A Riddle for you:

"If you say my name I won’t exist anymore”

Answer:


The real answer to the riddle is silence.. but the broader point is this:
I am criticizing how typical low stakes NL players utilize implied odds. “Implied odds” are often referenced and treated as some vague indeterminate force. A force that justifies questionable calls and absolves our hero from embarrassment. BUT such thinking is hold ‘em panacea abuse – a single cure for any-and-all confusing poker situations. Don’t abuse implied odds kids… side effects could include reverse implied odds, value owning one’s self, and tragic reductions in bankroll.

Implied odds are real – they can be counted and calculated – and most importantly implied odds can be leveraged to make optimum plays and boost your win rate. I am going to share my methods for quantifying implied odds. If you read this thread and mimic my formulas, that is a start in the right direction. However, what I really want to accomplish in the thread is to get players spending time at the table refining your own implied odds assumptions. I want you to develop a process of assigning implied odds mid-hand, determining call/fold, vetting results, and adjusting. (Observe, hypothesize, experiment, analyze, rinse/repeat… AKA – the scientific method). A lot of this is going to be “lol duh obvious”, but then say to yourself.. am I putting specific dollar amounts on implied odds? That answer needs to be “YES!”.

I am not about to launch into a “fold everything” rant. In fact, quite the opposite. I am going to go through some situations where we should be calling when “way” behind… but doing it with solid mathematical reasons.

Generalizations:

Rule 1) DIRECT ODDS COME FIRST (when do we use implied odds?)
Wait… rule 1 about implied odds is don’t use them? Well, yes…
Implied odds only come into play if direct odds do not settle the issue. There is nothing more concrete than direct odds. If the pot:call ratio outweighs your odds to hit - you have direct odds:
(cards in deck) / (# of outs) < (resultant pot $) / (call $)
... you have you answer already – do not fold!

If direct odds do not satisfy a call, we are by definition in a situation where
(cards in deck) / (# of outs) > (resultant pot $) / (call $)

So now we turn to our implied odds formula to figure out whether to fold or call:
The criteria to call is:
(cards in deck) / (# of outs) < (resultant pot $ + future villain $) / (call $)

** and if your opponent has redraws then we make a correction on the (result pot + future villain dollars) part. Simply, we take 1/5th of that amount away for every 5 villain re-draw outs. The formula becomes***

(cards in deck) / (# of outs) <? (25 - redraw outs)/25)*(resultant pot $ + future villain $ ) / (call $)

Note: it is not necessary to worry about redraws when calculating a call ON THE TURN. Redraws matter when calculating a call ON THE FLOP.

Every factor in that formula is exactly known except for future villain $. The rest of this thread deals with theory on how to arrive at an accurate number for FVD (future villain dollars).

Do not use a judgment/feeling on whether or not to call. Instead using a judgment/feeling on what amount is future villain $. THEN let the odds take over. Succumb to the formula ! Trying to develop a “feel for fold/call” is destined to fail. Especially when the odds are long – there is just too much confirmation bias when you miss a gut shot ten times in a row or miraculously make it twice in a row. However, developing a feel for future villain dollars is feasible and can be practiced during every hand at the table. Plus you are developing a flexible method for correctly figuring out implied odds.

Concrete Constraints on FVD (future villain dollars):
Rule 2a) COUNT THEIR STACK SIZE
Make sure said suckout victim villain can pay the debt that you are counting on. But ALSO know if villain is committed to a pot already. If villain is committed, it is much more likely you can get the rest of that stack no matter how obvious your outs are.

Rule 2b) COUNT YOUR STACK SIZE
Make sure you are *qualified* to take Villains money.

Rule 2c) …STOP COUNTING STACK SIZES (Big Stack to Pot Ratios)
There is a practical cap on your future payout. With extremely deep stacks and a small pot – you are not going to get paid off by QQQ for $1000 future dollars in a $10 flop pot. Stack size is not everything for implied odds… villains will use some sense. You might get runner-runner quads on your bottom pair 0.1% of the time, but you are not going to get paid 1000:1 implied odds. Don’t let your imagination get carried away…

Fluid Constraints on FVD (future villain dollars):
Rule 3a) OPPONENT’S RANGE MATTERS

-Stronger villain hands offer better implied odds – very simple, an opponent with a strong hand is going to be willing to commit more chips on future streets. Sets pay off straights. Overpairs pay off wacky 2-pairs,.. etc.

-Muddy ranges (AKA wide ranges) lead to a lot of uncertainty on implied odds. They also lead to reverse implied odds where your outs are “dirty”. Paradoxically, villain’s range will get clearer deeper in the hand. But as that range takes shape, we are burning cards and chips – and our opportunity to cash in on implied odds closes.
So what does this say? Basically, we should be more bold drawing against players who are easy to range. Against a narrow range we can accurately predict outs and pay-off. If we have nut-outs, then half of the mystery is solved (all outs are good), but it is still important to know what payout to expect. So don’t completely disregard Villain’s range when deciding whether to draw towards the nuts. We still need to know how much the nuts are worth.
Some of the easiest players to range EARLY in the hand are nits. “So you are saying I should be calling nits’ premium range?!?”.. kind of. We can find implied odds against all players who are transparent preflop and still pay off post flop. Those KK+ nits fit the bill. If we find ourselves with a draw on the flop against an overpair, we can be pretty certain about implied odds.
There are of course other ways that opponents can be transparent, even loose opponents. There are BET SIZING TELLS, POSITION TELLS, and even PHYSICAL TELLS can be leveraged for hero to range villains early and accurate. Also, some passive players are transparent on the flop when they make the unexpected raise. Don’t always run from these monsters, first do the math to see if you can draw. You can find +EV outside of our bread and butter “get worse to call” and “get better to fold”… there is real +EV in “call, catch up, charge them for my new hand”. Against narrow range opponents, we can identify these +EV implied odds situations easier, and be confident in our reads.

Remember, when wading in implied odds – you are going to be behind! Get used to this. Don’t let the strength of their hand leak into auto-fold. STRENGTH is good – it means the villain will pay off. I am not scared of sets, I am not scared AA pre-flop.. I am scared of the lights being off. That monster in the closet looks a lot like a teddy bear with the lights on. Now go take Teddy for a $1k pot, crack his aces, felt him without remorse. Scooping a huge pot with a wacky gutshot straight is also fantastic for your table image…. Poor Teddy.

Rule 3b) OUR SECRET RANGE
The more concealed our hand, the better implied odds it offers. Gutshot straights are concealed . Gapped two pair are concealed . Trips/Full-house boards are obvious . Flushes are obvious .

Two things to consider about implied odds and hands involving flushes:
a) Hero drawing for a flush REDUCES Implied odds (flush boards are obvious)
b) Villain on a made flush REDUCES Implied odds (paired boards are obvious)

The implied odds are not gone, they are just reduced. You will not find huge implied odds on any board making a flush.

The best implied odds come from winning with goofy straights, turned sets, and odd two pair hands. It is even better if we make one of those concealed hands when the board includes a missed flush draw, as all villains are suspicious of “missed my flush” bluffs.

Rule 4) KNOW YOUR VILLAIN
Specifically, know how you are going to extract your implied odds. Villains don’t have to call your bet to supply implied odds… they could keep betting themselves. To maximize implied odds, we are looking for aggro players or call stations. They are both people who move chips. Aggros and Stations just respond to different methods of extraction. Weak tights do not offer great implied odds. Know your plan for that miracle turn card before it comes. Are you going to let your opponent with AA continue to try to bet out flush draws? Are you going to overbet shove into a call station? Think through each scenario before calculating implied calling odds. It will help tremendously in gauging how much payoff you can collect.

Be aware of “pot unaware” villains. Against better opponents you can count on “implied odds are a ratio of bet/pot I am facing”. But many fish are pot size unaware – so their future bets or calls may not relate to pot size in any logical way. Several villains think in absolute dollar terms. Despite a $500 pot, a $300 river bet may be scary for fish X. Conversely, a terrible player may bet tiny and call huge – implicit odds are great in this situation. Make sure to consider this when approximating FVD.

So what do we do about weak-tight opponents.. they offer horrible implied odds – do we always fold?...
Well, they don’t bet much and don’t call much. BUT - If you can range them, you can still leverage these “draw boards”. Bluff them relentlessly when obvious draws come in. If they won’t pay you off for having the flush, then you never needed the draw in the first place. Add “bluff-outs” to your DIRECT ODDS calculations. Villain always folds when the flush arrives? Then draw at two pair and the “flush”. You may get paid on the sneaky two pair, and get a fold on the fake flush.


Formulas and Practical Application
(So tl;dr… basically I just described “learn poker and apply”… wow.. sarcastic-thank-you bip!..)

Well, hold on... now onto the math I promised!
Before I gave you my very simple formula, I wanted to give you the why. You can thus adjust the formula to your liking since you now understand my implied odds reasoning.

My simplified formula has three situations:

a) Not sure about my outs and if they are clean.
= Your implied odds are ZERO.

b)Villain is scared money
-or-
I am going for a flush or a 4-straight (obvious boards)
-or-
Villain has a flush and I am going for a Full House

= Your villain will call the same bet you just called for each street left. (so if I called $40 on the flop to make my draw on the turn, I can expect $40 turn + $40 river for a total of $80 Future Villain Dollars)

c) Draw is sneaky PLUS villain is aggressive
-or-
Villain is a call station

= We will get pot size bet for each street left. THIS GROWS EXPONENTIONALLY.

Situation C is where you can find some crazy long odds calls. Warning: be prepared for high variance poker chasing 10+:1 draws

***
That is it… my formula. Could have saved all that reading and skipped to this section… lucky you if you did skip here

***

AGAIN – why are we in implied odds territory:
- We have a good tight range on opponent and he has a relatively strong hand
- We are behind but certainly have some clean outs
- Villain will not fold to a semi-bluff
- We do not have direct odds to call. (usually because our outs are few or opponent made a decent bet)
- We know villains tendencies on future streets. (Does not always mean they stack off, just means we accurately depict them in our formula)

(Again, if villain is MUBS fold happy, then forget implied odds and add all obvious draw “outs” to your direct odds. These are “bluff” outs. That is not an implied odds situation, because we are not expecting calls.)


Exercise / Example Hands:


Weak-tight with overpair in BB, we have middle pair on the button:
$1/$2. Effective stacks $300. We are on BTN with 8c7c. Folds around, we make it $8. Weak tight on BB 3-bets to $20… he has been waiting for 3 hours to re-pop our relentless button raises. We call $12 and see a flop. Flop comes T73 rainbow. Pot is $41. Weak-tight villain seems just as happy as he was pre-flop and bets $20. His range is QQ+. What are our implied odds.

-We have clean outs and villain has a narrow range.
-Well, this more fits the “same bet we are calling” model. So let’s figure we can expect to make an additional $20 per street if we hit the turn (say villain bets turn, then check-calls one more bet):

Are our odds to hit less than payout odds? Use the math. Note villain has (3) tens, (3) 3s, and (2) QQ+ to redraw if you hit two pair. They have just (2) QQ+ if you turn trips. Let's balance that by setting villain outs to 5:

(45 cards) / (5 outs) <? ((25-5) / 25) * ($81 resultant pot + $40 future) / ($20 call)
9 <? ((0.8) * $121) / $20
9 <? 96 / 20
9 <? 4.8 … NO
Not enough implied odds to call… *with this model

Passive-tight with overpair in BB, we have middle pair on the button:
However, let’s say you have broken away from my basic situations… you have tuned your future villain dollar gut and you think this particular opponent is loose-passive. They will call a 3/4 PSB on each street if you hit:
(45 cards) / (5 outs) <? ((25-5) / 25) * ($81 resultant pot + $60 turn + $150 River) / ($20 call)
9 <? ((0.8) * $291) / $20
9 <? (~230) / 20
9 <? 11.5… Yes! We make money by calling here.

The point is picture your turn and river plays and get a feel for what you can expect in payouts. You can see the villain dependency of each play. There is a big difference between get pot proportioned bets on the river vs flat "same bets". The villains who call bigger bets offer better implied odds... of course
Now, if villain in the first example is really that much of scared money that they will fold to 3/4 pot bets on the turn and river… we still call on the flop.. but for an entirely different reason. We are going to float the flop and bluff the turn and river. See how screwed OOP villain is who cannot size bets properly? Do not be that villain. Also note that there are many other plays available. If you find that rare “fold overpair” for min bets villain listed in example 1 – you know how to bust that guy (.. if he existed - bluff relentlessly). The point is to exercise your implied odds feel – see how much future dollars really are – you can justify a lot of calls you might have previously stayed away from. Also, sometimes you miss and you can bluff anyways – there are scary turn cards that you can add to your “bluff outs”.

Now onto the real game changing long odds with villains who move money:


Villain has a set, we have a gutshot draw.
$1/$2. Effective stacks $400. EP limps, we raise on button with 9c6c to $10, bb calls, EP calls. Flop comes K75 rainbow. Pot $31, BB checks, EP checks, Hero bets $15, BB raises to $50, EP flats.. action to hero. Turn off your “Holy **** EP just flatted $50 cold” monster warning… the warning is right, but this may not be a fold:
What conditions are met:
- Villain has a monster
- Our draw is sneaky
.. so we can get paid off here with the exponential model. Let’s check the odds:

Very important – we close the action on the flop here. BB range is a good Kx+, but EP is pretty much always 77 or 55. Our outs are clean and are to the nuts. We want any one of four beautiful 8s on the turn. then we need to fade 10 redraw (full house/quad) outs from villain:

Note that the villain's stack exhausts, we cannot get POT,POT on turn-river, so cap the payout at their stack size + flop pot

(45 cards) / (4 outs) <? ((25-10)/25 * ($340 + $181)) / $35
..(practice these situations and the math gets more natural)...
~11 <? (0.6 * 521) / 35
~11 <? (312) / 35
~11 <? 9... .. not quite there.

HOWEVER, what if we were deeper?
Let's make effective stacks $800. In this case, the villain can handle a full POT-POT turn-river line. Math gets easier here. There will be 5 *pots* of payout (the pot on the flop, the pot size bet villain calls on the turn, and the 3 *flop pot size* bet villain calls on the river). We can shortcut the redraw math by simlpy removing 1 *pot* for every 5 outs. Villain has 10 outs, so the math is:

(45 cards) / (4 outs) <? (3 * resultant pot) / call
45 / 4 <? (3 * 181) / 35
~11 <? (~$540) / $35
~11 < ~15.5
.. That is right. We are in long implied odds territory. 10:1 to make it on the turn, but we are getting ~15:1 to call. How often would you have call a gutshot draw against a known set on the flop?... you missed out on $12.50 of EV if you did. 6 BB spot is nothing to scoff at.

Also, take note of this - $50 raise is too small to price out a GUTSHOT when deep! Now imagine if the board is wet - then you need to be slamming the bets with a set. Even if the board is dry, do not just flat cold call a raise and think it is sneaky. No one is paying you off for deception… beware when money goes in on the turn. If you are EP villain, go ahead and 3bet that flop!


Once you have made the hand, start charging your opponents! If we have picked our situation right, then:
- Villain has attachment to his strong hand and still believes he is ahead
- Our draw was concealed
- Villain often has redraws..!
So start claiming those exact implied odds you counted on. Often you will be check-raising OOP and raising IP. Just because the payouts were calculated with POT-POT line, does not dictate you need to follow that line. In the hand above, I would raise-shove the turn when I hit.


Best defense is a good offense
Now, beyond figuring out when to call – consider implied odds when placing bets yourself. The goal of betting is to make villain make an equity mistake. The size of your bet factors into this huge. You can easily determine a pot size bet makes almost any call by villain a mistake… but how to you properly adjust for implied odds? Playing from our perspective, one part of the mystery of implied odds is removed… you now know how much you will call. However, a more complicated part of the mystery is added in – what is villain drawing at? My advice, count on villain for 5 outs on dry boards, and 9 outs on wet boards. If villain has a huge draw (like 15 outs), you will typically get raised anyways and a new dynamic takes over (shove first opportunity when you believe you are ahead.. might be the turn). By betting as if villain has 5 outs (two pair/trips draw), you avoid putting yourself in situations like we demonstrated above. These are MINIMUM bets – always bet as big as you think villains mistake will go, but here is the math:

So on a dry board.
$1/$2. Villain in EP limps, Hero in MP w/ AK raises to $8. Folds to villain who calls. Flop comes AJ2 rainbow. Villain checks. Pot is $19, what is my minimum bet?
Villain is loose reg, but will bet ABC with the goods. Villains calling range OTF has lots of Ax and Jx hands in it. If I am willing to call 2 future streets of 3/4 PSB from Villain (turn and river), let’s try different flop bet sizes and see what odds we offer:
a) $10 into $19 pot.
Work through a case where villain has QJ. He has to call $10 OTF into what results in a $39 pot, yet he can count on us calling $30 on the turn and $75 on the river. We will consider our redraws at 4 cards. (If he hits trips, we have 2 outs. If he hits 2 pair we have 5 outs.) So his implied odds are:
(cards in deck) / (# outs) <? (0.84 * (resultant pot $ + future $) - call $) / (call $)

(45) / (5) <? (0.84 * ($39 + $105)) / ($10)
9 < 121 / 10
9 < 12.1 !!
.. we are offering him implied odds. Let’s now try it with a PSB on the flop:
b) $20 into $19 pot. And we will call $45 and then $110
(45) / (5) <? (0.84 * ($59 + $155)) / ($20)
9 < (180 / 20)
9 < 9... Wo!.. what does this mean

So ask yourself this – Would villain fold for $10 but not for $20.. and in which cases is he making a mistake? He is making a mistake to fold for $10, making the right play to call for $10... and he is indifferent at $20. So DO NOT REGRET THEM FOLDING FOR $20, YET CELEBRATE THEM CALLING FOR $10. You want to give the Villain a choice between 0EV and a mistake. Do not give them a choice between 0EV and +EV... and do not give them a choice betwee two 0EV options! So with the PSB on the flop (example above) - villain cannot make a mistake! This is not as bad as giving them +EV options, but I want to give villains as many chances as possible to make a mistake. Basically, go ahead and bet $25 (overpot) and give them an opportunity to mess up. What villain would call $20 but fold for $25?... not many... but the only mistake you can have him make is to call for >$20 .. present the opportunity to him!

** you can size down the bet a little bit if villain does not properly bet back when he hits. i.e. - if he would never 3/4 pot - 3/4 pot you in return... then you can bet smaller. But also factor in - he may never raise! you might have done that betting yourself. Be suspicious when a villain calls a proper size turn bet - your hand may not be good and you might want to throttle down on the river. OF COURSE, KNOW YOUR VILLAIN.

So on a wet board.
$1/$2. Hero open raises MP with KsKd to $8, BTN calls, BB calls. Pot on the flop is $25. Flop comes Th6d3h. BB checks to hero, hero bets $25, BTN folds, BB calls. Pot is $75, turn card is 4s, board is now Th6d3h4s. BB checks. Let’s assume BB Villain is on a flush draw and has 9 outs. However, this villain is a button clicker and capable of bluffing the flush board with a hand like JT so we are prepared to call a PSB on river. But Villain’s only has $230 left. Let’s explore what bet size is appropriate on the turn:

**in this turn example, there are no redraws because action is over on river. of course **

½ PSB of $40:
(44) / (9) <? ($155 + $155) / $40
~5 <? 310 / 40
~5 <? 7.75 .. NO
.. yikes , we did not charge correctly

PSB of $75:
(44) / (9) <? ($225 + $155) / $75 .. remember villain only had $230 on turn
4.9 <? 5.1
... Wow, still haven't priced him out...

Overbet of $100:
(44) / (9) <? ($275 + $130) / $100 .. remember villain only had $230 on turn
4.9 <? 4.1.. phew – that’s right OMC – bet to protect that KK… it is the right move.


Of course, don’t let this be the only factor in bet sizing. Blast away at call stations… Try to induce aggros with checks or small donks, etc… The above bets are just standard plays for standard situations. This is your default, but not your only trick.

Also, when considering your opponents implied odds… they may never bet into you after they make it. Be aware of passive opponents and value owning yourself. If their call on the turn makes no “odds sense”… then they might have outdrawn you already. Size down on the river.

In conclusion many players just opt out of long odds. At LLSNL, you can probably always fold anything without direct odds and get by as a winning player. However, every bit of EV helps – and solving for implied odds pays off big. It also helps your betting lines by recognizing spots where a line might be vulnerable. Hope everyone took something from my article – good luck at the table.

Side *related* Note about the most common implied odds misconception.. set mining:
Implied odds with respect to ranges are often mis-applied preflop when “set mining”… if you are taking 55 against a range that includes AQs, don’t count on that huge payoff. That does not mean “oh, so I only call with pocket pairs when I am sure they have me crushed?”.. No - there are other ways to win hands. Being in position, having the initiative, having the better hand – just don’t think you are always calling to *set mine*. Understand why you are making particular play X. If you are truly set-mining, then you must have ranged villain to a big pocket pair, and you have proof villain will pay off. “I follow a guideline that I need X:1 stack size to call pre-flop with pocket pair”.. Careful! Do not apply this in all situations.

You need > 9:1 to make “out flopping” AA +EV. As that range widens, there are more important factors than strictly stack size. Namely, position.

You see set-mining stack requirements listed all the way from 6:1 up to 15:1… hmm, why the discrepancy? The low odds are quoted to account for the times your pocket pair wins without improving. The high odds camp are conservatively quoted to universally protect players from making big mistakes against wider ranges.

? Hmm… so do the odds actually get lower or higher against wider ranges… the answer is…. It depends Of course Do not confuse two related situations just because your hole cards are the same! All those “in a vaccum” odds are wrong! Understand why you are making a play to plug some of these pocket pair leaks. When you are sure it is AA and the villain will c-bet and never fold – you need ~10:1 to profit. These are implied odds on set-mining. When the range is muddy, there is no universal ratio. Go play poker – weight your equity against his range, leverage position, opponent tendencies, etc. You are doing yourself a dis-service by applying 10:1 blindly for all situations pre-flop. Sounds counter-intuitive, but as that opponent range gets wider and if you are giving up position and initiative, 55 becomes a FOLD regardless of 10:1. If I have 55, I’d rather have fish with obvious AA behind me than a 2+2er with AJo+. In position, different stack sizes+villain+action might make it a shove, a 3-bet, a flat, any number of plays..

In these situations, you need to heavily weigh position, ranges, post-flop tendencies.. You are not playing “set mining” / “implied odds”.

(this thread had a "rough draft" where Aesah asked a question.. I fixed some errors and reposted the entire Original Post to become COTM - but wanted to include this exchange):

Let's just assume the AT,KT,QT,JT part of his range and us are going to showdown regardless... so this part of his range is bet size indifferent. Also, this part of his range is giving us HUGE +EV.. but don't let that blind us to making a slight -EV play against the remainder of his range (the flush draw)...

We can actually make a bet that is proper against the entire range including the flush draw - the slight overbet. Now, from Vs perspective - he does not have a range. He has a flush draw. He also doesn't know proper implied odds drawing math - so we will say he is going to call both a $75 bet on the turn and a $100 bet on the turn. However! He is making the proper call with the $75 bet whether he knows it or not. With the $100 bet, we force a mistake... Yet, you may argue - we shove anyways on river???.. yes, the bet size turned out not to matter when he made his flush. HOWEVER - we realize the EV on his mistake when he misses the flush (34/43 cards) - we make an extra $25 on the turn and he check-folds river. This is a huge +EV for us and huge -EV mistake by villain.

Realize if V acutally played optimally with the draw part of his range, he should have folded on the turn. One critical point to understand - if V is making the proper equity play by calling - THEN we would rather have the fold! As in the original post - I don't want to give V any choice of +EV lines. I want to make him choose between OEV (folding), and -EV by calling. In order to accomplish that against the flush draw part of the range, we must overbet.

(also, a sublety to realize - if we bet the *perfect amount - we give V a choice between two 0EV situations... oops - we just made it so V CANNOT make a mistake!... always give him a poor choice candidate - the overbet does this)

this is a good point - and important for everyone to realize how villain dependant implied odds are... especially with flush draws. Again, the overriding theme in the article is to picture and get a feel for what future dollars villain will commit if you make your draw, and plug that into the formula. I offer "previous bet size x streets left" as a minimum. I also say skip to scenario c (exponential growth) against call stations. Definitely tailor the future dollars amounts to your liking on each villain - but the shortcut formula holds true.

holy walls of text...read most of the first post.

i was not fortunate enough to skip to the formulas

very nice, well thought -out and entertaining read thus far.

scribbed

Everything you said makes a lot of sense. I just need to practice working with the formula before I sit down at the table. Thanks for posting this!

Nice job on the thread. Here is how I do the math which is easier for me to do in my head. My current method doesn't consider the re-draws so I may need to make some adjustments. For the sake of mental math, I assume there are 45 unseen cards (52- 3 on flop and 2 in my hand, 2 in villain's hand). I count my outs, compute the odds against making my hand, then multiply the odds by the size of the bet I'm facing. Lastly, I take the result and compare it to the potential payout if I hit.

Ex. 1
I'll just use the original posters example where we know the villain has an overpair and we are drawing to two pair or trips

Pot is $40, villain bets $20.

I have 5 outs out of 45 cards so the odds of hitting are 5:40 or 1:8 against. To call his bet I need to make 8 times the bet. He bet $20 so I need to make $160 (8x$20) for it to be a break even call. The put currently has $60, so for the call to be profitable, I need to make a total of $100 in future bets.

Ex 2.
Let's use the same bet sizes - Pot is $40 and villain bets $20 - but substitute with the nut flush draw. Here I have 9 outs so odds of making my hand are 36:9 or 4:1 against, so I need to make a total of $80 (4x$20) for the call to be profitable. The direct pot offers $60 in direct odds, so I need to make an additional $20 when my draw hits.

Thanks clubber. Also, that is pretty much similar math (minus the redraw correction).

To break it down how I think through it:

Step one: cards left / over outs.
cards left is almost always 44 or 45, and my outs are almost always 4,5,8, or 9... so those work out to: 11, 9, 5.5, 5... And I actually just generically use "10" or "5" - and sacrifice precision for ease. So remember the cards left / outs number and file it away. Let's call this number OUTS RATIO.

Step two:
This is where clubber goes ahead outs number and multiplies it by the call to figure how much he needs to make up. That is absolutely effective. However, I will start working on this number independently, let's call it PAYOUT RATIO, for two reasons: to make redraw correction easier, and to know how profitable the spot is. i.e. - if PAYOUT RATIO is 2x OUTS RATIO, then it is very +EV. If they are about equal, then I need to be certain on Villain and his range... etc.

PAYOUT RATIO = (pot + future dollars) / call.. pretty easy math.
Correct for redraws: take 1/5th away from payout ratio for every 5 redraw outs. Or more precisely, take 4% away for every redraw out... now this is your preferece... do you have an easier time taking $4 out for every out and $100 of (pot + future dollars)... or do you have an easier time taking 4% out of the result ratio - just get comfortable with either method.

step 3: Just compare OUTS RATIO to your correct PAYOUTS RATIO and decide +EV or not. Again, you don't have to retain much precision. If it works out that Payout ration is ~2x Outs Ratio, who cares if it is 1.89, or 2.13... it is clearly profitable. If they work out about the same, then it is ~neutral EV.. and just go with the ones where you are confident on range and may be able to get more out of villain.

If villain makes the right play by calling for $10, why should we celebrate? Shouldn't we celebrate when he makes the incorrect play of folding for $10? I didn't follow this part, or was it a typo?

Fantastic, and useful, posts. Liked the examples too, to clarify things.

So good for your meta-game when you stack someone after correctly calling with the gutshot. The villain flips, and the table thinks you're a muppet!

@ Jimmy, you understand the celebrate/fold part correctly - it reads funny, but yes, we DO NOT want a call for $10....


Thanks for the feedback!

OK, cheers. Good to know I understood the poker, just not the grammar!

Great stuff. Thanks bip! One of the most well thought out COMs in llsnl

What up bip! I just wanted to drop in and say thanks for this. Last night I called with a gutter in a HU pot for a good price because I remember part of your math here and thought to myself..."his range is weak, he's offering great odds now, king high may be good or if a K hits, I'm good too, plus a little bluff equity on future streets." Turn is check check, I bink the river, he leads 10x his flop bet...I lol in my head and thinking of this thread and the payoff ratio.

I'm going to have to review the math using a bunch of my own examples so it becomes automatic and super quick.

[x] would read again.

Subbed!

I'm a little confused about considering there to be 45 unknown cards on the flop and 44 unknown cards on the turn. Unless the villain is very predictable, it seems like there is enough uncertainty about his hand where we should consider there to be 47 (flop) and 46 (turn) possible cards that could still come out.

I guess this will rarely make or break a decision being +EV or not, but it seems a little generous to think this way.

Very interesting post though, thanks for taking the time for it.

It is a lot of this (change is negligible), but also still not a bad assumption because what strong villain hands include your outs? If opponents range includes weak 1-pair, you aren't really worrying about implied odds as much as his range versus your line and most effective plays.

Also 47 is a prime number.. I generically use 45 and even 40 cards to come to make math easy. The difference is "in the noise" so to speak.

Finally got around to reading this. Nice job, bip!

Nice post.

Calculating for redraws is a big deal. A lot of people assuming 100% equity when they hit, which is often not the case.

Bumped for dragging HUGE pots! Sometimes that small gamble with a big big payoff is worth a tiny risk when deep, against the right opponents.

Well this is about a year late and I'm not sure if anyone will respond to this, but I am a little confused about how your are doing your initial implied odds calculations.

In the begging of your formula when you are comparing your odds of hitting your hand vs. pot odds for flush ex:

45/9 > (Pot odds + FVD)/ Call $)

when im looking at it it seems to me that you would need to subtract your number of outs from the 45 cards to get an accurate ratio. Im am not describing this well i know but my thinking is, should it not be

36/9 > (Pot odds +FVD)/Call $)

36 times you dont hit vs. the 9 times you do instead of, 45 to 9?

Am i looking at this wrong?