Simple Maths in Poker for Beginner

[thang911]

This thread is to answer all maths questions in poker so it will help u to understand how to play every hand at different street.

[Acesfull1026]

For the sake of progressing this thread (although thats a great post Tim haha) lets say I have:

the blinds are 10/20 and we all have ~1500 chips. It folds to me and I raise to 60 with 8d9d and the button calls, SB folds, and the BB calls.
Pot is 190
The flop is Kd Td 6c
I bet 140, the button calls, and the BB fold
Pot is 470 (we have 1300 behind)
The turn is 2h (Kd Td 6c - 2h)
I check. How much can I call on the turn without it being a bad call? Is it ever appropriate or better to raise all in if he bets?

[thang911]

Your chance of hitting flush is 4:1 so u can call up to 1/2 pot sized bet which is 235$ if we don't consider implied odds here.
pot 470. If u call 235$ and hit flush 1 out of 4 times u will win 940, u invest 235*4 = 940$ which is break-even. So u should call any bet up to 1/2 pot sized bet.

If he makes big bet, for ex: pot bet 470, u shove on top 1270. You wouldn't check/raise all in with pair or set here so you are obvious on draw here. He would call u down most of the time. You are 1:4 dog so cEV=0.25*3k + 0*0.75 = 750 which is -EV in the long run.

[Vestvik7]

Your chance of hitting flush is 4:1 so u can call up to 1/2 pot sized bet which is 235$ if we don't consider implied odds here.
pot 470. If u call 235$ and hit flush 1 out of 4 times u will win 940, u invest 235*4 = 940$ which is break-even. So u should call any bet up to 1/2 pot sized bet.

If he makes big bet, for ex: pot bet 470, u shove on top 1270. You wouldn't check/raise all in with pair or set here so you are obvious on draw here. He would call u down most of the time. You are 1:4 dog so cEV=0.25*3k + 0*0.75 = 750 which is -EV in the long run.

First paragraph is wrong I think. You dont get imidate odds when he bets 1/2 pot. You get 3:1 on a 4:1 hit right? And its only because of implied odds we can call that bet.

Second one is very wierd. You make some assumptions here thats very wierd. Are you check /calling turn and checking again on the river with a set/strong top pair? I cant ever picture you are doing that.

When you calculate if a turn shove is profitable or not you gotta calculate the % of the time he gotta fold for it to be profitable, then make a educated guess if he folds that often no?

Might be totally of here.

[thang911]

First paragraph is wrong I think. You dont get imidate odds when he bets 1/2 pot. You get 3:1 on a 4:1 hit right? And its only because of implied odds we can call that bet.

Second one is very wierd. You make some assumptions here thats very wierd. Are you check /calling turn and checking again on the river with a set/strong top pair? I cant ever picture you are doing that.

When you calculate if a turn shove is profitable or not you gotta calculate the % of the time he gotta fold for it to be profitable, then make a educated guess if he folds that often no?

Might be totally of here.

1. You are right. I just went through the maths too quick last night lol.

We are getting 4:1 odds here so mathematically calling any 3bet >pot/3 is incorrect if we don't consider implied odds.
Quick Maths: If u invest 5 times and win 1 times, EV= 470+X+X-5X > 0 so X <470/3

Now if we consider his range 10s+, AJ, AQ, AK, JQ, K9+, 109+, flush draw (257 combinations). The odds that your opponent hits inside straight draw, OE straight draw, or set and u hits flush draw are negligible here (<44:1, 22:1,44:1). We only consider his calling range a bet on the river as 33, 1010, KK, AA, K9, flush<9 high which close to 1/3 of his range.
If u invest 15 times and win 2X bet on the river one time, you will win 470*3+2X+6X - 15X > 0 so X<470*3/7 = 201. Its defo smaller if we consider the chance he has better flush draw. I would say it is down to 180-190.

If he is bad enough to make a big bet on the turn and pay ur shove on the river, ur EV should be (470+1270)+X-5X > 0 so X<435


2. I don't know what u mean. I never c/c with top set or top pair here but most likely I bet/call with set and strong top pair on this board in mid-stake MTTs. I don't think its as +EV c/r with set or top pair as betting OTT unless u have played with this player a lot before this hand.

3. Imo your hand is face-up when u c/r all in on the turn so i give the chance that he folds to ur shove is fairly small once he makes a big bet. Its a clear -EV spot if u go through the details.

[Eemil]

Thang911, mods, regs, beast and others,

Could you please do an example of 4bet hand breakdown with math? Pre or flop action. Of course it can be also a link to existing thread.

I am sure it will be very helpful for many bbp members, especially me, who want to improve their aggression and spot selection.

[sqrltyler]

i'll add an easy way to approximately calculate odds/percentages in holdem:

Let's say we're dealt 5-6 of hearts, and flop two hearts. Our odds of hitting another heart by the river will be approx 36&#37; or 3 to 1. (we'll make a flush 1 out of 3 times)

You can figure this out by first finding the number of outs that you have.

So we have 5-6 of hearts, and catch two hearts on the flop.
There are 9 more hearts in the deck that make our flush.
2 hearts in our hand + 2 hearts on the flop = 4.
13 hearts in the deck minus the 4 in play = 9 outs.

If you multiply your number of outs by 4, than you will get an approx % of hitting your hand by the river (9x4=36%)

If we don't improve on the turn, our odds of hitting another heart on the river will be approx 18% or 5 to 1. (we'll make a flush 1 out of 5 times)

If you now multiply your number of outs by 2, than you will get an approx % of hitting your hand by the river (9x2=18%)

Soooo...

Flop = outs x 4
Turn = outs x 2

Easy!