No, it's not just "fun knowledge.". If you know the actual math behind it and work the accurate numbers away from the table, it improves your ability to quickly and more accurately estimate at the table.

If you guys can come up with a simple method to calculate equity without using pokerstove that would be impressive. Calculating pot odds and converting our outs to percentage of success is simple and there is no need to complicate it. What is the point of doing all that 7×4(8÷3+2-4)((8×6)) 2 when it is as simple as the rule of four and two ?
The influence of some training sites that are trying hard to impress with their math wizzards is obvious on threads like this.

Take a look at this for example.. all we need to know here is

- Quads = 0.24%
- Full House = 0.73%
- Set = 10.78%

The rest is chinese and you do not need it.

Because the rule of 2 and 4 is just an estimate, and it is worth knowing what is behind that estimate and how far off it can be.

Also because without understanding the underlying math, I could just through some BS rule-of-thumb that I completely made up like "If you have 2 overs you always have at least 12.5% equity" and you wouldn't be able to tell that it was baloney.

The rule of four and two is an accurate estimate very slightly off. Ofcourse it is worth knowing what is behind that estimate but not essential. Knowing the maths behind why you hitting a set 11% of the time will not make you a better poker player. Nor are you a better poker player if you know that actually flopping a set is 10.78% chance and not 11%.

It is worth knowing all the math behind these numbers but as I said for fun.

You are incorrect, sir. Depending on the number of outs, it can be significantly off, as small rounding errors add up.

In the meantime, if you don't see value in this thread, you are welcome not to participate. Laughing at others for actually studying what is actually going on behind the estimates they see thrown around is not welcome.

Rule of 2 accuracy
Outs 4 and 2 Actual Difference
4 (gutshot) 8% 8.7% -0.7%
8 (straight) 16% 17.4% -1.4%
9 (flush) 18% 19.6% -1.6%
15 (straight + flush) 30% 32.6% -2.6%

Rule of 4 accuracy
Outs 4 and 2 Actual Difference
4 (gutshot) 16% 16.5% -0.5%
8 (straight) 32% 31.5% +0.5%
9 (flush) 36% 35% +1%
15 (straight + flush) 60% 54.1% +5.9%

I do not see where it goes significantly off and I was not laughing at noone. Im sorry if I got out of line somehow.

Valuable information is the content of the thread quoted by Venice. Staff like that easy to read and valuable for your game I can read all day. Anyway good luck with your maths guys, take it easy

You really don't think a difference of 5.9% (out of 54.1, so overestimating EV by more than 10% of it's actual value) is significant? Good luck on the tables.

You are wrong. You should have figured it out as a math enthusiast that when you've got a +50% chance of winning the pot, calling is EV+ regardless of the size of the bet.

@TheStrumps: I disagree with your strong devaluation of the math. When I first started playing Hold 'Em, no-limit wasn't played at the casinos. When I stumbled upon Petrov's book on the odds, I knew it was an auto-raise otf vs. 5 Vs when I was last to act with a flush draw. When NL became the craze, knowing that you're 1.86:1 dog to make a flush by the river if you go all in otf & 2.18:1 to make a str8, was extremely valuable.

It was studying the math that allowed me to fully understand just how weak/vulnerable QTs was vs an EP o/r. I'm not from Missouri, but I'm a "show me" kinda' guy & that's what the math does. I don't have all the above memorized, but if a rookie understood that the odds of flopping 2 pair was 48.x:1, the rookie would still be able to fold [hopefully] even after spending an hour at the table watching several different people flop 2 pair.

Folding is boring for rookies & when they don't know the math & see people pullin' off these great catches & scooping pots with hands they would have folded, they begin to think they're doing it all wrong.

"Would you look at that! That guy just called a 6x bet OTB with J8o, flopped 2 pair for the best hand & then got runner-runner str8 to rub salt in the wound of his V's pocket kings! Now that's fun Hold 'Em!"

P.S. How much do you think math helps a NASCAR driver understand the limitations of his vehicle? Do you think he drives strictly by the seat of his pants?

And if calling bets were the only thing we had to determine, that rule of thumb would be all we had to know...

Again, if you don't think that actual math matters, you are welcome not to participate in the thread.

And for what it's worth, I'm not much of a math enthusiast. I hate math. I'm not very good at it and have to force myself to do it. Doing so has immeasurably improved my game, though.

Im sorry I meant to say any bet you make or call with +50% of winning the pot is EV+.

Again I think that math is important but not these numbers of the OP. I would not participate in the thread if you would not quote me again. I force myself too and maths have helped my game too so its cool.

I would bet that out of 10 NASCAR drivers 5 would not be able to calculate 3 divided by 5.

Since all we can do is estimate our outs anyways (i.e. we never really know exactly how many outs we have), then being off a bit with the rule of 2 and 4 isn't that big of a deal. Hopefully the rule will show us the times we have a clear call vs fold, but in the grey area times a lot more importance is probably on how accurate our outs / range estimating is.

Obviously the original math was required in order for someone to come up with the rule. But it isn't required knowledge necessary to succeed at the poker table.

Gnothatingatall,justsayin'G

Very much agreed, as Garbage In = Garbage Out. Hand reading is a separate topic though. We could definitely use a COTM on it, if anyone wants to volunteer. In the mean time, the fact that it's important doesn't mean that being familiar with the underlying math that affects the correct response to said ranges is not itself also valuable.

I'm confident that NASCAR drivers have someone on their team that can do this math and does the more complicated calculations. At the poker table, we don't have someone to tell us what the calculations are.

A difference between LLSNL players and mid-stakes pro is what they define as study. LLSNL players generally mean they are watching a video (if they are younger) or reading a book (if older). Mid-stakes pros are running Equilab or something else looking at equity results to learn something their opponents don't know.

Right, there's a lot of calculus and statistics, too.

You have memorized the things other people tell you are important. Knowledge of math allows me to discover myself what is important, which is much more helpful.

By all means, feel free to enlighten us as to what part of the math of poker requires calculus.

Thanks for the effort Vernon.

Off the top of my head, a lot of bet sizing optimization problems and the derivation of bankroll formulas.

Maybe we could have a Part II: Math to know post-flop.

Such as: You have 77 on a flop of 622

You bet & it folds to your aggro LAG who shoves. You deduce that he wouldn't shove with an over-pair here, because he doesn't have a big PP because he didn't 3! pre. So, you put him on two A2s, that he may shove with trying to get you to think he's weak [with a FD] & a flush draw with two overs, or a FD with A3s-A5s.

There are 2 A2s & 3 AXs that he would do it with: A9s & A8s & A7s & A5s. He is aggro enough to 3! pre with AJs+.

You have ~9% equity vs. the two A2s & ~54% equity vs. the four FDs, or 2:1

So, [9+54+54]/3 = 59% equity vs. his range.

If we're only putting in something like 35% of the money, if we call, we have a substantial overlay that can compensate for a reduced number of of FDs he may hold.

For instance, if he only has 2 FDs, it would 1:1 & [9+54]/2 = 32%, so we would need him having 2 FDs in the [A3s-A5s range] where he only has 1 overcard for [9+59+59]/3 = 42% equity.

So what we need to have memorized:
1. An overpair vs trips has 9% equity.
2. An overpair vs a flush draw with 2 overs has 51% equity.
2. An overpair vs a flush draw, 1 over & runner/runner str8 [under our PP] has 59% equity.

Regarding the statements:

-The number of flops where you make 2 pair is 3*3*44
-The number of flops we will have a flush draw on is (11*10*39)/2

In the flush draw second example, we divide by 2 because Kx8x4y and 8xKx4y are the same thing.

Why doesn't this apply to the two pair example as well (in that we don't divide it by 2)?

The order of the cards on the flop doesn't change the fact that we have two pair, isn't it?

@Vancouver: In the 2 pair example, you are isolating the two cards in your hand by saying 1 of the 3 on one of your cards & then 1 of the 3 of your other card.

You actually have 6 cards to pair on the 1st card otf & then 3 outs for the 2nd pair.

[6*3*44]/2 for 2 pair is the same as your formula for a flush draw.