How do I calculate my hand odds flop to river?

SwiftHax · Apr 16, 2014

Say, someone goes all-in on the flop and you have a flush draw. odds from flop to turn are 4:1, yet they turn to 2:1 when going in on the flop to river, so how exactly are they calculated? Is it exactly the same thing as the rule of 2 and 4?

If I had a gutshot for example, then my hand odds are 10.75:1 on the flop and 10.5:1 on the turn. The average of the previous two is 10.6, so by that my chances double and now my odds are 10.6:2 or 5.3:1? I'm sorry if this is a dumb question, but I just wasn't sure.

Thanks for taking your time

Ubercroz · Apr 16, 2014

The way you calculate it is you take the total number of unknown cards left in the deck and then determine how many of those are cards that you are looking for.

Lets say you have 67 and the flop was 892. The cards you are looking for are 5 and T. There are 4 instances of each cards left in the deck and there are 47 unknown cards (52-2(in your hand)-3(on the flop)=47).

So 8 cards out of 47 means there is a 17% chance that the next random card is going to be the card that you are looking for. Another way of looking at that is about a 1 in 5.8 chance of your card hitting on the turn.

Once the turn comes, the odds change a little. You have 8 out of 46 cards now (since the turn card did not help you). Its still just a little better than 17% chance on that one instance - or 1 in 5.8.

Given that from the flop to the river both cards could hit you have two opportunities for that 17% (or 1 in 5.8) chance. If do the math it comes out to be around 33%, since you don't exactly have a double chance... but its close enough for dirty poker math. 33% could be expressed as 1 in 3 chance. or maybe 2:1.

If you wanted to figure it out for a gutshot then you just take 4 outs in 47 unknowns and you have about an 8.5% chance or about 1 in 11.6, or 1:10.67 or so. Put it all together and you have about a 17% chance to hit it by the river or a 1:4.8 odds or however you want to look at it.

RickAversion · Apr 17, 2014

You need to Google "outs" and learn that.
Then Rule of 2/4

DrazaFFT · Apr 17, 2014

Hey swift!!! Easiest way to calculate it is as Ladybugger said by using rule of 2 and 4. As you alread y used example of one player going all in on flop you will be using an rule of 4 because you have 2 card to come after flop and there will be not future betting.
The rule of 4 is simply multiplying your outs with 4 and the result is the chance that your hand will improve in percentage. I asume that you know what out is, out is a card that improve our hand.

For open ended str8 draw lets say that we have 89 on a T7x flop, card that will give us str8 is any J or any 6, we have 4 jacks in a deck and 4 sixes in a deck which mean that we have 8 outs, following a rule of 4 we multiply our outs with 4 and get 32% chances that our hand will improve in next two cards

for a flush draw it is practically a same only that we have 9 outs, 9 remaining cards of a same suit of total of 13 cards of 1 suit (there are on the flop and we have 2) following the same math 9x4=36% chances that our hand will improve on a next two cards...

with more outs we have the less accurate rule of 4 gets, (over 9 outs) i can write about that too if you are interested...

I want to point the important thing, you do not want to use rule of 4 of player is not all in on flop or if you not absolutely sure that he will check river or that you will get paid even bigger if you hit your draw (implied odds), without knowing all this basically you want to use rule of 2 which is same as rule of 4 with an exception that you multiply with 2 and it gives you percentage that your hand will improve in next street...

SwiftHax · Apr 17, 2014

Thanks for the answers, but that was not quite what I was looking for. I completely understand the rule of 2 and 4 and I can calculate my odds and that's what I did with the above example: odds of a gutshot are 43:4 or 10.75:1 on the flop (47-4) but that only counts if I'm paying a sum to see one card. If my opponent shoves then I need to call only 1 bet to see 2 cards. According to the rule of 2 and 4 I have twice the percantage from flop to river, so by that, do my odds double as well?

Does 10.6:1 turn to 10.6:2? I find the rule of 2 and 4 nearly useless when calculating pot odds because it only gives me the percantage and I have to turn that into odds and determine whether the call is profitable.

trolaAa · Apr 17, 2014

DrazaFFT said:
Hey swift!!! Easiest way to calculate it is as Ladybugger said by using rule of 2 and 4. As you alread y used example of one player going all in on flop you will be using an rule of 4 because you have 2 card to come after flop and there will be not future betting.
The rule of 4 is simply multiplying your outs with 4 and the result is the chance that your hand will improve in percentage. I asume that you know what out is, out is a card that improve our hand.

For open ended str8 draw lets say that we have 89 on a T7x flop, card that will give us str8 is any J or any 6, we have 4 jacks in a deck and 4 sixes in a deck which mean that we have 8 outs, following a rule of 4 we multiply our outs with 4 and get 32% chances that our hand will improve in next two cards

for a flush draw it is practically a same only that we have 9 outs, 9 remaining cards of a same suit of total of 13 cards of 1 suit (there are on the flop and we have 2) following the same math 9x4=36% chances that our hand will improve on a next two cards...

with more outs we have the less accurate rule of 4 gets, (over 9 outs) i can write about that too if you are interested...

I want to point the important thing, you do not want to use rule of 4 of player is not all in on flop or if you not absolutely sure that he will check river or that you will get paid even bigger if you hit your draw (implied odds), without knowing all this basically you want to use rule of 2 which is same as rule of 4 with an exception that you multiply with 2 and it gives you percentage that your hand will improve in next street...

+1 :top: The best detailed answer! I think next time I'll be careful with u Draza

DrazaFFT · Apr 17, 2014

SwiftHax said:
Thanks for the answers, but that was not quite what I was looking for. I completely understand the rule of 2 and 4 and I can calculate my odds and that's what I did with the above example: odds of a gutshot are 43:4 or 10.75:1 on the flop (47-4) but that only counts if I'm paying a sum to see one card. If my opponent shoves then I need to call only 1 bet to see 2 cards. According to the rule of 2 and 4 I have twice the percantage from flop to river, so by that, do my odds double as well?

Does 10.6:1 turn to 10.6:2? I find the rule of 2 and 4 nearly useless when calculating pot odds because it only gives me the percantage and I have to turn that into odds and determine whether the call is profitable.

when you need to pay only one bet to see 2 streets with no further betting involved you need to use rule of 4!!!!! The calculation you are using is not rule of 2 nor rule of 4. with these two rules you only count your outs... SEE MY ABOVE POST Rule of two you are using when you want to calculate your chances on only one street to come, no madder is it the turn card or the river card, the NEXT CARD. You are using rule of 4 to see the chances on a next two cards to come (turn+river)!!!

for converting percentage to odds you can use numerous converters online or you can convert it by using a simple math

http://www.thepokerbank.com/tools/odds-charts/ratio-percentage/

RickAversion · Apr 17, 2014

SwiftHax said:
Thanks for the answers, but that was not quite what I was looking for. I completely understand the rule of 2 and 4 and I can calculate my odds and that's what I did with the above example: odds of a gutshot are 43:4 or 10.75:1 on the flop (47-4) but that only counts if I'm paying a sum to see one card. If my opponent shoves then I need to call only 1 bet to see 2 cards. According to the rule of 2 and 4 I have twice the percantage from flop to river, so by that, do my odds double as well?

Does 10.6:1 turn to 10.6:2? I find the rule of 2 and 4 nearly useless when calculating pot odds because it only gives me the percantage and I have to turn that into odds and determine whether the call is profitable.

Yes, the problem with Rule of 2/4 is that it's in percentages. You'll need to convert in your head, or as you said, just double your odds if seeing 2 cards.

Arjonius · Apr 17, 2014

SwiftHax said:
I find the rule of 2 and 4 nearly useless when calculating pot odds because it only gives me the percantage and I have to turn that into odds and determine whether the call is profitable.

It's not hard to convert. So for example, if you have 6 outs with the turn and river to come, multiplying by 4 gives you about a 24% chance of winning, and therefore about 76% of losing. Look at this as 76:24 and you can see it's close to 3:1.

The rule of 2 and 4 isn't completely accurate anyway, so this bit of rounding isn't likely to matter.

DrazaFFT · Apr 17, 2014

trolaAa said:
+1 :top: The best detailed answer! I think next time I'll be careful with u Draza

Dont be to scared, im good with theory but my practice is awful

SwiftHax · Apr 17, 2014

Ladybugger said:
Yes, the problem with Rule of 2/4 is that it's in percentages. You'll need to convert in your head, or as you said, just double your odds if seeing 2 cards.

So a straight draw for example, 5:1 when seeing one card and 2.5:1 when seeing two cards?

I'm sorry if I was unclear because I understand how to use the rule of two and four. I was just wondering if I can apply it when calculating my hand odds.

Ubercroz · Apr 17, 2014

SwiftHax said:
So a straight draw for example, 5:1 when seeing one card and 2.5:1 when seeing two cards?

I'm sorry if I was unclear because I understand how to use the rule of two and four. I was just wondering if I can apply it when calculating my hand odds.

Basically yes. Yoh have a 17% chance 2 times. Which works out to be close to 33% chance over all.

That could be expressed as ~2:1, roughly. Your chances don't exactly double, but because of the relatively small number of possibilities in poker, doubling you chances for two streets gets you close enough to make a good decision.

rhombus · Apr 17, 2014

2/4 Rule and if you struuggle to convert % just google a chart and stick at side of PC for odds

rhombus · Apr 17, 2014

to get the proper number work out the chance of not hitting
so
flop probability is =47/9 5.22222 or 19.1489362% 80.85106% to miss
Turn probability is =46/9 5.11111 or 19.5652174% 80.43478% to miss

Multiply 80.85% * 80.43% =65.03238
65.03% to miss so chance of hitting is 100 - 65.03 = 34.97

TO work out individual streets just bad cards divide by good cards so on flop theres 47 unknown 38 bad and 9 good so 38/9 =4.222/1
On turn 37 bad still 9 good so 37/9 = 4.111

Samango · Apr 17, 2014

SwiftHax said:
... I understand how to use the rule of two and four.

Hmmm, you don't really... this whole thread is about how to understand and use the 4/2 correctly

John A · Apr 17, 2014

Fyi, to get some practice on this exact thing you can get ace poker drills. The odds and outs drill is free for life. It should help you.

SwiftHax · Apr 17, 2014

Samango said:
Hmmm, you don't really... this whole thread is about how to understand and use the 4/2 correctly

I was just asking if I can use it when calculating my hand odds because when talking about 2 and 4 we only mention the percantage.

SwiftHax · Apr 17, 2014

OUTS ODDS FLOP TO TURN ODDS FLOP TO RIVER EXAMPLE
1 45:1 22:1 Smaller set vs Higher set
2 22:1 11:1 Higher pocket pair vs Smaller set
3 15:1 7:1 One overcard
4 11:1 5:1 Gutshot straight draw
5 8:1 4:1 Middle pair vs Higher pair
6 7:1 3:1 Two overcards
7 6:1 2,5:1 Gutshot straight draw plus overcard
8 5:1 2:1 Open-ended straight draw
9 4:1 2:1 Flushdraw
10 4:1 1,6:1 Gutshot plus two overcards
11 3:1 1,4:1 ---
12 3:1 1,2:1 Gutshot and Flush draw
13 2,5:1 1,1:1 ---
14 2,4:1 1:1 Straight draw plus two overcards
15 2:1 1:1 Flush draw plus two overcards

I found a neat list on Pokerschool. Basically your odds do double on flop to river.

scorpion1367 · Apr 17, 2014

The percentage gives you your odds....scorp

SwiftHax · Apr 17, 2014

scorpion1367 said:
The percentage gives you your odds....scorp

Yeah, but I would much prefer having to calculate my hand equity in odds by using the formula 47-x:x because it seems much more accurate than rule of 2 and 4. I was just asking if I could calculate my odds flop to river using the following formula 47-x:2x and how accurate would it be?

JusSumguy · Apr 17, 2014

Ahem... it's the rule of 4/2.

-

How do I calculate my hand odds flop to river?

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