OT: Hold Em Probability Question

[primelord]

I was going to post this in Quik's poker update thread, but I decided it didn't really fit there. Hopefully someone more mathmatically inclined (Quik I am looking in your direction) can help me through this problem.

Ok I know that if I am holding two cards of the same suit and two more of that suit come on the flop that my odds of making the flush by the river are 1.86 to 1 against. Now putting aside whether or not I am drawing to the nut flush etc as long as I am getting 2 to 1 on my money from the pot odds it is clearly worth a call.

However if the turn comes up a blank and I am still one short of my flush the odds are now 5 to 1 that the river will be of my suit. My question is do I then need the pot odds to be greater than 5 to 1 to call? Or am I still banking on that 1.86 to 1 that it would be in one of the next two cards?

It seems like I should be going off of the 1.86 to 1 odds and still just need 2 to 1 pot odds to call. Otherwise I wasn;t really betting on making the flush by the river, but rather making the flush by the turn. Anyone have an explination for which odds I should be going by?

[Bee]

go with the 5 to 1 odds to compare to the pot odds. Every turn should be considered separately and the odds evaluated accordingly. The 1.86 to 1 odds no longer apply and that was used for that call. You now know that one of the cards came up blank, so based on that information the odds have changed and have to be evaluated accordingly.

[QuikSand]

Personally, I think that the notion of assigning odds based on each betting round just falls apart as the game goes onward. It may well be a worthy thumbnail at the flop, but as you are preparing to see your last card, this seems to make no sense -- of course you don't necessarily demand that you have at least five other callers in order to call a bet at this point.

If, like in your case, you have four to a flush -- and the flush would be a winner (say you have the ace, and there are no pairs on the board) -- then I think it's a matter of looking to the pot odds here. Say the bet to you is $6.00 (from a nice little $3-6 game) and you're in late enough position relative to the bet that there is no risk of a subsequent raise. It seems to me that the relevant consideration is: how much will I win if one of my outs hits? As long as that number is at least 5 or more times the amount of this bet, then I think it makes sense to call this bet. So, consider the amoutn currently in the pot, plus what you expect would come there after the next round of betting (and presumably a raise from you) into your calculation in this case.


By the way -- the simple math here: there are 46 cards you have not seen, and there are 9 spades remaining. 9/46 is just about one in five (that's not the same as 5 to 1, buy the way) so we'll use that shortcut for simplicity's sake. You should be getting better than 4-1 on your odds here, though, in most cases.

Of course, the 1.86-to-1 standards is completely out of the picture -- that calculation only holds if you have two remaining cars to come.

[primelord]

Ok so lets say you are in the big blind in a $2-$4 game and you hold Ad 6d. One other player limps in, the small blind folds and you check putting $5 in the pot. The flop then comes out Kd Ks 2d. You check figuring the other player may have made trip K's and he bets. So you are getting 3.5 to 1 from your pott odds on a call here. That is clearly better than 1.86 to 1 to make your flush by the river so you call. That puts $9 in the pot.

The turn is a 6h blank. Again you check and your opponent bets. So now with his $4 bet you are only getting 3.2 to 1 oddos on your call and since it is now roughly 5 to 1 for you to make your flush you are saying the correct call is to fold?

I am not arguing that is worng, but if that is the case weren't you really betting on making the flush on the turn as opposed to over the next two cards on the river? And if that was the case then you weren't getting the correct odds to call the bet on the flop.

[Radii]

Originally posted by primelord
Ok so lets say you are in the big blind in a $2-$4 game and you hold Ad 6d. One other player limps in, the small blind folds and you check putting $5 in the pot. The flop then comes out Kd Ks 2d. You check figuring the other player may have made trip K's and he bets. So you are getting 3.5 to 1 from your pott odds on a call here. That is clearly better than 1.86 to 1 to make your flush by the river so you call. That puts $9 in the pot.


You're getting 3.5:1 pot odds to see the turn. I am not sure what the right answer to your question is, and if it can be spoken in terms of certain odds, but I know your logic above is flawed. Your odds of making the flush by the river are 1.86:1, but your pot odds are only for the next card, so you're comparing apples to oranges. You know that if you don't make your flush on the turn you're going to have to call a $4 bet. You're going to have to put $6 into the pot to win $11, wouldn't that make your pot odds 11:6? But even if my math on those odds is correct, and it may well not be, that isn't enough to say I'm willing to call to the river. You would have to factor in the following things:

1) You say your opponent has trip kings. That means he could hit a full house as you hit your flush.
2) If you make your flush on the river, will your opponent call your raise? The implied odds here change the dynamic a bit.

Is there anything else?

This all feels very, very shaky to me from a math perspective. I can understand the pot odds of one card to come. When we start talking about making the decision to chase your flush all the way to the river I clearly get shaky. Its made worse by the fact that I'm a no-limit player and the strategy there is very different. :P

[Radii]

dola, this gets even more complex I think:

2) If you make your flush on the river, will your opponent call your raise? The implied odds here change the dynamic a bit.


You're first to act. If you make your flush can you safely check-raise and get that extra bet in the pot? If you try to check raise and your opponent doesn't bet, you've lost a lot, but if you know your opponent well enough to know he will bet into the potential flush, and that he'll call your check raise, then you can factor that into your implied odds to continue calling to try to make your flush...


But, in general, I think you want a lot of callers in the pot to chase a flush. My menial understanding of poker theory seems to tell me that going after a flush with just one opponent is rarely a good idea.

[Bee]

Originally posted by Radii
But, in general, I think you want a lot of callers in the pot to chase a flush. My menial understanding of poker theory seems to tell me that going after a flush with just one opponent is rarely a good idea.

Definitely agree. I never chase a flush with only one other caller unless I have other outs.

[Bee]

dola:

also remember that comparing pot odds vs the odds of your hand coming through are just a basic "guide". You have to use experience and knowledge of the table to adjust your play.

[Vegas Vic]

As mentioned in a prior post, don't forget about "implied odds". "Pot odds" are calculated against the money that currently exists in the pot. "Implied odds" are a bit trickier. You must estimate the number of bets that your opponent(s) will put into the pot, and adjust accordingly. This can work in your favor, or it can work against you. For instance, if you calculate that the pot odds justify a call, but there is a possibility of a raise behind you, then you must adjust the odds significantly lower.

For those who don't have it, I would recommend "The Theory of Poker" by David Sklansky. These topics are covered in detail.

[robbgmaier]

It's all a lot more complicated that it might first appear. I get a lot of this kind of thing dealing with the doubling cube in backgammon. Whether or not you are getting the correct "odds" to take a cube depends to some degree on whether or not when things go your way, your opponent will have the correct odds to take your recube.

In this case, Primelord I believe has hit the nail on the head. Deciding whether or not you have the odds to call to see the turn depends in part on whether or not you will have the odds to call to see the river if the turn is a blank. (Assuming, your opponent is going to bet again whatever shows up). It also depends on what your opponent is going to do if you raise when you hit on the turn.

Short answer, your odds of actually hitting the flush with two on the flop don't tell you much.

Longer answer, considering Primelord's example, which I'll repeat.

You are in the big blind with A6 suited, one other player limps and the small blind folds. There is $5 in the pot. The flop hits KK2 and you now have a four flush. You check (rightly or wrongly), and your opponent bets, and you think he's got a king (which seems wierd, but never mind). You also decide that he's going to bet at his turn after each card if you check into him....

So, there are three main possibilities if you call.
1 - You hit the flush on the turn.
2 - You hit the flush on the river.
3 - You miss your flush.

In (1), you will be planning to check raise I presume, and then leading out on the river, presumably getting a call. There were $9 in the pot before the turn, and in the end there was $33. Just pretend that your opponent isn't ever going to complete his hand and work with me :). (You put in 14 of that, don't count the blind, so you're +19)

In (2), you will be calling on the turn and check raising on the river. This turns out to be the same $33. Of course, if your opponent is scared of the flush, you might not get him to bet, and then you'd have $17. If you decide to bet yourself, he probably just looks at you and calls. Let's just for sake of argument say it will be worth $25. (You put in $10 of that, you're +15)

In (3), if you really think you're beat, you're folding on the river. (You're -6).

To figure out the odds on the flop, you have to fast forward to the turn. You have 9/46 to hit the flop and go +15, and 37/46 to miss and go -6. +135 versus -222 means that it is not correct to call on the turn if you haven't made the flush yet.

Now we can go back to the flop. If you hit the turn, you're going to end up +19, else you will be folding, ending up -2. 9/47 to be +19, 38/47 to be -2. +171 versus -76, so it's correct to call.

Obviously we're making a lot of assumptions here, but hopefully you get the idea. Anyone want to check my math, I kind of get into this stuff once I get started.