Required overlay for flush draw on paired board

[34TheTruth34]

I didnt read all the way through the math junk, but Barry is right. This is an easy call. Another thing you failed to mention (at least in what part of it I did read before I drifted off to sleep) is that a lot of times an ace will be good and another percentage of the time pairing your kicker will be good (assuming it's a 7 or higher). We'll assume your friend picked up the backdoor flush draw as he didn't bet the flop. Some of the time I'd even raise if they are the types of opponents who could be pushed off a small pair. Most of the time nobody will have anything here, and sometimes your ace high is even good. If you are folding hands like this, you are giving up way too much.

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You guys are way overthinking this, IMHO.

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I think you're right. We are discussing minutiae (board variations and holding-by-holding EV analysis) of a subcase of the general problem (just when the bettor has at least trips, not a six or a bluff). I sorta stumbled into it this, though; I stumbled into the subcase because I originally erroneously concluded that this subcase was enough to show that the overall call was profitable; I stumbled into the minutiae because TaintedRogue questioned some of the calculations.

Still a questionable way to spend one's time...

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Look at the board. There is very little chance that the BB is full here.

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Change the 6 or 2 to a broadway card, then you just might have a point.

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I don't really understand what you mean by this. There was no raise preflop and the flop checked around, so the BB has totally random cards. He has equal chance of being full with any board.

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4:1 to make the hand, pot is laying 5.5:1. That's good enough for me.

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If we assume that the BB has at least a 6, then he has tens and sixes 56% of the time (123/218 combos), trips 35% of the time (76/218), and a boat or quads 9% of the time (19/218).

If he has trips, you have 7 outs. If he has a boat or quads, you have 0 outs. If he has a 6, you have 11 outs. But if you always call on the end when you pair your A, you'll be paying off his better hands 44% of the time, too, so it's more like 8.5 outs.

That averages out to about 7.3 outs.

This is a quick, dirty approximation of the situation, but it should be enough to show that you calling in this spot when you are getting 4:1 is always a losing play. 5.5:1 is probably okay.

Big dog David Sklansky will tell you, though, that using the 4:1 figure in your heat-of-battle calculations rather than the more accurate figure is a pretty minor error (in terms of hourly expectation); the situation comes up quite rarely, and you cost yourself only a fraction of a bet each time it comes up. Math dorks like myself make more significant errors all the time, but we try to compensate by grinding out a few more decimal places in our calculations on 2+2.

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EV_trips_spade_kicker = 7/44 * 6.5 + 36/44 * -1 + 1/44 * -2

shouldn't it be 6/44? He cannot catch the spade in his opponent's hand either.

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Say the board is T[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/spade.gif[/img]2[img]/images/graemlins/heart.gif[/img] T[img]/images/graemlins/spade.gif[/img], villain holds T[img]/images/graemlins/club.gif[/img]4[img]/images/graemlins/spade.gif[/img], hero holds A[img]/images/graemlins/spade.gif[/img]5[img]/images/graemlins/spade.gif[/img].

Hero makes a winning boat with these 7 spades: 3789JQK
Hero makes a losing boat with this 1 spade: 2
Hero misses with the 36 non-spades

[TaintedRogue]

Ok.........so I'm definitely not paying close enough attention, which I will attempt to remedy.
Now you're equation:
EV_trips_spade_kicker = 7/44 * 6.5 + 36/44 * -1 + 1/44 * -2
I compute that as:
(7/44*6.5)+(36/46*-1)+(1/44*-2)
(.1591*6.5)+(.7826*-1)+(.0227*-2)
1.0342 + -.2174 + -1.9773 = -1.1605

Is that correct?

Thanx
Ken

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Don't crunch numbers by hand; just use a calculator. Google has a built-in calculator that you could use: just type "7/44 * 6.5 + 36/44 * -1 + 1/44 * -2" into Google and hit "Search".

EV_trips_spade_kicker = 0.170
EV_trips_non_spade_kicker = 0.148
EV_trips = 0.152
EV_boat = -1.2

Google Calculator also does combinations. They're written like this: 52 choose 2