B2B - back to basics - the basic maths of poker

Hello let me see if I can help you with this,

First of all, calling with over cards can be reverse implied odds, for this reason, lets say your opponent has AT here and you call, and the turn is an Ace you have TPTK and your opponent has T2P, so your screwed here, I believe your outs because of this reason are reduced, and thus you have more like 3 outs to make up for the reverse implied odds.

Onto your point

On the flop you have 6 outs witch using the rule 2-4 you have 12% flop to turn and 24% flop to river

12% is actually more like 8-1 pot odds here is an easier calculation, since its it can only go to 100%, you divide 100 by 12 since its 12%, witch gives you 8.3 = 8.3-1 pot odds required flop-turn, the 24% is flop to river and you usually use this when a player shoves all in on the flop, and you are faced with a call or fold times your outs by 4 in this case 6 like you did and got 24% again divide 100 by 24, witch gives you 4 = 4-1 pot odds required flop-river.

Another important thing when counting outs, on the turn you counted 6 outs, but the board has paired a T if the player has a T you have 0 outs, witch brings me to the topic of clean outs, lets say you hold A♠:K♣: on a flop of T♥:7♥:2♦: you have to discount the A♥:K♥: because there could be a flush that beats you if one of these 2 cards appears on the turn, so althought you have 6 outs you only have 4 clean outs, 4 x 2 = 8 now 100/8=12.5 so you need 12.5-1 pot odds, here after discounting clean outs, this gets easier as you get more experienced and you don't even really need to think that much about it.

I hope this was helpful, it explains all this in the strategy section in better detail you should read it

The flop is dry, villain is betting small, so you can call with AK. You should be carefulwhen you hit A or K on turn and not go crazy.
On turn, with paired board, we can fold.

Just a few thoughts on the hand in general. First of all I'm really not a fan of cold calling off-suited hands, so rather 3b and call some suited connectors instead. On the flop with very few out to improve I would bet flop and give up if unimproved. Had the flop been 5T2ddx or 5T2ccx we could x/c flop and barrel turn and river if checked to again.

Just a few thoughts on the hand in general. First of all I'm really not a fan of cold calling off-suited hands, so rather 3b and call some suited connectors instead. On the flop with very few out to improve I would bet flop and give up if unimproved. Had the flop been 5T2ddx or 5T2ccx we could x/c flop and barrel turn and river if checked to again.

Pre-flop, this would normally be a 3-bet at NL2, although there are some reasons why you might want to flat this hand in this position (e.g. if you 3-bet SCs and don't want your 3-bet range to get too large or if UTG is a nit).

Frozenelf's maths is unfortunately not completely accurate. Given a probability p that an event will occur, the odds of it occurring are (1/p - 1):1. So for example if an event is equally likely to occur as not, the probability is 50% and the odds are 1:1 (where Frozenelf's formula would incorrectly given you 2:1). However, it may be easier just to look up the odds on a table like this one.

The rule of 2 and 4 is good enough for most practical poker purposes. Your actual chance OTF of improving to at least a pair by the river is 24.14% and your odds are 3.1:1, so your numbers are close enough. OTT you've applied the rule of 2 and 4 correctly, but the odds calculation is wrong. It looks as if you've added 1 when you should have subtracted, so you've got 9:1 when you should have 7:1. The true probability is 13.04% and the true odds 6.7:1.

Your calculation of the pot odds OTF is incorrect, which is strange, because that ought to be the easy part. OTF there are 38c in the pot and you're asked to bet 12c. Your pot odds are therefore 3.2:1 (a half-pot raise always gives pot odds of 3:1). OTT there are 68c in the pot and you're asked to bet 18c, so your pot odds are 3.8:1 (it looks like you've just made a rounding error here).

Unfortunately, you've calculated the wrong thing. On the flop, you're not interested in your odds of improving by the river (unless you're going all in). What you care about is your odds of improving on the next card. You can see the reason here, because when you don't improve and the villain bets again you're forced to fold so you never see the river. You have odds of 6.8:1 of improving on the turn and you have pot odds of 3.2:1. So you need to expect another 3.6 times your bet (in this case another 43c), which will be roughly equivalent to getting villain to call a pot-sized bet when you hit. Your problem is that if an A hits the turn and you bet the pot, it's going to pretty obvious what's happened. Plus the villain is betting in a 4-way pot, so he could well have a set, in which case you get killed if you hit an A or K. So looking at it that way, this should be a fold.

However, it's not as simple as that (of course), because we also have to consider the possibility that the villain is bluffing. I think quite a few players at NL2 are betting in villain's spot just because he acts last and sees that no-one else appears to like the flop, so he can steal the pot. If he has overcards, you will have the best hand.

We can call or 3bet preflop. The iportant thing is that if we 3bet and face a 4bet, we can comfortably turn our hand into a bluff and fold vs unknown at NL2. It's hard to do the postflop math when we call because we can't be sure what our outs are. The math for 3betting preflop is simple. If we 3bet to $0,18, we need him to fold in 0,18/(0,03+0,06+0,18)*100 = 66,67% of cases to make our 3bet auto-profitable. If he is calling too much to 3bets, we can expect to be ahead on the flop very often, but even if we are not, we will win many pots thanks to our positional advantage. Overall, I think that 3betting this hand preflop would be more profitable at NL2 than flatting.

Folding AK is not ok. We can call if there are passive players behind us and we can 3 Bet if there are active ones.

Thank you a lot for your replies, I really appreciate it.

The goal I have is to learn fully the mathematical side of poker and to know that what I count, I count correctly. The problem I have, that I find bits of information here and there, some videos as well but I did not find one place from a to z about all the numbers and what is right.

Would you be able to recommend such a place (to read/to see videos) where I could go through all the numbers from the beginning to advanced?

Thank you.

Look at our site.

Originally posted by Lathdari
Pre-flop, this would normally be a 3-bet at NL2, although there are some reasons why you might want to flat this hand in this position (e.g. if you 3-bet SCs and don't want your 3-bet range to get too large or if UTG is a nit).

Frozenelf's maths is unfortunately not completely accurate. Given a probability p that an event will occur, the odds of it occurring are (1/p - 1):1. So for example if an event is equally likely to occur as not, the probability is 50% and the odds are 1:1 (where Frozenelf's formula would incorrectly given you 2:1). However, it may be easier just to look up the odds on a table like this one.

The rule of 2 and 4 is good enough for most practical poker purposes. Your actual chance OTF of improving to at least a pair by the river is 24.14% and your odds are 3.1:1, so your numbers are close enough. OTT you've applied the rule of 2 and 4 correctly, but the odds calculation is wrong. It looks as if you've added 1 when you should have subtracted, so you've got 9:1 when you should have 7:1. The true probability is 13.04% and the true odds 6.7:1.

Your calculation of the pot odds OTF is incorrect, which is strange, because that ought to be the easy part. OTF there are 38c in the pot and you're asked to bet 12c. Your pot odds are therefore 3.2:1 (a half-pot raise always gives pot odds of 3:1). OTT there are 68c in the pot and you're asked to bet 18c, so your pot odds are 3.8:1 (it looks like you've just made a rounding error here).

Unfortunately, you've calculated the wrong thing. On the flop, you're not interested in your odds of improving by the river (unless you're going all in). What you care about is your odds of improving on the next card. You can see the reason here, because when you don't improve and the villain bets again you're forced to fold so you never see the river. You have odds of 6.8:1 of improving on the turn and you have pot odds of 3.2:1. So you need to expect another 3.6 times your bet (in this case another 43c), which will be roughly equivalent to getting villain to call a pot-sized bet when you hit. Your problem is that if an A hits the turn and you bet the pot, it's going to pretty obvious what's happened. Plus the villain is betting in a 4-way pot, so he could well have a set, in which case you get killed if you hit an A or K. So looking at it that way, this should be a fold.

However, it's not as simple as that (of course), because we also have to consider the possibility that the villain is bluffing. I think quite a few players at NL2 are betting in villain's spot just because he acts last and sees that no-one else appears to like the flop, so he can steal the pot. If he has overcards, you will have the best hand.

I think your missing the point in what he is trying to ask witch I believe I explained to him correctly, your saying all of this player that seems pretty new to the game, so he wants a basic understanding of how to calculate pot odds, and work from there, even I didn't understand half the stuff you just said and ive been playing for 5 years

That being said can you explain this part to me in more detail without leaving words out or using slang please, im happy if you found a weakness in the way I calculate pot odds and would like to know more

Frozenelf's maths is unfortunately not completely accurate. Given a probability p that an event will occur, the odds of it occurring are (1/p - 1):1. So for example if an event is equally likely to occur as not, the probability is 50% and the odds are 1:1 (where Frozenelf's formula would incorrectly given you 2:1). However, it may be easier just to look up the odds on a table like this one.

I don't understand what your saying here, given the probability p that an even will occur? What is P if this is algebra, I unfortunately got kicked out my school before I started on this

In fact I dont understand any of it

Just because you got kicked out of school, doesn't mean OP was, so hopefully he understood me.

You said

12% is actually more like 8-1 pot odds here is an easier calculation, since its it can only go to 100%, you divide 100 by 12 since its 12%, witch gives you 8.3 = 8.3-1 pot odds

That's the wrong calculation. You have to divide 100 by 12 and then subtract 1, which gives you 7.3-1 odds (and not pot odds). OP appears to have added 1 instead of subtracting, giving him 9-1 instead of 7-1 which is the answer he ought to have got (he correctly doesn't attempt to give a decimal place as he is aware that the calculation is approximate). In fact in this situation 6 outs gives him a probability of 13.04% (6/46, since there are 46 unseen cards). 100 divided by 13.04 is 7.7, subtract 1 is 6.7 so his true odds are 6.7-1 as I said.

You can see that your calculation is incorrect, because if winning and losing are equally likely, the chance of winning is 50% (also known as 0.5). Your calculation would say 100/50=2 so the odds are 2-1, but we know that the odds are actually 1-1 (also known as evens).

I hope that's clear.

Also, I don't think whether OP is new to the game is relevant. He's said himself that he wants to understand the maths and he can understand the maths even if he's never played poker at all. It's pretty simple maths, TBH.

Originally posted by Lathdari
Just because you got kicked out of school, doesn't mean OP was, so hopefully he understood me.

You said

12% is actually more like 8-1 pot odds here is an easier calculation, since its it can only go to 100%, you divide 100 by 12 since its 12%, witch gives you 8.3 = 8.3-1 pot odds

That's the wrong calculation. You have to divide 100 by 12 and then subtract 1, which gives you 7.3-1 odds (and not pot odds). OP appears to have added 1 instead of subtracting, giving him 9-1 instead of 7-1 which is the answer he ought to have got (he correctly doesn't attempt to give a decimal place as he is aware that the calculation is approximate). In fact in this situation 6 outs gives him a probability of 13.04% (6/46, since there are 46 unseen cards). 100 divided by 13.04 is 7.7, subtract 1 is 6.7 so his true odds are 6.7-1 as I said.

You can see that your calculation is incorrect, because if winning and losing are equally likely, the chance of winning is 50% (also known as 0.5). Your calculation would say 100/50=2 so the odds are 2-1, but we know that the odds are actually 1-1 (also known as evens).

I hope that's clear.

Yes that makes sense, thank you