Rule of 2

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Running Nose II

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Phil Gordon was the first to coin "Rule of 2 and 4", where you multiplied our outs by 4 on the turn and by 2 on the river. Multiplying by 4 appears to be on the wane, probably because of the huge margins of error .Example : you have 15 outs and multiply these by 4 giving you a 605 chance to win. 605 equates to 0.67/1 against 2,07/1 true odds.
A Rule of 2 (and occasionally 4) evolved to overcome this problem.
You multiply your turn odds by 2. You multiply your river outs by 2 and multiply your turn outs by 4 if opponent goes all-in on the flop.
However even this has its shortcomings as will be shown

Outs X2 Odds to 1 True Turn odds True River odds
3 6% 15.67 14.67% 14.33%
6 12% 7.33 6.83 6.67
9 18% 4.55 4.22 4.11
12 24% 3.17 2.92 2.83
15 30% 2.33 2.13 2.07
18 36% 1.78 1.61 1.55
21 42% 1.38 1.24 1.19
A B C
Although on face value these figures appear acceptable, and they are after all approximate values, they do have their flaws.

Outs % Error on % Error on
Turn, A & B River, A & C
3 6.82 9.35
6 7.32 9.89
9 7.82 10.70
12 8.56 12.01
15 9.39 12.56
18 10.56 14.84
21 11.29 15.97

All figures are to two decimal places, rounded. column A is the percentages converted to a ratio.
If you are happy to use the rule of 2 with the errors shown, carry on. All I'm pointing out are the errors.
 
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Running Nose II

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This is nothing like my original thread. Some %s came out as 5. Spacing gone to hell in a handcart. Wonder if the boss can fix it?
 
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Thenightrain

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Brilliant post, this is how I learnt and massively helped my game.
 
oakthyago

oakthyago

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The post is good but you guys could fix the "%". organization will not kill anyone.
 
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Running Nose II

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oakthyago If you have a problem with this, let's hear it - spout it out.
 
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Running Nose II

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Can anyone in the forum please tell me how you form columns with separation, so that I can sort out the mess above. Thanks.
 
vinnie

vinnie

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I have no idea where some of your conclusions came from.

15 outs times 4 is 60%

Actual odds: 54.4% (give or take with actual cards)

That is a little better than 1:1 not 2:1.

The rule of 4 has its shortcomings, primarily when you have a lot of outs, but it isn't wildly inaccurate. It is usually good enough given that you don't have perfect knowledge of your opponent's hand and what cards are live/dead.

Now, multiplying by 4 is not encouraged. Using the rule of 2 is encouraged, mostly because you might be facing further action. You may not see the river because of a large turn bet. So, when the flop bet doesn't put you all-in, use the rule of 2 unless you are sure you will commit to any bet on the turn anyway. If you are going to be all-in or not fold the turn bet, then use the rule of 4.
 
eberetta1

eberetta1

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I use periods or dashes to create columns...

A......2.25
B......4.72
C......8.86
D....12.99
 
OzExorcist

OzExorcist

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Oh dear...

First of all, I'm pretty sure Phil Gordon didn't come up with the "Rule of 4 and 2", though a lot of people probably encountered it for the first time back in the day in his Little Green Book.

Second, we had this exact same discussion a few months ago and I still don't think you understand how the guideline is supposed to be applied. Here's the previous version if anyone wants to check it out before going over old ground again: https://www.cardschat.com/forum/learning-poker-57/rule-four-two-326009/

Third if you want something to display as a table, do it in Excel or Word or something then screenshot it and upload it as an image (see the one one I uploaded in the previous thread as an example).

We need Chemist to come back in here quoting Hitchiker's Guide again methinks. It worked last time :p
 
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Running Nose II

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Vinnie, I only gave the 15 outs as an example to show the margin of error multiplying by 4. My figures are accurate, perhaps you should revise how to convert percentages to odds.
 
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Running Nose II

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OzExorcist, I wasn't knocking the guidelines, I was merely pointing out the percentage errors in this system
 
vinnie

vinnie

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Vinnie, I only gave the 15 outs as an example to show the margin of error multiplying by 4. My figures are accurate, perhaps you should revise how to convert percentages to odds.
I am quite proficient at doing such conversions. I think your problem comes from not understanding the rule you are critiquing.
 
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ph_il

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Sure, 15 x 4 = 60%, which is a bit off from the actual 54% you're actually getting, but that's a pretty minor detail as it's pretty much an instant call getting better than 50% odds to win a hand.

Here is what you seem to fail to understand: the rule of 2 and 4 is a way to get a quick estimate of the percentage chance your hand has to win. That's it, it's a quick guide-nothing exactly 100% but a fast mathematical method to get close enough.

If you want, in some parts, you can +n/-n after some of the x2/x4 to get a bit closer to the actual percentage.

The way it is applied is meant to be a quick and easy way to see if you're getting the proper odds to call a bet. Lets say, for example, I have 9 outs for flush:

9 x 2 = 18 or a ~18% chance to win. Actual odds is 19.1%

Opponent bets $30 into a $90 pot. I have to call $30 to win $120. $30 is 25% of $120, so the pot odds is 25%

I know 25% pot odds > 18% hand odds, so it's an easy fold.

I did not need to know the exact 19.1% hand odds in order to make this decision.

The rule of 2 and 4 is a guide and nothing more. For more accurate hand odds v pot odds, do the ratio method, but do them correctly. Both method works, but be sure you're doing them correctly when it comes to comparing hand/pot odds and when you need to call/fold. For example, don't do percentage method for hands odds, ratio for pot odds unless you can convert one of them into the other. Ratio: Pot odds > Hand odds = Call. Percentage = Hand Percentage > Pot Percentage = Call
 
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Rational Madman

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I am one of these people who is very bad with numbers but brilliant with actual logic itself.

I picture four columns in front of me (suits) and 13 rows (card types) then I imagine the outs lighting up for me and combo-ults light dimmer while the singular outs shine bright. This helps me with turn odds and river odds. This is all I need to do to completely comprehend what proportion of cards that CAN come up on the turn and/or river will help me, draw me dead or cooler me.
 
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C3H6S

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these its a excelent post ...studing outs and odd...not ever its my way
 
johnny tigre

johnny tigre

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Those number rules will just make you dizzy.

I'd prefer the rule of guts and luck, where you multiply your outs with you gut feel on the turn, and hope that luck will multiply your stack on the river.
LOL
 
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