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After the flop, for pot odd does the rule of 2 or the rule of 4 apply, or said differently, do you take into account that there are still two card to come, or do you just look at the next card?

To give an example, suppose after the flop I have a flush draw with four suited cards (two on the board, the other two I am holding). Now we know that we have approximately a 33% chance of hitting the flush on the turn and the river, but just a 17% chance of hitting it at the turn.

So in calculating your pot odds, what probability should be used? For example suppose the pot has size 600, and I have to call 200 to stay in the game. If I call my share at the pot is 25%, or my pot odds are 3:1. Based on the chance of hitting the flush on the next two cards, I should call, as I have a positive probability of winning in the long run, but based just on the next card I should not call.

This always disturbes me, for example when people bring up this standard example of a flush draw and talking about this 33% chance of hitting it. The way I see it we should just take the 17% into account, and the 33% just apply if this is an all-in situation for me, i.e. what happens in the next round isn't relevant for me as I cannot participate, or when I expect that I have not to pay for the river (but this is a very unreasonable assumption in my eyes).

So what do you think? Does this chance of hitting your draw considering both cards to came has any relevance for your betting strategy and pot odds considerations? And if so in what sense does it differs from the chance if you just consider the next card?

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This depends on number of things you have to consider, not only the direct odds. What I mean:

  • The pure odds you calculate should be used if you expect your opponent to check the turn and you see free river.
  • Always calculate implied odds! People usually bet on turn and river!
  • If you expect your opponent to bet on the turn, you have to calculate this too - you must observer opponents and may have clue how much he will bet on turn (1/2 pot, 3/4 pot, pot size). This bet has negative impact on your decission, because you have to put those money to see the river if you do not hit on turn.
  • If you expect your opponent to bet turn/river if you hit, you have to calculate this as positive outcome.
  • If you have observerd your opponent well, you have to calculate his draw bettings too. What I mean: if you have 56 of clubs and you know he keeps pressure on flush draws you have to ask yourself if he is not on better flush draw. Than you have reverse implied odds, meaning that you may loose big if you hit flush and maybe even win if you miss the draw and bluff him on the river.
  • Your position - the most important thing. What is the percentage you may bluff him away if he shows weakness? A danger card for him comes on turn/river, he checks and you bet big?

Hope this helps :)

  • In summary: It isn't that easy :) – StefanH Apr 7 '16 at 10:35
  • It is not, sorry :( – Satory Apr 7 '16 at 11:52
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That depends on what you're contemplating, and what you think future action will be. For example, if you're contemplating a bet that will put you or your opponent all in, then the odds of the next two cards are what matters, because you're buying the right to see both of them. But if you're contemplating calling for a draw, and you both have stacks, well then your call is only buying one card--your opponent will almost certainly bet again--so calculate your odds for only the next card.

This is further complicated by implied odds. If, for example, you're drawing to something that will be well-hidden and you expect your opponent will call your bet or raise if you make it, you can lower your necessary odds a bit.

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Those number are wrong
19.15% turn
19.57% river
34.97% turn or river
(I think you are missing that 5 cards are out)

At the flop if either are all in then you can count on no more bets on the turn.

You have to base it on what you think your opponent will do on the turn

  • If you don't hit
    If they bet in to you on the flop then highly likely they are going to bet turn
    Even if they don't put you on a flush draw it is likely they will c bet
  • If you do hit
    Did your opponent put you on a flush draw?
    Will they shut down if a flush hits on the turn?

You have to expect more bets if you don't hit. The question is can you expect more action if you do hit?

I like : odds
turn 4:1
turn plus river 2:1

4:1 then yes call as you are getting immediate odd
Less than 2:1 then NO as you are not even getting odds for 2 cards

If you think you can get more action if you hit then 3:1?

So assume you can get a 1/2 pot call on the turn plus river if you hit and they bet 1/2 the pot (3:1)
Ev = -1/2p + 1/5*(2*3/2)*p
= 1/10 P
-1/2p is what I had to call
1/5 is my chance of hitting on the turn
2 is the size of the pot after the after the flop
3/2 is the assumption can can get at least 1/2 pot bet called on the turn/river
Positive EV if you think you can get 1/2 pot action if you hit
So 3:1 is maybe
Note if you cannot get any action when you hit then your EV is -1/10p
But on the up side you may get more action than 1/2 p

Continue after the turn if you don't hit is another thing! One big factor is if you hit on turn you have you have two more rounds to get paid off. If they fire off 1/2 the pot again that is 1/2 of a much bigger pot and now you would need to get paid off on 1/2 of much much bigger pot on the river if you hit - not likely. And you need consider they are likely on 2 pair or trips to fire twice like that so now two of your outs are gone to a boat. Your outs are 7 of 46 = 4.6:1. At this point you hope they check to you as about all you can call is a 1/4 pot bet. I see a 1/2 pot call on the flop as trap you only use in the right situation that either gets sprung on the turn or not. If it works you don't want to just get paid off - you want it to sting. Let them think you cannot be chased off a draw with 1/2 pot bet.

Same thing with 1/2, 3/4, and full pot call on flop. If you can get that same action between the turn and river if you hit then a positive EV.

In summary

  • don't expect a free turn

  • if they bet 1/3 the pot or less then stay

  • if they bet the pot then leave

  • if they bet 1/2 the pot (or more) then be confident you can get equal action if you hit

  • if the board pairs then be wary

If someone bets out 1/2 the pot and you call then you have disguised your draw. If you hit the draw they are likely to bet out again. You just have to get 1/2 the new pot (double the flop pot) to call. If they shut down and check to you then chop it into 1/4 turn and 1/4 river. Out of position it is harder to get paid off so go with immediate pot odds unless you are sure you can get more action. In position with a nut flush draw and enough chips to gamble then I might call up to 1/2 pot and maybe even a full pot on a small pot. They probably have top pair, over pair, set, two pair, or just a c bet. You might still get a lot of action even if you hit. If the board pairs then hit the brakes.

  • I do not understand your EV formula? I lose 1/2p, where p denotes the pot size (?) if I bet and do not hit, but what's the other term 1/5*(2*3/2)*p? And why are there not probabilites in your EV formula? – StefanH Apr 7 '16 at 10:33
  • @Stefan 1/5 is the probability of hitting the flush – paparazzo Apr 7 '16 at 10:40
  • Okay, but then you have to multiply -1/2p by 4/5 at it represents the other case with probability 4/5 then? And also where comes the 2*3/2 in your formula from. If I hit, I win 2*1/2*(number of player other then me), i.e. 1/2 for each bet on turn and river (and assuming everyone stay in the game), but why 2*3/2? – StefanH Apr 8 '16 at 20:45
  • @Stefan the pot was p. On the flop it was raised 1/2 (each) so now the pot 2p. Then the assumption is can get 1/2 pot bet called (payoff) on the turn (or river). Add that up and and it is 2*3/2. No I don't multiply -1/2p by 4/5 as the 1/2 p call is what it cost me see the flop period. My 1/2 p call is in the money I get back (if I hit). If you don't believe get some play chips and play it out. – paparazzo Apr 8 '16 at 21:00
  • Ok, I see. But what if you do not hit, neither on the turn nor the river. Then your total lost is -1/2p - p = -3/2p (1/2p from the first betting round, and p from the second), or not? – StefanH Apr 8 '16 at 21:05
0

You always need to consider turn and river bets, yes.

It is very important to consider positions. IP, it is much easier to see ways you can make money OTT and OTR, regardless if you hit or miss. OOP it is a bit trickier.

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