I hit) * 0.66*turn pot size*N*50%
Here, basically, I think that when I hit, there's 50% chance that I can extract 66%* the pot size after my Turn call from any Villain.

4. you may bet on the Turn and have to decided wether or not you bet
More or less the same as in previous spot.
Maybe a bit more than 0.66 because I am the aggressor.
So let's say the average number would be 0.8


Let me know what you think about these estimations.
I didn't take into consideration the position IP/OOP, which I guess is important too. I'd say we can get 40% more when IP compared to OOP?

Please let me know your own estimations in these spots.
I didn't mention the "Raise" scenario : if you have any idea, feel free to let me know.

Also, maybe we could get this kind of information from a databse, but I don't know how to do that : if you have any idea on how to sort out this kind of estimation, your advice is welcome !!!

Hope this thread might be helpful... at least to me ;-)

up 1 time
still think that is interesting and helpful to estimate well your implied odds...

There is a simple equation for determining how much you must win on the next street when your drawing hand is sure to win if one of your outs hits and villain will always call your bet. This amount added to the current pot determines the required implied odds. The equation is as follows:

FB$ = C$*(Card Odds – Pot Odds)

where

FB$ is the minimum future bet you need to justify calling on the current street

C$ is the amount you must invest (call) on the current street

Pot Odds = P$/C$, where P$ is the pot on the current street after villain has bet.

The implied odds are then IO=(P$+FB$)/C$

Example: Initial turn pot is $50 and villain makes a pot size bet increasing the pot to $100. You have a nut flush draw with equity of approximately 18% (9 outs -2x rule). You want to know what future bet you must make to justify calling the current $50 bet with the condition that if you do not hit on the river you will not bet and will fold to villain’s bet.

P$= 100 C$= 50 eq= 0.18

Card Odds-CO=0.82/0.18 = 4.56

Pot Odds –PO = 100/50 = 2 : 1

FB$ = C$*(CO-PO)= 50*(4.56 – 2)= 128

As a check, EV= eq*(100+128) – (1-eq)*50 =0 .18*228 -0.82*50 = 0

The associated implied odds are (P$+FB$)/C$= 228/50 = 4.56 : 1, the card odds.

The above is not new. This simple model can be extended to include the conditional probability of a win given a hit as well as the probability villain will call your future bet if you hit.

This is what I do, may be just a tad simpler;
(for example assume in position with naked flush draw on the turn)
$50 in the pot
villain bets $50
odds are 2 to 1
I believe there is about 25% of villains range that will bet my improvement cards and his most likey or mean bet size is 1x pot another 25% will check and call a pot sized bet. 25%+25% = 50% of the pot sized bet is $75 so you can just add that $75 to the $50 pot and the $50 bet and arrive at $175, you have to call $50 so your "adjusted pot odds" would be 175/50 or 3.5 to 1.

Then you just have to ask yourself if there are other ways you can improve the value of this spot. Can you bluff effectively (and i mean PROFITABLY) on some cards by virtue of a range advantage or just as an exploit (break even bluffs will not help you ADD value to the call)? Can you hit some cards that will allow you to win at showdown when the river goes check check and if so how often will this be the case. If you can figure out how often it is and how much you win then you can figure out what percent of the pot you will capture in this way and add it to the adjusted pot. Are there some branches in the decision tree that will have your opponent betting and you raising and him calling with worse? What % of his range will bet and call and lose if you use a given size? Take that % of the value of the bet and call and add it to the adjusted pot.

If stacks are very deep then you can go on on and on like this and, while it may not be practical to do so in game I have worked these problems out off table and come to some sort of perplexing results (for instance about how much more valuable semi bluffs can be than you may think at a quick "glance". I found that semi bluffs are much more valuable than the sum of their parts "fold equity + equity does not get you their" and I have found that doing this kind of long drawn out break down of certain spots can really help you to build up intuition about all kinds of spots in NLH, some of them that are not obviously correlated.

I know this off topic a bit but consider a spot where you have a naked flush draw and are pondering a bet or check. The temptation of just finding the EV of your check call and adding the fold equity to it could have you undervaluing the power of semi bluffing. That's because the act of betting your draw effects your opponents range differently than checking and calling so that you fold out a lot of the hands that would not have paid you off and you keep in the hands that are more likely to pay you and in the process you increase the size of the pot once you are called. It may sound kinda obvious now but this was quite an insight for me anyway when I came across it.

OP, i think it's good that you are trying to add this kind of structured thinking to your game. It may seem like the work you do off table will just never make it's way into your in-game play but it really does start to creep in a bit at a time and over the long haul you'll find yourself having a really good feel for what kind of bets are OK to call among so many other things.

I am tempted to launch into a brag about the things I discovered that seemed to go against conventional wisdom and seem to have turned out true. I will give you an example where I don't think a consensus has yet been formed or at least where my opinion is not yet the consensus (i do think YET).
Many players think it is correct to open a tighter range in MTT's when there are short stacks behind you that could shove on you and force you to call them but this violates some of the things i have come to believe as "truisms" about NLH that I found by doing exactly the kind of work you seem to be doing in the OP but across different spots. I expect it to eventually go the other way.. players will eventually realize that they can open wider not tighter when there are short stacks behind them who could move in on them forcing a marginal but +EV call. It seems to obvious to me I can't imagine someone reading what I just typed and not thinking "well, yeah, duh". But that's not been my experience.

Anyway, your OP just reminded me of how happy I am that I have taken time to try and quantify spots and get a structured understanding of common and uncommon situations and analyze them trying to see what "makes them tick". Even if you don't have anything particularly ground breaking and even if no one is super impressed with the conclusions you reach doing work like that I am confident that the process of doing that work will cause light bulbs to come on and aha moments that will help you see the intricacies and strange connections within the game space of NLH poker strategy.

Nice post,
Good Luck!
(keep working things out like this and see what you discover)

Amazing stuff in here...

@Statmanhal the FB/Future bet is the amount we need to make to break-even right so in your example the pot is 100 OTR, and say we hit our draw we need to bet 128 and then villain needs to call 128 for us to break-even/make the EV of calling turn 0... given the other factors as well.

Had another question in regarding a very frequent spot preflop, when hero raises and faces a 3! (assume hero is IP and we are 100bb deep) how do we determine our implied odds for calling with stuff like T9s,87s, or 56s do we use the same FB equation or is there another way?
^
Also now assume we are 200bb deep+...

I think i've heard of a generic rule preflop something like 10 x for pp's 20 x for SC's and 30 x for SG's... i think it's a pretty terrible rule now a days but yeah depends on villain + stacks and a lot of factors.

The pot is 100 after villain bet on the turn, the decision point for calling his bet by considering what may happen on the river .

The generic rules you mentioned are presumably based on experience and/or educated guesses. I don't think I have never seen any analytical justification for them except for noting what the minimum implied odds would be for the case where you always win if you hit, villain always calls your bet and the effective stack is large enough for +EV.

For example, for a set, the chance of a hit is about 12% so the resulting odds are about 7.3 to 1. But they are not enough because you don’t always win with a hit or villain may not have enough stack to give you +EV. When you account for the fact that hitting a low set doesn’t guarantee a win, a model I developed shows required implied odds of 12.7 to 1 for a six pair so the 15 to 1 rule of thumb is not too bad actually. See this thread for some more details.

http://forumserver.twoplustwo.com/32...liway-1667378/

How profitable/+EV will it be to call vs a 3x 3! sizing IP vs a 4x 3! sizing IP?
(Hero raises IP, blinds 3!)

We know that vs a 3x we'll need 33% equity roughly as opposed to vs a 4x we'll need 37.5% equity (not factoring in implied odds)

Hero's Range for raising:


Villain's 3!ing range (assumed a tight range given pop @ my stakes):


This is the equity we have vs villain's range (not factoring in implied odds):


And yeah vs a linear or even polarized 3!ing range our equity is gonna be much higher

---

EV vs a 3x:


EV vs a 4x:

^^^
So let's say we factor in implied odds & the fact we are 200bb deep+ do all these Suited Ax, SC & SG hand combos become +EV?

I dont think this is correct first looks like you assume every next card hits your draw,you need to calculate times you miss next street,I think you should multiply with chances that next card will be card that improves you.
For example you could hold pocket pair and only two cards improve your hand and V bets looks like you odds are the same as you hold monster draw.
And V is folding bit too much(he is folding 67 % when he checks) so it looks like you can float him with any two.

@Evoxgsr96-equtiy is not same as chances your hand is best right now.Stronger range will over realize so even your Axs have more then 33 % equity you lose more money when V has better A so that effectively lowers your EV plus your will not be able to see all 5 cards so your effective equity is much lower then possibility your hand will be the best on SD if you go all in right now.

I dont like this
Let's say that :
-S2PR is infinite
-Numbers of Villains still in the hand on next street = N
-betsize at the current street = X (% of the pot)
If SPR is that high then EV of drawing to the nuts probably go whey up and the lower draws go down in value esp as number of players goes up.I dont think you can make too simple because even computer cant calculate this things.I would try to solve some turn HU examples so you have good feel how good your odds are.Assume some normal SPR then give V and yourself some ranges and go from there.

Reverse implied odds isn't that big of a factor for me as long as i can make exploit folds.

We are IP we will get to realize our equity much more as opposed OOP and again it depends on villain type, again you forget to factor implied odds and vs a 3x 3! sizing with proposed villain's range i think we should def be calling more and then range construction is another story.

Let's assume we have 87s vs proposed villain's range and villain 3! to 3x

Eq = 0.342, Pot = 80, C$ = 40, FB$ = ?

FB$ = 40*(65.8/34.2 - 80/40) = -3.52 lol? (i guess we are getting 2:1 already in direct pot odds still don't get why this number is still -3.52...)

EV = 0.342*(80 - 3.52) - (1-0.342)*80 = 26.15 - 52.64 = -26.49 lol?

Statmanhal plz help

As you noted you have the direct odds to make a call so a required future bet for implied odds need not be calcaulated.

Anyway, if you did the arithmetic correctly, it still works out though the concept of a negative future bet is meaningless.

The equation for future bet in this example is FB$ = 40*(65.8/34.2 - 80/40) which is -3.04, not -3.52 as you have. The corresponding meaningless EV equation is
EV= 0.342*(80 - 3.04) - (1-0.342)*(40 ) = 0

I guess this shows that even meaningless math can work out

Gotcha man thank you for the response btw i really appreciate everything,

So even though we have the direct pot odds to make the call, why is implied odds still not needed to be calculated/factored in?
So is it only times when we don't directly have the direct pot odds to call we have to try to factor in implied odds and see if it will be profitable?

Sort of confused still since we still should have implied odds for calling here correct and that adds a bit of extra EV to our already profitable call?

You are deciding whether to call a bet or not. A primary criterion for such decision is EV. If it is positive then a call is justified (though other choices may be better). Direct or immediate pot odds is one way to make this evaluation. If the pot odds indicate the call decision is not +EV, then you might consider implied odds – the additional odds you gain if you hit your outs and possibly stack your opponent with him calling and you winning the hand.

If you want to do an implied odds calculation when you have the right immediate odds, go ahead. The calculation doesn’t make it more likely you will win, obviously, but can provide more support for your call. BTW, your previous statement, that you are not particularly concerned with reverse implied odds is questionable IMO. Hitting a low set, for example, doesn’t assure a win with a chance of being outset or worse (e.g., flush) being at least 25% under typical circumstances.

Hm...

I guess i misunderstood the relationship between EV and implied odds then?

Like lets say we are 200-300bb deep and villain 3! us and we have 87s (and we know villain is a loose passive/someone who will stack off light/not be able to make folds), why is the fact that we can potentially win a 400bb pot not factored into our EV calcs, that fact alone should apply to all scenarios regardless of sizing?

TBH I guess it's sort of different because we are playing deepstacked so even if we make a potentially -EV decision preflop, as long as we can make +EV decisions postflop it might work out...

I did not say you do not factor in potential winnings when doing EV analysis. If you carefully read my response it says you need not do so if you have the immediate odds for a +EV call on the current street.

Post #4 in the following thread shows the implied odds/EV mathematical relationship

http://forumserver.twoplustwo.com/15...stion-1667847/