Chasing with a Paired Baord

[Chuckster]

Posted this in MTT thread, but I think this might better apply HERE:


If you are getting the correct odds to call a flush or str8 draw, but the board is paired up, either on the flop, or on 4th street, is it overall +EV, to chase the draw?

I seem to be running into lots of boats lately, although I am getting proper pot odds to chase my draw.

This mainly applies for the 1st few levels of MTT, where I like to play my suited connectors.

How do you guy play this?

Thanks in advance

[revots33]

[ QUOTE ]
I seem to be running into lots of boats lately, although I am getting proper pot odds to chase my draw.

[/ QUOTE ]

When calculating the pot odds, are you discounting outs for the possibility of a full boat? Might be enough to swing a call to a fold I'd think. I'm no expert but I'd think a paired board would require better odds to continue chasing the draw, because of the added possibility you're drawing dead.

[gaming_mouse]

This really depends on the action.

Let's assume the worst. The flop action is crazy, it is likely that someone already has trips or a set, and you want to know if you should give it up right there.

In this situation the chance of a boat coming, assuming that your hand does not pair with one of the two remaining flop cards or the turn card (and assuming that no one already has a boat), is:

1-(42/48)*(38/47) = .29

The cleanliness of you own outs is also important, because you are really interested in the chance that your draw comes in without pairing the board.

If your own outs are all clean in that none of them can possibly pair the board (eg, in the case of a flush draw, the two non-paired flop cards are both of your suit), then you should be more inclined to bet. In this case, the turn cannot possibly make someone a boat and give you a flush at the same time. Assume pot size of X BB. Either (further explanation below):

1) You miss your flush.
Gain: -2.5BB
Chance: (39/48)*(38/47) = .6569

2)
a. You make your flush on the turn and someone rivers a boat b/c the board pairs.
Gain: -1.5 BB
Chance: (9/48)*(9/47) = .0359
b. You make your flush on the turn and the river is safe.
Gain: X + 2.5
Chance: (9/48)*(38/47) = .15

3)
a. the turn is a blank (no flush and no additional pair) and then the river pairs the turn and puts a flush on the board.
Gain: -1.5BB
Chance: (33/48)*(1/47)= .0146
b. turn is a blank and the river safely completes your flush
Gain: X + 2.5
Chance: (33/38)*(8/47)= .1478

The numbers under "Gain" need some explaining. I assumed that your decision is whether or not to call an additional bet on the flop, and that you are closing the action, or feel confident that no one will raise behind you.

In addition, assume it will cost you only another bet to see the river, and you will fold the river if the board pairs. If your flush arrives safely, you will gain another bet on the river. You can adjust this number upwards if there are multiple oppos, but HU against a perceptive oppo this is a conservative/realistic assumption. Your EV (in BB) is thus:

.6569*(-2.5) + (.0146 + .0359)*(-1.5) + (X + 2.5)*(.1478 + .15)

.2978*X -.9735

==> X=3.26 to break even.

Which implies that you should usually playe these draws. When all your outs are not clean, this number will be higher. Also, I ignored the case of quads, which will also make the break-even number slightly higher. Finally, we assumed that no one already had a boat. On a flop like AAK, with lots of PF action, this assumption is dubious. I would fold immediately in cases like this.

Anyway, given all the assumptions, I think you could safely play profitably in a pot of 4BB or more.

I'd appreciate any comments on the above... there's a lot of calculation, and I may have made a mistake.

gm

[Lost Wages]

Keep in mind that if your opponent has trips that he can also fill by hitting his kicker which usually proves expensive if you also happen to make your flush.

In general though I agree with your conclusions that you need to consider the action and that it's usually fine to draw to a flush on a paired as long as you have a decent overlay.

Lost Wages

[gaming_mouse]

[ QUOTE ]
Keep in mind that if your opponent has trips that he can also fill by hitting his kicker which usually proves expensive if you also happen to make your flush.

[/ QUOTE ]

Very good point. I should really redo the analysis to account for that. I thought the minimum pot seemed a little to small....