Rule of 4-2

Running Nose II · Sep 4, 2016

I know that this may cause some heated discussion, but does any other member think that the Rule 4-2 is seriously flawed statistically? The reason is that it uses figures to combine the turn and the river to show a composite result It then goes on to justify this figure to give an answer for the outs on the turn. and a different answer for the river. Assuming a flush draw, two in hand and two on the flop, there are 47 unknown after the flop and 46 after the turn. As near as damnit 4/1 in each case. One card of a difference. There can't be that amount of difference between percentages and odds.

rhombus · Sep 4, 2016

its only an approximation, and gives a good idea of percentages.

There is a slight flaw but that's when there are over 8 outs and there is a modified 4 - 2 rule for that

as for 47 Cards and 46 card you just divide outs by Cards to give the Percentage
Flop to Turn 9/47 = 19.15%
Turn to River 9/46 = 19.57%
Using 4 - 2 each answer is 18% so close enough

FLop to River approx 35%
Using 4 - 2 each answer is 36%

vinnie · Sep 4, 2016

"Seriously flawed"? Certainly not. It gives a good enough approximation within an acceptable margin of error considering that our opponents exact hand is unknown. Sure, it might be off by a few percent, but that difference is surely smaller than the uncertainty of the exact range we are up against. It gives us a good idea if we have enough equity to continue. If the numbers are far from close (we easily have enough equity or we clearly don't), our decision won't change based on the error. If things are really close, it is just going to be a marginal decision either way. We could be off on the number of outs we have/need by more than the percentage. In that case, the error of the calculation isn't our biggest confounding factor.

GWU73 · Sep 4, 2016

The best thing to do is memorize odds for common situations. That way you are not having to do extra calculations when you are playing. This is very useful when multi-tabling.

Otherwise you can do a standard calculation or compute as: outs *2+2 to approximate percentages, and then convert to odds.

chronical · Sep 5, 2016

it's "easy" math to give you a ballpark estimate of where you are at. If you want 0.01% difference between hands either math-up to calculate it evety time or study eatch % for each hand.
Althoug there is obvious difference between 51 % 52 it's not that big that it shoudl affect your play... IMHO

seventhsense · Sep 5, 2016

4 and 2 is good.

It is certainly useful to know the proper maths but I wouldn't bother yet. There are more important components of the game to learn first.

Four Dogs · Sep 5, 2016

rigor mortis said:
I know that this may cause some heated discussion, but does any other member think that the Rule 4-2 is seriously flawed statistically? The reason is that it uses figures to combine the turn and the river to show a composite result It then goes on to justify this figure to give an answer for the outs on the turn. and a different answer for the river. Assuming a flush draw, two in hand and two on the flop, there are 47 unknown after the flop and 46 after the turn. As near as damnit 4/1 in each case. One card of a difference. There can't be that amount of difference between percentages and odds.

You're not looking at it the right way. Yes, in each case you're getting about 4:1 (4.2:1 on the Turn and 4.1:1 on the river) but the rule of 2 and 4 are two related but essentially different things.

The Rule of 2 is used when trying to determine your approximate odds of making your hand on only the next card, the TURN if facing a bet on the FLOP, or the RIVER if facing a bet on the TURN.

The Rule of 4 can only be applied on the FLOP and is a combined estimation of your odds of making your hand with exactly 2 cards to come.

So you see how with about the same number of outs your chances of making your hand with 2 cards to come (TURN and RIVER) are about (but not exactly) twice as great as they are with only one card to come (just the TURN or just the RIVER).

edc1 · Sep 5, 2016

i wasnt aware it was flawed i use the 4-2 rule its fast and easy it doesnt have to be perfect to be effective-i do like four dogs expelenation of it seems like its spot on

George Lewis · Sep 6, 2016

All of these sorts of things just give you a reason to act. We sit for hand after hand folding J-2 off suit then finally find ourselves in a hand and on the flop have a flush draw. We haven't got a made hand but with the draw and not having had any action in a while this gives us a reason to go dog nuts in the hand. If there is a bet we raise! If nobody else bets we do! Why? We have a rule that says we have the right to semi bluff and we finally get a chance to do something! This is great when it works but it sends us into deep depression when it doesn't. Sniffle. These situations work best when we win without having to complete our draw. Causing the current better hand to fold is a beautiful thing. Whether we actually have the odds to call or not as long as we are able to take advantage of fold equity it changes things.

Adict · Sep 6, 2016

George Lewis said:
All of these sorts of things just give you a reason to act. We sit for hand after hand folding J-2 off suit then finally find ourselves in a hand and on the flop have a flush draw. We haven't got a made hand but with the draw and not having had any action in a while this gives us a reason to go dog nuts in the hand. If there is a bet we raise! If nobody else bets we do! Why? We have a rule that says we have the right to semi bluff and we finally get a chance to do something! This is great when it works but it sends us into deep depression when it doesn't. Sniffle. These situations work best when we win without having to complete our draw. Causing the current better hand to fold is a beautiful thing. Whether we actually have the odds to call or not as long as we are able to take advantage of fold equity it changes things.

Do you really need the 4-2 rule to play like this though?

rhombus · Sep 6, 2016

edc1 said:
i wasnt aware it was flawed i use the 4-2 rule its fast and easy it doesnt have to be perfect to be effective-i do like four dogs expelenation of it seems like its spot on

its only slightly flawed, unlike OP who said seriously flawed.

When you have more than 8 outs it isn't as accurate, i.e. if you have 15 outs on the flop with an OESD and Flush Draw you have 15 outs but that isn't 60% (15 * 4)

There is a modified version whereby every number over 8 you subtract that from the final total, so in example above
15 outs x 4 = 60 - 15 is 7 above 8 so take off 7 and the answer is 53%

See pic below and compare the actual odds (Turn or River) to the 4 2 Rule column and Modified column. As you can see the difference gets bigger in the normal 4 2 Rule, whereas in the modified it stays pretty close.

At 20 Outs Actual is 67.53, 4 2 Rule is 80 and Modified 4 2 is 68

Chemist · Sep 6, 2016

42 is the answer to life the universe and everything.

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