We all know that calculating the chances of improving your hand on the turn and/or river is fundamental information for good poker performance. Naturally, you can use software like PokerStove to calculate the exact odds of improving your hand. But in practice you need to do this calculation in your head and quickly. But how?
Let's analyze a game situation.
Practical example:
Blinds at 10/20. You're in the big blind with :As :5c . The whole table folds until the small blind, a solid and aggressive player, raises 60 chips (3BB). You call. The pot is 120 chips.
Flop: :Jc :4d :3h
The villain, first to speak, bets 1/2 the pot (60 chips). Now what?
The 4-2 Rule
An excellent approximation for the chances of improving the hand can be calculated using the Rule 4-2:
Count the number of outs (cards that improve your hand) you have. If you're on the flop, multiply the number of outs by 4; if it's on the turn, multiply by 2 the number of outs. The result is the approximate probability (in %) of improving the hand.
Returning to the example, let's consider that the opponent, a solid player, made a high pair (let's assume he had JQ or KJ). To beat him, you'll need to hit an Ace (there are 3 left in the deck, so 3 outs) or a 2 (to make a straight there are 4 outs). So you have 7 outs. Multiplying 7 by 4 gives you 28, which means you have around 28% to improve the hand until the end.
As the opponent has bet 60 chips, the pot has 180 chips and you need to pay 60 for a final pot of 240, i.e. 60/180+60 = 1/4 = 0.25 = 25%, so the call is mathematically correct*. You call.
*Why is this mathematically correct? If you have a 28% chance of winning the pot, and you have to pay 25% of its value to continue, it means that, in the long run, you will make a profit in situations like these. Keep this concept!
Turn: :5s
You've hit a pair, but you're still losing to a bigger pair. You still have the previous 7 outs, but two outs are added, because the three of 5 would make you win the hand. With 9 outs, according to the rule above, you make it 9 times 2 (because you're on the turn), which equals 18, so you have about 18% chance of improving your hand on the river.
The opponent bets half the pot again (120 chips). Once again you would have to pay out 25% (120 for a final pot of 480), but now your chances of winning are around 18%. Folding would be the mathematically correct move (always remembering that many other variables must be taken into account when deciding to fold, such as the villain's ability to bluff or the villain's chance of folding the hand if a raise is made, but that's another more advanced discussion).
By way of comparison, doing the exact calculation with statistics programs (considering the opponent's hand as :Js :Qd), the probability of improving by adding turn and river is 29% (using the rule 28%), and with :5s on the turn (missing only the river) is 20% (with the rule 18%).
It's an easy method that helps a lot in doubtful situations. Apply it in your daily life and stop chasing pots when it's not mathematically correct to do so!
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very good !!!!
congratulations Petrillo, this was exactly the subject we discussed on skype and I see that you've done what you promised... now I understand and I'll be using this at the tables... ah watch out for me hein, I'll be even more competitive.....rsrs
Petrillo, I just have one comment about your article. A beginner will tend to think from your explanation that with 7 outs on the flop there is approximately a 28% chance of hitting on the turn, which is not true. These 28% refer to the chances of hitting one of these outs until the river, meaning that another bet can still be made, which makes the calculations not so simple. To find out the chance of hitting your outs on the turn, use the 2+1 rule, the statistic is very close to that of the river. Ex: 7 outs on the flop, the chance of hitting your card on the turn is 7×2 =14 +1 = 15% approximately (real chance = 15.55%).
Good people, this post has been calculated by programs, it's unlikely to go wrong, and those of us who follow poker on TV, see this propapility for sure, directly I see in the High Stake, on the turn the probability drops by half, or less.
Thank you very much TSawyer and Bruno!
Bruno, your comment is perfect. I didn't actually forget this detail, it's just that I considered it advanced. So it will be in Part 3: Advanced Concepts.
And that's just it, the probability of improving the hand until the river when you're on the flop is the number of outs by 4. If you only count the turn, it's by two as well.
OK, Petrillo! I was sure you knew that, I just wasn't sure if you'd forgotten to comment or if you'd left it for the next parts. Excellent article! This kind of article is very good because it attracts a lot of people to pokerdicas. Who hasn't gone to google and typed in some concept about poker that they wanted to know? Having this content here on the site gives POKERDICAS more visibility!
Thanks for all the compliments on the article. We'll be publishing part 2 soon, just wait!
Good article, objective and clear. Remember that this rule works well for a few outs, considering the optimistic model (none of your outs are in the opponent's hand). I don't know why some authors prefer this model to considering the opponent's 2 cards as random.
Obviously the opponent's cards aren't totally random, you can work out what they are, but in a flush draw, for example, can you tell if the opponent isn't holding one or two cards of that suit?
Just to think about it. The difference in the end is not that great (from 2% to 14 outs), it hardly makes a difference at the table. What really counts is the comment above about not forgetting to bet after the turn.
Petrillo great article!
That's really good, it really helps when it comes to betting.
I would like to know if you have any other articles about the probability of winning with a certain hand according to other cards, or if you know of any site or place that can help me, I would be very grateful, thank you.
What is the ratio between the pot/call calculation and my probability of winning, to at LEAST accepting the play?
if my odds of winning are 70%, for example, and the pot/call is 72%, should I call or fold?
thank you
ooou petrillo ... putss eo I got all tangled up trying to follow the line of thought and pans...
do you have an email or something so you can explain it to me properly :S
thank you
I couldn't understand this part about "outs", I didn't find the article very clear.
Hi Elton, I've edited the article to make it clearer, thanks for the tip.
[...] Rule 4-2 (Part 1): Basic Concepts * Bankroll Management: The Ladder to High [...]
Very good, even though I already knew these articles, I've learned a little more...
Thanks Marcelo PD!
In this situation, I like to raise to 120 after the flop to see what the small player's attitude will be.
It's mathematically incorrect (if my calculations are correct) to put in 120 and a pot of 360 (33%) with a chance of 28, 29% but I think it's good because it's important information that avoids a bigger loss on the river.
What do you think?
Congratulations on the blog! Very good!
If it's mathematically incorrect, and the opponent calls your bet, it's going to hurt you in the long run.
I'd like to know more about the 4-2 rule because I'm confused about outs because I'd necessarily have to count the cards on the flop or just the cards that would make my hand better?
Those already on the table are not counted. Only those to come matter!
If more players call, does the calculation remain the same?
Yes, your chance of improving your hand theoretically doesn't change. But if you pay a small amount into a big pot, it usually pays to chase your draws.
Hi, I recently had a nice experience and I'd like to hear from you experts, because in my calculation this rule has been broken...
Look at the details of the hand:
My hand: 8s 8d
Villain: Jh 2h
Flop: 4h - 5s - 6h
I go all in, the villain calls and says: I had to call, I had 52%.
Great, it turns out that he actually had 16 outs.... (flush=9 outs, straight= 4outs, parJ= 3 outs)
using the proposed rule we have: 16 outs x 4 + 1 = 65%
Putting these numbers into PokerStove gave 52%, the same probability that the villain calculated at the time.......
WHERE IS THE ERROR?
ps: in the end the villain won with a JJ on the river...
Renã, you counted 4 outs for the straight when in fact there are 3 (one has already been counted for the flush). That's 15 outs, which according to the rule would be 60% until the river. It turns out that calculations for more than 10 outs don't follow this rule so well, you have to adjust it down a bit.
That's because you can beat his card and still lose. For example, hit the "J" and then an "8", and you win. Or hit the 8h, he flushes, but then folds a card on the river and you go full.
So the tip is that with more than 10 outs you have to reduce the calculation.
It looks like you need to eliminate 2 more Outs for 8h, out of the 15 Outs you mentioned for counting flush Outs and Straigt Outs, since 8h would favor Renã's hand. This way, you'd have a total of 13 Outs x 4=52%
Have I made a mistake?
Excellent article.
I've never done calculations like this before and I've been playing for a while.
Continued.
Cool Marcelo, what amazed me was the fact that he calculated it on the spot and such.... is there any other rule to calculate the probability?
It's impossible for him to calculate correctly on the spot.
You see: he wasn't sure that the pair of "J"s would win, nor that his flush would win. He could only assume these things. I think he must have only considered 13 outs, and by calculation he arrived at 52%.
The "mathematically" correct call, I think, is wrong, because you considered the outs of the turn and river but only the turn bet. Not to mention that you assume that the villain only has KJ or QJ, disregarding the As that the villain could have and take a much bigger pot if the hero thinks the game is won... I think that would be an easy fold anyway.
Likewise, if you hit your card, more money can go into the pot. The 4-2 rule is just an estimate, and must be evaluated for each action.
With regard to the article, I have a question:
How do you calculate the number of outs if you're two cards short of a straight?
Example: I have 6 and 7 in my hand, and on the flop come 2, K and 9.
For me to complete a Straight, it would have to be 8 and 10, or 5 and 8. How many outs would I have to use in the first calculation?
Congratulations on the article!
In this case you should practically ignore this hypothesis. The chance is 24% for one of the right cards to come on the turn, plus 8% for the river. Using a statistical calculation, the total chance is approximately 2%. It will hardly pay to make a decision relying on this 2%.
Dude you explained it well, but over time playing poker you'll see that outs aren't always effective, in this case you'll have to be sure that the villain has something like KJ or QJ, unless you're sure, and in poker we never have 100% of certainty, I would only push the outs to the nuts in this case any 2, danod 4 outs.
In your example you have pot odds of 4 - 1 which is wrong for 7 outs, for your EV to be positive the pot on the flop should be at least 5.5 - 1:
E. V = (7/47 x 240) + (40/47 x - 60)
E. v = (0.14 x 240) + (0.85 x - 60)
E.V = (33,6) + (-51)
E. V = - 17.4 in the long run you are losing...
I don't understand the part about paying 60 to win 240. I have to have 60 chips to capture the 180 in the pot, i.e. 33%. If my odds are 28%, I have no pot odds. If I have to put in 60 to win the 60 I just put in, I shouldn't consider them. Am I wrong?
Dante, the count is always made with the final pot. The pot doesn't represent your "profit", just how many chips you have.
So for the calculation, you take what you need to pay divided by the final pot (what you had in the pot plus the value of your call).
In this case, it's 60/(180+60).
Another way of doing it, very common in the US, is to say that you have odds of 3:1 (180:60), which represents 25%.
The percentage of 33% is when I have odds of 2:1.
Vlw! 😀
Thanks for the clarification Petrillo.
Hello. I didn't understand the result of the pot calculation. 60/180 + 60
Hi. Please post your question in our forum: https://pokerdicas.com/forum/perguntas-de-iniciantes/
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