So basically I got into an argument with my cousin that bet sizing makes no difference stealing the blinds, and even worse cbing in 3bet pots.

So they dont have to take my work.

If you raise 2bb to steal 1.5bb what % does it need to work to be profitable with no action after the flop, eg we check and fold, or check to the river.

same for 2.3bb for 1.5bb

and same example but if we bluff into a 20bb pot with 10bb how often does it need to work,,

He dont trust my maths, so I said I know a place THEY KNOW MATHS

please help solve a bet

or just give the maths to prove him wrong

Well, you first have to define the term "stealing the blinds”. I see it as the hand folding to you in late position and you, with a marginal holding, hope to win the pot by betting such that both blinds fold.

Clearly the bet size matters. For example, if you limped, the small blind has to only contribute 0.5bb and the big blind gets a free pass to stay in the hand, whereas, with a large bet, both may fold.

An easy way to determine needed equity given no fold is the find the ratio of your investment to the total pot after all bets are made. Here with a raise of 2 your investment is 1+2 = 3. BB has to then call the raise of 2. The total pot after villain calls is 1.5 + 3 + 2 = 6.5. Then the required equity is 3/6.5 = 46%.

Of course, if BB calls, there most likely will be future betting so this is a first-cut look at the situation,

I think what you are looking for is something for which there is a fairly simple answer, but the way you are asking may be confusing. I am thinking you are making the assumption that you will raise and win the blinds if both fold, but will lose your raise amount when called. While this is not a realistic assumption it does make the needed success probability easy to calculate. You are risking the raise amount to win 1.5 bb. Success probability must be at least risk/(risk+gain), or in this case r/(1.5+r) where r is the raise amount in bb. For example for a raise to 2.3bb you need to get 2.3/3.8 = 60.5% folds to break even. For a 2.5 bb raise it would be 2.5/4 = 62.5%. In general the bigger the raise the more folds you need.

Always a good conversation .. but I think you need to be more specific since you may be mixing things up a bit when you mention 'cbing in 3bet pots'.

As shown above the 'simple' math is comparing your risk (bet) to what you will win. The format above gives you a 'win' percentage to break even.

If you want odds then you just compare the risk to the 'existing' pot. If a Button bets 2bb in an effort to 'steal' the 1.5bb in the blinds then they must be successful 4 out of every 7 attempts to break even. The 'pot' odds in this case are 4 to 3.

EVERY play in poker has a break even point that can be calculated if ALL THE RELEVANT facts are known. Since poker has human aspects to it, those facts are variable from opponent to opponent. This may or may not be what your cousin is referring to ..

Both the SB and BB have a range of hands they will play 'for a price'. If you bet in a manner that prices them out of playing, then you will have a successful steal. The higher you make your bet, the higher/better a holding they must have to continue. But remember you will only win 1.5bb each time .. so if you bet 90bb each time you can only lose once in 61 tries in order to break even.

In the 20bb pot, a 10bb bluff must work 1 time for every 3 attempts to break even (10/30 = 33% or 1 to 2 odds). In the same spot the opponent only needs to win 25% of the time to break even, so they may play more often than if you bet 20bb.

So bet sizing 'always' makes a difference in stealing .. The main talking point for this is that there's usually no amount you can bet for an opponent to fold AA unless there are other factors involved .. money bubble, ICM.

It appears that you already know this, but there's also a factor involved that you may still win the pot even if they call, but that's way more math than we need to look at here. GL