# Why does rule of 2/4 give "wrong results" as compared to Flopzilla on a (edited from title: "help!")

Las VegasRed Chipper Posts: 27 ✭✭
edited May 22
At the risk of sounding stupid, I have to ask because I am trying to learn and get better. My hole cards are QcJd. I assigned Villain a 40% range. The flop is KJ3 hearts. Now, here's the question: I assume I am behind right now because the villain's range has over 100 combos of Kings and most of his range is suited. I assumed I wasn't losing to a made hand already (flush), so a Queen (3) or a Jack (2) may win the pot for me (assuming he isn't sitting on KQ or KJ...maybe even AJ). All of these are in his range and raising hands in CO. Question is: when I run this through Flopzilla, I get a 61.2% equity. My problem is, I'm coming up with only 20-22% using the 4/2 rule and my five perceived outs. Which is correct? And how does it get to 61%?
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• Posts: 3,623 -
edited May 22
1AMPOKER_ wrote: »
At the risk of sounding stupid, I have to ask because I am trying to learn and get better. My hole cards are QcJd. I assigned Villain a 40% range. The flop is KJ3 hearts. Now, here's the question: I assume I am behind right now because the villain's range has over 100 combos of Kings and most of his range is suited. I assumed I wasn't losing to a made hand already (flush), so a Queen (3) or a Jack (2) may win the pot for me (assuming he isn't sitting on KQ or KJ...maybe even AJ). All of these are in his range and raising hands in CO. Question is: when I run this through Flopzilla, I get a 61.2% equity. My problem is, I'm coming up with only 20-22% using the 4/2 rule and my five perceived outs. Which is correct? And how does it get to 61%?

Over 100 combos of Ks? I suspect not. Besides, with that wide a range, most hands don't contain a K, so why would you conclude you're behind? Plus if most of V's range is suited, that still means at most 25% of her holdings are flush draws.
Moderation In Moderation
• Posts: 3,623 -
FWIW it's impossible to have simultaneously 1) a mostly suited range; 2) more than 100 combos that include a K.
Moderation In Moderation
• RCP Coach Posts: 1,867 -
edited May 22

The best way to get help is to ask good questions. I am here to help you make this into a good question that will get answered.

When you say the Villain has a 40% range, not all 40% ranges are made equal. I have to assume that you mean a 40% straight slider percentage from Flopzilla. I am using this one:

AA-22,AKo-A9o,KQo-K9o,QJo-Q9o,JTo-J8o,T9o-T8o,98o,87o,76o,65o,54o,AKs-A2s,KQs-K2s,QJs-Q8s,JTs-J7s,T9s-T7s,98s-96s,87s-85s,76s-74s,65s-64s,54s-53s,43s-42s,32s

When I run this through flopzilla (QcJd vs the above range on KhJh3h) I get an equity of 58.1% versus that range. You claimed 61.2% so this is similar considering you did not specify the Villain range precisely.

The rule of 2/4 is for your hand versus a SPECIFIC hand.

Against a range, you might

* have some or all of your outs when behind
* weight between the above two groups can vary wildly against the range

All of this bookkeeping is beyond a simple rule like 2/4.

Title: Why does rule of 2/4 give "wrong results" as compared to Flopzilla on a monochrome flop?

Body: I am coming up with an equity with the rule of 2/4 that differs from that given by Flopzilla. The details of the hand are not particularly important.

My hand: QcJd
Flop: KhJh3h

AA-22,AKo-A9o,KQo-K9o,QJo-Q9o,JTo-J8o,T9o-T8o,98o,87o,76o,65o,54o,AKs-A2s,KQs-K2s,QJs-Q8s,JTs-J7s,T9s-T7s,98s-96s,87s-85s,76s-74s,65s-64s,54s-53s,43s-42s,32s

Put this in Flopzilla yourself to see my exact scenario:

[Flopzilla v1.8.6]
[Use Ctrl+I to import into Flopzilla]
[www.flopzilla.com ]
[KBH+IXqFP3pRHpwkM0udDLPUZataiitqNpsfF60j9EG4u+6ZzN]
[N9XCE0nQWpDI+IEm2gSDSSH4SvABygwAVYqwCuPvRBSmH9gNYB]
[NGTsLvhi39ewsYkY6TikUfQ6ASMpi2zcGbW83B47gQL+BacZ84]
[1pdiDCy8hVuJtQX+ydaLD6A+WKsm3GRGPeOGzpw+Zz4GcEP9xh]
[hUyW+t1u1rIj6WOeSFYz3IUmPx1plgzG+Q+sfIan2t]

I see this as a situation where I have 5 outs (three Queens and two Jacks) With two cards to come I would multiply 5 times 4 for 20% equity.

The equity of the hand from Flopzilla is 58.133%

What is the nature of this seeming conflict in calculating equities?

Co-founder Red Chip Poker,
Author Poker Plays You Can Use
Author Poker Workbook for Math Geeks
• Las VegasRed Chipper Posts: 27 ✭✭
A few things to unpack: why do you call it the "2/4" rule? Am I also getting that wrong as well? I thought it was multiply outs by 4 on flop and 2 on the turn?
Also, I am very grateful you helped with showing me how to ask a question correctly. Thanks for also teaching me that 4/2 or 2/4 is designed for specific hands and not ranges.
Villain's range is 22-TT, 43s-QJs, 53s-KJs, 63s-KTs, 95s-ATs, A9-A2s, K9-K2s, 87-KQ, J9-AQ, Q9-AJ, K9, AT-A2. That's more of a 39.9% range.
What do you mean by "ranges can be different"?
I feel like I should explore more of Core before I ask questions. This may be annoying for you guys
• Posts: 3,623 -
Not annoying at all, just a process.

Doug's comment about 40% ranges can be different reflects the fact that the so-called "%-form" does not uniquely specify a range. It just tells you how many combos are in a range.

"2/4" and "4/2" are used interchangeably. Same rule.
Moderation In Moderation
• Posts: 3,623 -
To get back to your original question, @1AMPOKER_ the fundamental source of the apparent discrepancy is your assumption that you're behind on that flop. Against any sensible 40% range you're not, as Flopzilla tells you.
Moderation In Moderation
• Las VegasRed Chipper Posts: 27 ✭✭
Great advice guys! And you're right, it is a learning process. I do feel like if I stick with RedChip then I will get there in no time. But I will continue to ask questions. I appreciate all the help
• RCP Coach Posts: 1,867 -
Glad to. We are big on clear and concise questions, it is an art. The good thing is in formulating a good question, you often answer it. See rubber ducking:

https://en.wikipedia.org/wiki/Rubber_duck_debugging

Co-founder Red Chip Poker,
Author Poker Plays You Can Use
Author Poker Workbook for Math Geeks