Pot Odds - a little confused

[TheTouch]

Hi there, first post so please be gentle. And I did a search, but couldn't find anything specifically on this topic.

So I've recently been trawling the internet looking for poker strategy tips, and I've come across the concepts of hand odds (rules of 2 and 4), pot odds, implied odds, range, opponent types, bnakroll management etc. and they've really helped me improve my game and understand why I should be taking certain actions at certain times. The one thing I'm really struggling to get my head around is pot odds, and this seems like the right place to ask about it.

My problem is this. Standard advice would have you play the following hand something like this:

You are dealt KQ offsuit.
3 people call the bb, you raise to 4 bb, and that raise is called by one opponent - there is now 12.5 bb in the pot.
The flop comes down with JT8 rainbow, giving you an open-ended nut straight draw, provided no further K or Q comes up (because your opponent could have AK or AQ).
You have 8 outs, giving you a 32% chance of hitting the nut draw by the river - you bet half the pot (6.25 bb, giving you pot odds of 3 to 1, a break even chance of 25%) and it is called by your opponent - there is now 25 bb in the pot.
River comes up as a 2 - with no chance of a flush draw.
You now have a 16% chance to hit your 8 outs on the river - you bet 5 and it's called - there is now 35 bb in the pot.

Standard advice as I've read it would be that you have 6 to 1 pot odds (14.3% break even) and 5 to 1 hand odds (16.7% chance to win the hand), so you should bet, because over 100 hands you will win 35*16.7=583.3 and lose 5*83.3=416.7, giving you an EV of +0.17 bb for the hand, even ignoring the value bet that you can put in if you hit your nut straight. But I'm having a problem understanding the reasoning behind the advice. The problem manifests itself in two ways - first, using the rule of 4 after the flop, when betting only for the turn card; and second, not taking into account the total investment in the hand when calculating pot odds.

1) Why is it standard advice to use the odds of drawing an out over 2 cards when my bet is only relevant for 1 card? It seems to me that if I'm going to be using the odds for drawing over 2 cards, I should be factoring in my bets over 2 cards as well. By this I mean that if I have a 32% of drawing my nut straight by the end of the river, then I should only bet up to 32% of the pot as it will be by the end of the river, rather than 32% of the pot as it will be by the end of the turn.

2) When I look at the example, I can't help but see a situation where playing the overall hand 100 times would actually only win you 19.75*16.7=329.17 (total pot minus total investment), and which would lose you a massive 15.25*83.3=1270.83 (total investment), giving an EV of -9.417 bb for the hand after the turn.

I don't understand why the standard pot odds advice seems to be out of line with the segment of the game you are actually play. Don't get me wrong, I've been using the advice as given, and it has been working, but I'd prefer to properly understand why it works, so that I can feel a little more comfortable in my play, rather than being paranoid that the advice will bite me in the ass at some point.

I hope my confusion makes sense, and thanks to anybody who can help a newbie understand these things a little better.

[celtic123]

Pot Odds - Poker Dictionary Definition

[couriermike]

what you're calling hand odds, most people call equity. you shouldn't fold a draw if equity > pot odds. the rule of 4 is for evaluating flop all-in decisions, not for evaluating flop calls with money left behind (as you suspected), in that case use the rule of 2. betting or raising is different than calling because of fold equity (the percent of times villain folds). usually if fold equity + showdown equity > 50%, you should bet. money already bet is held in escrow by the dealer for the winner of the hand, those are sunk costs and should be counted only as potential winnings, ie part of the pot.

[Openside]

Hey mate. Grats on your first post! A step in the right direction. Somebody more knowledgeable will probably reply before i rattle this answer off but hey, its good for me too so here goes.

You are dealt KQ offsuit.
3 people call the bb, you raise to 4 bb, and that raise is called by one opponent - there is now 12.5 bb in the pot.
The flop comes down with JT8 rainbow, giving you an open-ended nut straight draw, provided no further K or Q comes up (because your opponent could have AK or AQ).
You have 8 outs, giving you a 32% chance of hitting the nut draw by the river - you bet half the pot (6.25 bb, giving you pot odds of 3 to 1, a break even chance of 25%) and it is called by your opponent - there is now 25 bb in the pot.
River comes up as a 2 - with no chance of a flush draw.
You now have a 16% chance to hit your 8 outs on the river - you bet 5 and it's called - there is now 35 bb in the pot.

K, the rule of 2 and 4. If you are facing a decision on the flop then you can only apply the rule of 4 if it is an all-in decision. i.e. you can only use the odds of hitting on two streets if there is no subsequent betting. So in the above example the odds of hitting your straight on the turn are 8*2 = 16%. This is your equity. Lets apply this to your example and you are facing a bet in position. The villain opened on the flop for 6.25 into a pot of 12. You need 6.25/(12.5+6.25+6.25) = 25% equity to call, which you don't have therefore its an easy fold (if we have to hit the straight to win).

Ok, now lets consider the villain checks and you bet 6.25 (a continuation bet [cbet]). The water gets a whole lot murkier now bc its not a straight question of equity, he has checked out of position (oop), which often means he hasn't a strong hand and will likely fold if you Cbet, the chance that he will fold is your fold equity. So the EV of a bet encompasses your equity in the hand and the FE (Fold Equity - Poker Dictionary Definition).
How do we begin to quantify our FE? its situational! Consider how you have seen the villain play and put them on a range! This word is going to haunt your nightmares lol! Have you seen the villain fold a high percentage to cbets? Yes? Then you have significant FE, Cbet. No? Then you FE is reduced and Cbet may not always be best. Range refers to hands the villain is likely holding. As a rule of thumb (a huge generalisation) the later in position a villain is the wider their range. Lets assume villain is a conservative player and he opens pre-flop from UTG. We can put him on a small range. JJ+ (this means pockets pairs from Jacks and up), KQs+, AKo/s. On a flop such as JT8 his range crushes us, we have very little equity and FE. It is unlikely that he would check but if he did he is calling your cbet with his overpairs and draws.

Download this program PokerStove: Poker Software and Analysis. It will help a ton when considering villains range and calculating your equity.

I hope this begins to aim you in the right direction. GL!

[spoonitnow]

1) Why is it standard advice to use the odds of drawing an out over 2 cards when my bet is only relevant for 1 card?

Welcome to FTR.

To answer this question, in general it's not standard advice. However, if you're getting all-in on the flop then it's relevant, etc.

[TheTouch]

I guess I've just come into contact with poor implementations of the rule of 4 then - I thought it made more sense to just apply rule of 2 on the turn bet, and you've all just confirmed that. Thanks

--edit--

I'm still unsure why you only take into account the amount of the bet you're making on that round of betting when calculating pot odds though. In my example we're at 12.5 bb going into the turn. If he bets 2 bb, then standard advice says I have a 12.1% break-even threshold if I call (2 bb / 16.5 bb - 7.25:1 odds) and 16% equity (8 outs, rule of 2, 6.25:1 odds) so I should call. But even if I hit the nut straight, I still look at the numbers and see it, without a further value bet, as making 10.5 bb profit 16% of the time and losing 6 bb the other 84%, giving an expected outcome of -3.36 bb.

Sure, this is where implied odds comes into play, but I still can't help looking at the situation and thinking that actually I'm looking at this particular bet resulting in a total investment of 6 bb (my 4 bb from pre-flop and the 2 bb needed to call on the turn) compared to the pot of 16.5 bb and thus I have 1.75:1 pot odds, with a break even threshold of 36.4%. I'm finding it difficult to understand how the bet is profitable at that point in time, without factoring in the implied odds of future value bets. My expected outcome over 100 hands would be a profit of 10.5, 16 times, and a loss of 6, 84 times. 16*10.5=168, 84*6=504, average expected outcome is -3.36 bb for every time I play the hand.

Yes, if I fold then I will be down 4 bb every time, so playing the hand is more profitable than folding, but it seems that the result is that simply by playing the hand (remember it was KQ offsuit, which is hardly a marginal hand) I put myself in a lose-lose situation. Clearly people do make money playing poker, employing rules and techniques such as these, and indeed they've been helping me since I adopted them, but I'm struggling to wrap my head around how and why the numbers play out the way they do.

[spoonitnow]

I still can't help looking at the situation and thinking that actually I'm looking at this particular bet resulting in a total investment of 6 bb (my 4 bb from pre-flop and the 2 bb needed to call on the turn)

Your pre-flop bet is already in the pot, and is no longer part of your investment (ie: it's no longer yours) since you don't have the option to remove it from the pot when you fold. Hope that helps.

[couriermike]

But even if I hit the nut straight, I still look at the numbers and see it, without a further value bet, as making 10.5 bb profit 16% of the time and losing 6 bb the other 84%, giving an expected outcome of -3.36 bb.

This part is wrong. It's a common misunderstanding, but very very wrong.

Previous bets do NOT count as potential losses from later decisions. They DO count as potential winnings. Previous bets are part of the pot. They do not belong to you. You cannot risk them again in a future decision.

For example, if someone bets at you, at any time in any hand, the EV of folding is always zero. No matter how much you'd previously put into the pot.

In your example, when villain bets 2 into a pot of 12.5 and you call, you're risking 2 to win 14.5, period.

Potential wins and losses must always be calculated from the MOMENT OF THE DECISION, not from the beginning of the hand or any other time. Hope that helps.

[NightGizmo]

Think of the entire hand as a kind of decision tree, and each possible action has a total summed EV underneath it. At each possible decision, you want to pick the one that has the best total summed EV. So, preflop you choose to raise with KQ because you think it's better than checking. That means that you expect the "raise" decision, on average over all possible outcomes, to have a greater EV than checking.

Now you get to the flop, which is just one possible flop out of many. Taking into consideration the flop, your villain, the pot size, and the effective stack sizes, you now have to make a new decision that does not care how much you bet previously. You only have to focus on "what is the most +EV decision for this situation?" If you make the most +EV decision on each street (which sometimes means checking or folding), then you will win in the long run.

For your specific example, however, it's confusing because you wouldn't be betting on the flop or turn based on "pot odds". If your equity in the pot was the only thing that mattered, you would check and maybe call based on your pot/implied odds. The reason you could bet is as a bluff to get better hands to fold, but with the added benefit of possibly making the best hand if you do get called. This type of bet is a "semibluff" and the added value you get from making your villain fold is called "fold equity".

[TheTouch]

OK so your pot odds are based on only your current bet because nothing you can do can change what's already happened, and thus the only odds that are relevant are the odds to make changes from the position you already find yourself in. Is that about right?

--edit--

I missed NightGizmo's last post. That makes perfect sense. Thank you, everybody.

[spoonitnow]

OK so your pot odds are based on only your current bet because nothing you can do can change what's already happened, and thus the only odds that are relevant are the odds to make changes from the position you already find yourself in. Is that about right?

--edit--

I missed NightGizmo's last post. That makes perfect sense. Thank you, everybody.

Yeah exactly. Imagine everyone at a table has $10 stacks with $0.05/0.10 blinds. You're first to act pre-flop and accidentally raise to $9.90 with 72o. It folds to the big blind who shoves. Should you ever fold here?

[spoonitnow]

OK so your pot odds are based on only your current bet because nothing you can do can change what's already happened, and thus the only odds that are relevant are the odds to make changes from the position you already find yourself in. Is that about right?

--edit--

I missed NightGizmo's last post. That makes perfect sense. Thank you, everybody.

Also, when we make a play (bet/check/raise/fold/etc), we're worried about the EV of that current play, not the EV of the hand as a whole.

[Icanhastreebet]

you need 35.1% equity to call with 2:1. Just sayin.

[Icanhastreebet]

unless ur a baller.

[couriermike]

^lol. Another way to think about it is that EV only measures the profitability of the current decision and not cumulative winnings/losses.