The rule of 4 and 2

[Gen Sterling]

A couple of questions from the quote below.

[ QUOTE ]
Alice holds J[img]/images/graemlins/diamond.gif[/img]7[img]/images/graemlins/spade.gif[/img]. Bob holds K[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/spade.gif[/img]. After the flop, the board is 5[img]/images/graemlins/heart.gif[/img]6[img]/images/graemlins/heart.gif[/img]8[img]/images/graemlins/diamond.gif[/img]. If both hands are played to a showdown, Alice has a 45% chance to win, Bob has a 53% chance to win and there is a 2% chance to split the pot...

[/ QUOTE ]

The above is from a Wikpedia article. My question: with 14 outs (3 sevens, 4 fours, 4 nines and 3 Jacks), why isn't Alice's chances about 56%, according to the Rule of 4 and 2?

Okay, let's subtract the hearts, since runner-runner heart would give Bob a flush, and say that she has only ten outs: 2 sevens, 3 fours, 3 nines and 2 Jacks. This would make her chances about 40%, no?

How do we arrive at Bob's chances?

Finally, do we need to discount BOTH the 7[img]/images/graemlins/heart.gif[/img] AND the J[img]/images/graemlins/heart.gif[/img], since if only one more heart arrives, it won't make Bob a flush?

[Micro Donk]

the rule of 4 and 2 arent perfect. theyre supposed to only give an approximation. as the number of outs gets higher, it gets more inaccurate

[cheburashka]

First, you have to subtract outs over 8: 4X14-(14-8)=50. Then, as you mention, some of these aren't clean outs, due to the possibility of a heart flush. And finally, if Alice hits an out, the remaining kings become outs for Bob. So 45% looks about right. But to remove any doubt, you could download (for free) pokerstove, which will do all of these calculations for you:


Board: 5h 6h 8d
Dead:

equity win tie pots won pots tied
Hand 0: 45.859% 44.75% 01.11% 443 11.00 { Jd7s }
Hand 1: 54.141% 53.03% 01.11% 525 11.00 { Kh6s }

[Gen Sterling]

WOW, Pokerstove is nice, tks for the tip.

Yep, I failed to consider that Bob could win with a redraw to the King.

Discard outs above 8? I hadn't heard that. Thanks again.

I'm off to watch J Harman bust up these other chicks on Poker After Dark [img]/images/graemlins/smile.gif[/img]

[cheburashka]

[ QUOTE ]

Discard outs above 8? I hadn't heard that. Thanks again.


[/ QUOTE ]

Careful--it's not discard outs over 8; it's subtract them from your total. So if you have twelve outs, you should win 44% of the time (4 times 12 equals 48, minus the 4 outs over 8 equal 44).

[binions]

[ QUOTE ]
[ QUOTE ]

Discard outs above 8? I hadn't heard that. Thanks again.


[/ QUOTE ]

Careful--it's not discard outs over 8; it's subtract them from your total. So if you have twelve outs, you should win 44% of the time (4 times 12 equals 48, minus the 4 outs over 8 equal 44).

[/ QUOTE ]

Rule of 4 works fine to 11 outs on the flop. Then every extra out is worth 3%. So, 12 outs = 47%. 13 outs = 50%, 14 outs = 53%, 15 outs = 56%.

The reason your equity can be less than your outs suggest is if there are tie outs or foe has redraw outs.