QJo BB flops OESD, turn gives TPGK

[00Snitch]

[ QUOTE ]

Boz is right, but if you don't get it, for some people a more intuitive thought process is you don't add the probabilities of the two events (hitting on the turn or river) together because you have to discount the probability you hit them both, i.e. the union of the probabilities.

Thus: (8/47) + (8/46) - ((8/47)*(8/46)) = 31.45%


[/ QUOTE ]

OK, I'm getting really nitty here over a couple of percent (or maybe I'm being maths dumb again...), but don't you not care if you hit on the turn and river?

So, if you hit on the turn, great, we don't care what comes on the river (disregarding redraws). If we miss on the turn, but hit on the river, that is just as good?

Also, if that second term is the chance of hitting on the turn and river, shouldn't it be ((8/47)*(7/47))?

I'm not being nitty for the sake of it, I just don't know this stuff well. What am I missing?

[marchron]

[ QUOTE ]
[ QUOTE ]

Boz is right, but if you don't get it, for some people a more intuitive thought process is you don't add the probabilities of the two events (hitting on the turn or river) together because you have to discount the probability you hit them both, i.e. the union of the probabilities.

Thus: (8/47) + (8/46) - ((8/47)*(8/46)) = 31.45%


[/ QUOTE ]

OK, I'm getting really nitty here over a couple of percent (or maybe I'm being maths dumb again...), but don't you not care if you hit on the turn and river?

So, if you hit on the turn, great, we don't care what comes on the river (disregarding redraws). If we miss on the turn, but hit on the river, that is just as good?

Also, if that second term is the chance of hitting on the turn and river, shouldn't it be ((8/47)*(7/46))?

I'm not being nitty for the sake of it, I just don't know this stuff well. What am I missing?

[/ QUOTE ]
FYP, even though the answer is no.

This is a little nitty when for most circumstances a rough approximation will do, but since you asked: The reason you can't count both is the same as if you have a flush draw and a gutshot you don't count the card that makes your straight and your flush twice. You have 12 outs, not 13.

Similarly here, we don't care if we hit the turn AND the river, just OR the river. Thus, we discount the times we hit both so we don't double-count them.

If it helps, think of it this way: Eight out of 47 times we'll hit the turn . . .

(8/47)

. . . the other 39 times we'll miss, but 8 out of 46 times we'll hit on the river . . .

(8/47) [+ (39/47) * (8/46)]

. . . = 0.3145 = 31.45%, exactly the same result we get through either Boz' or shu's method. If you want to get algebraically supernerdy you can prove that all three equations are the same. Since I am algebraically supernerdy, here goes:

Let x be the odds we'll hit our draw on the turn, i.e. 8/47. Let y be the odds we hit our draw on the river if we miss the turn, i.e. 8/46.

shu's equation is the simplest to see algebraically:

x + y - xy

But boz puts it like this:

1 - [(1 - x) * (1 - y)]

Here we go . . .

= 1 - (1 - y - x + xy)
= 1 - 1 + y + x - xy
= y + x - xy
= x + y - xy, QED.

Mine is:

x + [(1 - x) * y]

Don't worry, this one's quicker:

= x + (y - xy)
= x + y - xy, QED.

[00Snitch]

Yep. Got it. Because we can:

(hit the turn) or (miss the turn and hit the river).

hit the turn = 8/47
miss the turn * hit the river = 39/47 * 8/46

= 8/47 + (39/47 * 8/46)

Ty march. Pretty easy to forget that crap when you havn't done it since high-school. [img]/images/graemlins/tongue.gif[/img]

If I ever go back and do maths, im so gunna use LDO for QED! amirite!

[texnewb]

:newb grunch:

I think I can see merit to both playing this aggresively and passively. The real problem is that the turn was a J of hearts and you now might be dealing with people chasing the flush, in which case you should raise. On the other hand, you might have people drawing only to a chop with you (hence less outs for them) or two pair. The other thing that worries me is that MP1 fired a second bullet into a field where no-one folded the flop (overpair?). If you raise behind him and drive everyone out, and he reraises you with QQ+ thinking you only have your Jack, you'll be calling as a 78/21 dog. Because of this I think I'd probably call the whole way, but I'm interested to see what others have to say.