Good morning,
due to the fact that suited connectors can make straight or flush 8% at the turn and 16% at the river, how is it possible to calculate the exact BB of the effective stack that I need to play profitable?
I calculate that in a single raised pot for example I have to invest more or less 25 BB to see the river card. So 84 times I will spend 25 BB for a total of 2.100 BB. So 16 times I have to win these 2.100 BB for a total of 131 BB...
Could you help me to understand better this from a mathematical point of view?
keep in mind that the real world is much more complicated than just saying you hit your flush a certain percentage of the time and then get paid off. you can miss and still be good. you can hit and he makes a better made hand. he can have marginal value and not bet the river. but assuming you have improve p percentage of the time and he always jams the river and you are always good when you hit and never good when you miss, then the evs are:
ev_f=S
ev_c=p*(2*S+P)+(1-p)*(S-B)
so the break even point is:
p=B/(S+P-B)
where B is his turn betsize, P the potsize at the turn and S the remaining stacks at the turn.
Either you can learn the hard way that paying full price on a low flush or straight is a reason to fold preflop or you can assume that you should fold preflop until you have studied preflop opening ranges and postflop equities to the effect that you are positive that calling or reraising are profitable. The key to understanding this is that playing drawing hands is only slightly profitable even for experts; depending on the opponents and your position you might break even or you’re earning a fraction of the pot. You can’t go into it thinking you’re going to win a big pot often then you’re going to be brutally disappointed.
I don’t think the question has much meaning. You apparently cited hitting a flush or straight by the river with dealt suited connectors. But there will be bets and cards to come so the probabilities and rewards/risks will change.
For example, if you had 78dd and the flop was As Qc 2s and villain bet 0.7*Pot, you’re unlikely to call, I would think.
An alternative question would be if you restricted your pre-flop bet to be all-in but that makes little sense with such a low showdown equity unless villain is likely to fold. If a fold is a good possibility the suited connectors will have played no significant role.
how is it possible to calculate the exact BB of the effective stack that I need to play profitable?
The short answer is that it isn't.
"Implied odds" for pre-flop hands is a bit of a fuzzy term. It doesn't even work very well for set-mining, as each pocket pair differs in strength, in much the same way that some suited connectors realize their equity better than others.
Don't treat poker like a slot machine. In the modern day, you can't say "my stack is 20x the price of calling, so it must be an +EV call, because I'll win a stack at least once every 20 times I make the call". Poker doesn't work like that. It's much more complicated, and - generally speaking - very few suited connectors make money as calls pre-flop.
The profitability of calling speculative hands has almost nothing to do with how often you hit, but everything to do with how good your opponents are. Bad opponents will pay you off all the time with weak holdings, good opponents will rarely pay you off and when they do most of the time they will have your hand dominated.
If the opener is weak and the blinds are weak you can justify calling almost anything suited on the button.
I know that there are a lof of factors that can influence the way of playing, but my question is only in a mathematical point of view.
It seems that theoretically I need from 50 to 76 BB of effective stack to make this play profitable, depending from the size of the bet on flop + turn.
