Limit Omaha Hi/Lo $0.50/$1, three backdoor draws on the flop

[MattS]

At first I want to thank everybody, who have answered to my first two posts. The remarks were really helpful.

Here comes another problematic hand:

Paradise Poker
Limit Omaha Ring game
Limit: $0.50/$1
9 players
Converter

Pre-flop: (9 players) Hero is MP1 with 2[img]/images/graemlins/club.gif[/img] Q[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/club.gif[/img]
UTG calls, UTG+1 calls, Hero calls, MP2 calls, MP3 calls, CO calls, Button folds, SB calls, BB checks.

Flop: 3[img]/images/graemlins/diamond.gif[/img] J[img]/images/graemlins/club.gif[/img] 9[img]/images/graemlins/diamond.gif[/img] (8SB, 8 players)
SB checks, BB checks, <font color="#cc3333">UTG bets</font>, UTG+1 calls, Hero calls, MP2 folds, MP3 calls, CO folds, SB calls, BB calls.

Turn: 4[img]/images/graemlins/spade.gif[/img] (7BB, 6 players)
SB checks, BB checks, <font color="#cc3333">UTG bets</font>, UTG+1 folds, Hero calls, MP3 calls, SB calls, BB calls.

River: 9[img]/images/graemlins/club.gif[/img] (12BB, 5 players)
<font color="#cc3333">SB bets</font>, BB calls, UTG folds, Hero calls, MP3 folds.

Results:
Final pot: 15BB

On the flop I have a backdoor nut low draw together with a backdoor nut flush and a weak backdoor straigt draw. Getting 1:10 pot odds, I felt a call is correct. Would have anybody folded the flop?

On the turn I get my nut low draw therefore I call.

The board pairs on the river. Do I have to call with aces up?

[talou]

I'm not very experienced at Omaha (and don't claim to be any good), but I probably fold the flop.

[benwood]

Pre-flop:Most posters are going to tell you to raise with this hand.Its not as clearly correct to me as it is to most,but I do think that the raise is right.After 2 up front callers,it's very likely that one or both of them has an A in his hand,making the chance of flopping a set a distant possibility.If a raise narrows the field enough,it could cause you to win the high end with A's up when a pair hits the board &amp; doesn't make trips for anybody.

Flop:There are 25 cards out of the remaining 45 that will cause you to pick up a nut draw.The pot is laying you 4 to 1 for 1/2 of it.So,1/2 of the time,you will be throwing away a bet,&amp; the other 1/2 of the time,you will be drawing to a low with the odds 2 to 1 against completing or drawing to a flush with the odds of 4 to 1 against completing.All in all,it looks like the call is correct.(This is not the classical way of figuring the odds for back-door draws,but I firmly believe that it is the correct one.)

River:After the turn action,there are 12 BB's in the pot,meaning that if you are heads up on the river,your high end will win 6 BB's.If more players call the river,your high end will be a little more,but your chance of winning it will be a lot less.It's a judgement call as to whether one of the other players has a 9 in his hand more or less than 1 time out of 7.Howover,this does show the value of raising on the flop to increase your winning chances by narrowing the field.

Good luck to you,Matts. Ben.

[JMAnon]

[ QUOTE ]
The pot is laying you 4 to 1 for 1/2 of it.


[/ QUOTE ]

You can't just split the pot in half to figure what your pot odds are when drawing to half the pot. For example, imagine the pot is $8 and it is $1 to you with only one card to come. If you will win 1/2 the pot when you hit, what are your immediate pot odds? If you call and win, you will be returned 1/2 of $9 or $4.50. But it cost you $1 to win the $4.5, so you take only $3.50 from the pot. Thus, your true immediate pot odds are 3.5:1 rather than 4:1 in the example. When drawing to 1/2 the pot, your immediate pot odds are always worse than 1/2 pot : bet. Gergery had an excellent post about this sometime last year, but I am too lazy to search for it.

[niss]

Anyone consider raising the flop bet?

[JMAnon]

I would have raised preflop. That hand is almost as good as it gets and I wouldn't care whether I shut people out with it.

On the flop, I would fold with the pot that size. That is about as big a whiff as you can have, and there is a reasonable chance that it will be raised behind you. Other than a low club, there aren't any turn cards that give you a strong 2-way hand.

On the turn, I would call. The pot was big enough to chase a low.

On the river, when the SB comes out betting and the BB calls, you can pretty much pack it in for your hand, not to mention there is MP still to act. I doubt you even beat the SB 1/15 times the way the betting went down, let alone everyone else in the hand. Then again, this was $.5/1. Was SB so bad that he would lead into four players if he couldn't beat aces up?

[benwood]

Josua.I think you didn't read my post corectly.The bets were in the bot BEFORE any action on the river.In your example,The opponent has already bet the river.In other words,there were 7 bets in the pot after the turn in your example,3 1/2 for each of you.Opponent bets making it 8 in the pot.You call &amp; you each of you still win 3 1/2 each.

In my example,there were 12 bets in the pot BEFORE the next round. Opponent bets making it 13 to you,&amp; you call &amp; you each get 6.My statement abuout how much you will win is correct.

However,I don't want to quibble(what a word)about numbers.I also said that you have 25 chances out of 45 &amp; then proceeded to talk about this as if it were exactly 1/2.I was more interested in the general concept of figuring back-door outs this unique way rather than being numerically accurate,so I know I was a little slack on my numbers.

Thanks for your input,&amp; if you have any critical input about this concept for figuring back-door draws,I would appreciate it.Thanks. Ben

[talou]

There are 10 clubs that keep the flush alive (two of those pair the board, but leave that aside for a minute). The probability of making the flush is 10/45 x 9/44, or about 21:1. The three or nine of clubs could possibly make a boat for somebody, making the high even less attractive to me. An ace gives you a set, but again, the ace of diamonds may make somebody a flush.

For the low, you need one of 20 cards on the turn, plus one of 16 on the river, so I get 20/45 x 16/44, or about 6:1 for the low half.

Is my math right?

I left off the aces because I'm not sure what to do with them. Two outs to make a set, but that opens up somebody else's possible straight (or flush if it's a diamond). 91% of the time you won't get an ace on either street. Sheesh, I'm over my head.

[Baxter]

Talou, great stab at it, now just put it all together. The raw math isn't my strong suit, so I'll let guys figure it out. I think that this would be easier if the OP would have raised preflop though. In these games people will play with any four cards without a raise, but with a raise they won't. This is one of the few hands I'll cap with preflop.

[JMAnon]

Hey Benwood,
I don't think there is anything wrong with calculating odds for a back door draw by treating it as a draw to a draw. It is quite a complicated way to do things (as opposed to throwing the hand into a pot equity calculator). If that is the approach you want to take, here is an example of how I would do it:

If 20 of 40 (to use even numbers) cards will give you a draw on the turn, you have a 50% chance of picking up the draw. To see if it is worth taking a card off, I next need to know how often the draw will come in.

Now say 16 of the remaining 39 cards will complete the draw on the river. Thus, I will have about a 40% chance of making the draw if I pick it up on the turn.

Thus, when all is said and done, I will make my hand 20% of the time (50% * 40%), and 30% of the time (50% * 60%)I will see the river and miss. Now to figure if I should take a card off in the posited scenario, I need to make some assumptions.

To simplify, I will assume the pot is heads up, and that there are 4 big bets in the pot before the flop action. If my opponent bets at me, and I assume he will bet on the turn, it will cost me 1.5 big bets to see the river. If I miss on the turn, it will cost me .5 big bets. If I make it to the river, the pot will contain 7 big bets. Lets assume my opponent always pays me off when I hit by check-calling, for a total final pot of 9 big bets.

So 50% of the time, I lose .5 big bets by taking a card off and missing the turn

30% of the time, I lose 1.5 big bets by taking a card and missing the river

20 % of the time, I win 6.5 big bets (9 - the 2.5 big bets I put in).

In 100 trials, I expect:

to lose .5 big bets 50 times for a total of -25 big bets;

to lose 1.5 big bets 30 times for a total of -45 big bets;

and

to win 6.5 big bets 20 times for a total of 130 big bets.

You would expect to win 60 big bets over 100 hands by taking a card off in the given example. Thus, taking a card off in that situation would be + EV versus folding if you were drawing for the whole pot. Unfortunately, not many draws to the whole pot are as good as the one posited here.

Now imagine you are drawing for half the pot. Everything stays the same, except that when you win, you win a mere 2 big bets when your draw comes in (1/2 of 9 - the 2.5 bets you put in). You now expect to lose 30 big bets over 100 hands.

I recognize that this is a highly stylized example, but it demonstrates how difficult your approach is. If you need to factor in scooping draws and 1/2 pot draws together (like in the poster's hand), it becomes quite complicated quite quickly.

The example also illustrates how bad it is to draw to a backdoor low, because in the example, the pot was big on the flop and it still would have been a big mistake to take a card off, without even factoring in the chance of getting 1/4ed.