In this article grisan discusses a rule for PP domination http://www.railbirds.com/blog/39314
So here we will consider in the same respect the rule of 4 and 2
also this video explains the rule of 4 and 2 http://www.railbirds.com/video/39224 (grisan)
Here is an Out chart that I calculated in excel: works only for a 2 hole card game like Holdem
| outs |
turn |
river |
turn and or river |
| 1 |
2.13% |
2.17% |
4.26% |
| 2 |
4.26% |
4.35% |
8.42% |
| 3 |
6.38% |
6.52% |
12.49% |
| 4 |
8.51% |
8.70% |
16.47% |
| 5 |
10.64% |
10.87% |
20.35% |
| 6 |
12.77% |
13.04% |
24.14% |
| 7 |
14.89% |
15.22% |
27.84% |
| 8 |
17.02% |
17.39% |
31.45% |
| 9 |
19.15% |
19.57% |
34.97% |
| 10 |
21.28% |
21.74% |
38.39% |
| 11 |
23.40% |
23.91% |
41.72% |
| 12 |
25.53% |
26.09% |
44.96% |
| 13 |
27.66% |
28.26% |
48.10% |
| 14 |
29.79% |
30.43% |
51.16% |
| 15 |
31.91% |
32.61% |
54.12% |
| 16 |
34.04% |
34.78% |
56.98% |
| 17 |
36.17% |
36.96% |
59.76% |
| 18 |
38.30% |
39.13% |
62.44% |
| 19 |
40.43% |
41.30% |
65.03% |
| 20 |
42.55% |
43.48% |
67.53% |
| 21 |
44.68% |
45.65% |
69.94% |
the chance on the turn = outs / 47
the chance on the river = outs / 46
the chance on the turn and or river [ T and or R ] = (1 - chance on turn)*chance on river + chance on turn
here we add in the rule of 2 and 4 and find the deviation between the estimates produced by the rule, and the actual values:
| Outs |
turn |
river |
T and or R |
rule of 2 |
rule of 4 |
dif 2 |
diff 4 |
| 1 |
2.13% |
2.17% |
4.26% |
2% |
4% |
0.13% |
-0.26% |
| 2 |
4.26% |
4.35% |
8.42% |
4% |
8% |
0.26% |
-0.42% |
| 3 |
6.38% |
6.52% |
12.49% |
6% |
12% |
0.38% |
-0.49% |
| 4 |
8.51% |
8.70% |
16.47% |
8% |
16% |
0.51% |
-0.47% |
| 5 |
10.64% |
10.87% |
20.35% |
10% |
20% |
0.64% |
-0.35% |
| 6 |
12.77% |
13.04% |
24.14% |
12% |
24% |
0.77% |
-0.14% |
| 7 |
14.89% |
15.22% |
27.84% |
14% |
28% |
0.89% |
0.16% |
| 8 |
17.02% |
17.39% |
31.45% |
16% |
32% |
1.02% |
0.55% |
| 9 |
19.15% |
19.57% |
34.97% |
18% |
36% |
1.15% |
1.03% |
| 10 |
21.28% |
21.74% |
38.39% |
20% |
40% |
1.28% |
1.61% |
| 11 |
23.40% |
23.91% |
41.72% |
22% |
44% |
1.40% |
2.28% |
| 12 |
25.53% |
26.09% |
44.96% |
24% |
48% |
1.53% |
3.04% |
| 13 |
27.66% |
28.26% |
48.10% |
26% |
52% |
1.66% |
3.90% |
| 14 |
29.79% |
30.43% |
51.16% |
28% |
56% |
1.79% |
4.84% |
| 15 |
31.91% |
32.61% |
54.12% |
30% |
60% |
1.91% |
5.88% |
| 16 |
34.04% |
34.78% |
56.98% |
32% |
64% |
2.04% |
7.02% |
| 17 |
36.17% |
36.96% |
59.76% |
34% |
68% |
2.17% |
8.24% |
| 18 |
38.30% |
39.13% |
62.44% |
36% |
72% |
2.30% |
9.56% |
| 19 |
40.43% |
41.30% |
65.03% |
38% |
76% |
2.43% |
10.97% |
| 20 |
42.55% |
43.48% |
67.53% |
40% |
80% |
2.55% |
12.47% |
| 21 |
44.68% |
45.65% |
69.94% |
42% |
84% |
2.68% |
14.06% |
I have often heard Chris Fergesun say that he wants at least a 40% chance to win a hand to call... using the rule of 4 we would need 10 outs, but in reality we would need 11.
and lastly we calculate the % error ( the absolute error / the actual value )
| Outs |
turn |
T and or R |
rule of 2 |
rule of 4 |
dif 2 |
diff 4 |
% diff 2 |
% dif 4 |
| 1 |
2.13% |
4.26% |
2% |
4% |
0.13% |
-0.26% |
6.00% |
6.00% |
| 2 |
4.26% |
8.42% |
4% |
8% |
0.26% |
-0.42% |
6.00% |
4.97% |
| 3 |
6.38% |
12.49% |
6% |
12% |
0.38% |
-0.49% |
6.00% |
3.91% |
| 4 |
8.51% |
16.47% |
8% |
16% |
0.51% |
-0.47% |
6.00% |
2.83% |
| 5 |
10.64% |
20.35% |
10% |
20% |
0.64% |
-0.35% |
6.00% |
1.73% |
| 6 |
12.77% |
24.14% |
12% |
24% |
0.77% |
-0.14% |
6.00% |
0.60% |
| 7 |
14.89% |
27.84% |
14% |
28% |
0.89% |
0.16% |
6.00% |
0.56% |
| 8 |
17.02% |
31.45% |
16% |
32% |
1.02% |
0.55% |
6.00% |
1.74% |
| 9 |
19.15% |
34.97% |
18% |
36% |
1.15% |
1.03% |
6.00% |
2.95% |
| 10 |
21.28% |
38.39% |
20% |
40% |
1.28% |
1.61% |
6.00% |
4.19% |
| 11 |
23.40% |
41.72% |
22% |
44% |
1.40% |
2.28% |
6.00% |
5.46% |
| 12 |
25.53% |
44.96% |
24% |
48% |
1.53% |
3.04% |
6.00% |
6.77% |
| 13 |
27.66% |
48.10% |
26% |
52% |
1.66% |
3.90% |
6.00% |
8.10% |
| 14 |
29.79% |
51.16% |
28% |
56% |
1.79% |
4.84% |
6.00% |
9.47% |
| 15 |
31.91% |
54.12% |
30% |
60% |
1.91% |
5.88% |
6.00% |
10.87% |
| 16 |
34.04% |
56.98% |
32% |
64% |
2.04% |
7.02% |
6.00% |
12.31% |
| 17 |
36.17% |
59.76% |
34% |
68% |
2.17% |
8.24% |
6.00% |
13.79% |
| 18 |
38.30% |
62.44% |
36% |
72% |
2.30% |
9.56% |
6.00% |
15.31% |
| 19 |
40.43% |
65.03% |
38% |
76% |
2.43% |
10.97% |
6.00% |
16.86% |
| 20 |
42.55% |
67.53% |
40% |
80% |
2.55% |
12.47% |
6.00% |
18.47% |
| 21 |
44.68% |
69.94% |
42% |
84% |
2.68% |
14.06% |
6.00% |
20.11% |
Notice that the rule of two is always 6% wrong ( it should be the rule of 2.1276595... ).
The rule of 4 works best at 6 ( maybe 7 ) outs, and OVERESTIMATES as you increase outs. (It starts by UNDERESTIMATING at 1 and up til (including) 6).
It's still a good rule, but if you wanna make better decisions, you might study this (or any other) out chart a bit
© Copyright 2008
10 comments
***** = 4
Okay. That's enough math for me!
I wouldn't expect anyone to do these calculations on the fly, while playing cards, I just suggest you understand that the rule is an ESTIMATE only, and know when it is damn close, and when it preforms worst, and how bad.
I also made some calculations that evalutated the error of the rule.
It is good some people pick it up from time to time because it is IMO the most important and most useful tool to make decisions for novice to intermediate players. I still use it frequently although in many situations you develop a sort of automatic play with some experience.
The comment about chris ferguson and a 40% chance is interesting. I never heard about that but of course it makes sense. With 10 outs it is always mathematically correct to call a pot-sized bet on the turn. It is questionable to call a bigger bet or all-in. You would need more outs to comfortable call this. 14-15 outs seem to be the minimum for this.
There is one important thing you should consider when using a table or rule like this. Even when you calculate your odds with it they can be deciptive. For instance if you have an open enden straght draw after the flop the rule of 4 gives you a win chance of 32%. This seems good enough to call a pot-sized bet against 1 opponent because you get 2:1 on your money. This would only be a (mathematically) correct call if you can see the turn and the river for that amount. This is usually not the case, because you will face another bet on the turn. If you did not hit your draw by then you can't call unless your hand or outs improved. Thats why you should not call pot-sized bets with straight and flush draws unless it only costs you a small portion of your stack. The implied odds improve the situation a little. If you hit your draw you will usally get a big pay off that compensate for the other calls. Implied odds are always important. If you are facing a pot-sized bet after the turn without a made hand how many outs would you need to call? Calling would mean getting money odds of 2:1, so you would need a 33% chance of hitting your hand. with 15-16 outs you have about the 33% with only one card to come. But if you actually hit your hand it is very likely you can get more money out of your opponent because he will likely call a bet from you that is small enough. If you hit your hand, your opponent checks and you bet 1/3 of the pot you are very likely to get called. This improves the money odds to about 5:2 or 28,5%. So if you consider implied odds you only need 13 outs to call a pots-ized bet after the turn. This is of course only if you are pretty certain that your opponent will call 1/3 of the pot after a scare card came.
eh... it is what it is grisan... I'm not telling you HOW to play lol
I just heard Chris say something about 40% chance to win... in a certain situation that I am not clear about... maybe a pot sized bet, maybe not, but i think it was three handed on the flop (maybe 6 at the table preflop), and CERTAINLY the chip stacks matter ( if you pay to hit, and hit, you need to be able to get PAID, so it's better if both you and your opponent have alot left )
You could be outs counting on the turn, and really drawing dead, or you could have the best hand anyway, and your opponent is bluffing... but the percentages are FACT, not strategy, what you do with it, you do at your own risk LOL, I take no responsibility
There ARE strategy "guidlines" people play with, that use these percentages, I just like to know what the percentages are, as far as strategy, lol, I ain't telling ( and i don't think I realy know either)
This is your original article grisan (which I had not read at the time I authored this)
http://www.railbirds.com/blog/23114