Can someone please explain the 2 4 rule in holdem

[cuddyblack]

i was told if u multiply your outs by a certain number for the turn and the river it gives u the percantage to make your hand can someone please explain thanks

[d10]

With 1 card to come, your # of outs multiplied by 2 is your chances of hitting that card expressed in %. It is off by 1-2% but it's close. For example a flush draw with 9 outs has about a 9*2=18% chance of coming in on the river (in actuality it is 19.56%). With 2 cards to come you multiply by 4. So the flush draw is now 9*4=36%.

[blaze666]

wow, iv'e never heard of this rule, it is very helpful.

[LINES]

yup. It's great.

[Nottom]

Its a reasonable estimate if the number of outs is low, as you start to get some big draws it can give you some numbers that are pretty far off.

Ex:
You hold Ks Qs on a Js Ts Qc board against Jd Td.

I have a 20 outs draw which makes me a favorite against his 2-pair but I'm certainly not hitting 80% of the time. (It's more like 65% or so)

[MtDon]

[ QUOTE ]
i was told if u multiply your outs by a certain number for the turn and the river it gives u the percantage to make your hand can someone please explain thanks

[/ QUOTE ]

The rule is based on the fact that on the flop you know 5 cards, so the chance of any specific card (such as the 4 of hearts) being delt is:

1/(52-5) =1/47 which is aproximately 1/50 = 2/100 = 0.02 = 2%.

On the river, you know 6 cards, so:

1/(52-6) = 1/46 which is aproximately 1/50 = 2/100 = 0.02 = 2%.

-- Don

[LINES]

ok, you took something as easy as 4/2 and made it even more complicated. Now, i don't evne know what the hell you're tlaking about :S

[Orpheus]

The following shows some of the inaccuracies in the 2/4 rule It'll be long. Please skip it if you don't care.

In short strokes, the 2% rule is reasonably accurate, if you understand why it works. At various stages in various games (Hold-em, Omaha , etc.) you will have a "known number of unknown cards" (i.e. 52 - # cards in your hand - # cards showing on the board) You should simply *know* these numbers for the game you are playing.

IN HE, there are 47 and 46 unknown cards before the river and turn, respectively. In Omaha, there are 45 and 44.

Each of these numbers is pretty darn close to 50. your chance og getting 1 card (1 out) from 50 unknown cards would be exactly 2% (1/50). 1/45 or 1/48 are pretty close, so you get a good estimate for the turn OR river

HOWEVER, the "4% rule" (for turn AND river together)is much less accurate. You can't simply add the results of the 2% rule for the tuen and river separately to get the correct total result. Why? Because the outcome on the turn will alter the probability on the river -- and you need to understand how this effect works for the draw you want to make

Lets say you have pocket jacks, and flop rags. What are your chances of getting a jack on the turn? 1/47 (4.26%) On the River? 1/46 (4.35%) -- 2%/out is 'close enough'.

If you have a flush draw after the turn. Your odds of making it on the river are 9/47 (19.57% -- almost 20% instead of 18%) That's because the slight difference between 1/46 and 150 adds up, the more outs you have. In some situations, this make a difference in calculating pot odds.

Example: JoeAces raised preflop from the SB, which you (savvy reader that you are) know he ONLY does if he has AA. You called with T9s, and because you live a pure life, the flop came 789 rainbow. You have 19 outs to win (4 6s, 3 7s, 3 8s 2 9s 3 Ts, 4 Js) but that also means 19x the error.

In this example, in a multiway pot, you wouldn't fold if you missed the turn, because you'd be 19/46 = 41.3% to make the river. But if it's heads-up at the final table of a tournament, you might want to know your exact postflop pot odds to size your raise. the 4% rule says 76% BUT that's an overestimate. It doublecounts the cases where you draw an "out" on both the turn and river, and we all know you don't get extra credit for making your straight twice, drawing three pairs vs two pairs, etc.

A more accurate postflop estimate of your chances of beating JoeAces would be Pt + (1-Pt)*(Pr) where Pt is your chances of drawing an out on the turn, and Pr is your chances of drawing an out on the river. This result (65%) doesn't count the "overkill" situations. (An even more accurate esitmate would factor in JoeAce's chances of making his set of aces, which would kill many of your outs, but that's beyond the scope of this example)

This is much more important in Omaha, where you can be drawing to [e.g.] two different flushes with one hand, but you should understand it in TXHE -- though it'll rarely change your decisions in actual play, Since the difference will, at worse, turn a slight +EV decision into a slight -EV in uncommon situations, using the 4% rule can only be a small leak, and the time/energy it saves can make it +EV overall, by letting you focus on your opponent.

[chuddo]

[ QUOTE ]

You have 19 outs to win (4 6s, 3 7s, 3 8s 2 9s 3 Ts, 4 Js)

[/ QUOTE ]

AA vs 910s on a 789r flop? how might one go about winning with 7 or 8? by hiding pips?

[LINES]

you are a genius Orpheus. I finally understand, and i can now do this properly at a table.

[kiddj]

[ QUOTE ]
you are a genius Orpheus. I finally understand, and i can now do this properly at a table.

[/ QUOTE ]

To sum it up: the 2% part is accurate enough, the 4% to have your one of your outs on the flop come in by the river is close enough up to about 12 or 13 outs. If you are having trouble with small edges in equity with a lot of outs, you should be using other information to help determine if you can raise/call anyway.

[Orpheus]

[ QUOTE ]
[ QUOTE ]

You have 19 outs to win (4 6s, 3 7s, 3 8s 2 9s 3 Ts, 4 Js)

[/ QUOTE ]

AA vs 910s on a 789r flop? how might one go about winning with 7 or 8? by hiding pips?

[/ QUOTE ]
Good point. I constructed my example incorrectly. In my defense, it was 3am Monday, after a L-O-N-G weekend

I also see that I could have been a little clearer on how I constructed the "revised" turn+river odds.

It's generally: [outs on the turn/47] + [non-outs on turn/ 47]*[outs on river/46]
or equivalently: [outs on the turn/47] + [non-outs on turn]*[outs on river]/[47*46]


Since the denominator of the river term of the postflop win% is always (47*46) = 2162, you could memorize the inverse of 2162 (= .046%), but I'd just bracket it using 2000 and 2500. Since 1/2000 = .05% and 1/2500 = .04%, these numbers won't strain your brainbone. (The actual answer will be ~2/3 of the way between the 2500 and 2000 estimates, to within several parts per million)

Another useful technique is the Poisson method (not to be confused with the Poisson distribution). It sounds fancy, but simply means "sometimes it's easier to calculate how often something WON't happen, vs. how often it WILL" If you're AA v KK with a A37r flop, you'll win UNLESS he draws two Kings. It's a LOT easier to estimate 2/(46*47) ["2" because he can get the two remaining Ks in either order] than to multiply out and add the 2160 cases where you win.

(Using the bracket method above you'd say "the odds are 1/3 of the way between .08% and .10%" = .0933% -- which is only off by about eight parts per million. I'll tell you what: you keep dealing me AA, and I'll eat all the -EV from the inaccuracy, okay?)