When you speak about "maths" you mean odds ? or is it even more vast that i thought ? XD
Yes, odds. A simple example would be facing an all-in bet on the turn while holding a flush draw. Assume there was $100 in the pot after the flop and the bet you are facing is $50 and you were sure you would win if you hit your flush. You can see six cards, including the two in your hands and the four on the board, which means there are forty-six unseen cards. Nine of them will give you a flush as there are thirteen cards of the correct suit in the deck, of which two are on the board, two are in your hand and the other nine are somewhere else. So nine good cards and thirty-seven bad cards gives you odds of 37-9 or approximately 4-1 against hitting the flush. As the pot is laying you odds of only 3-1 ($50 to win $150), you can't call. To illustrate further, if you ran the hand 100 times, you would win $150 20 times (slightly less really because the odds are actually 37-9) and lose $50 80 times. $3000 (win) - $4000 (lose) is a net loss of $1000 over 100 hands or $10 per hand. In other words, in terms of expected value every time you call this bet you are losing $10, whatever actually happens. If the bet you were facing was $25 then your pot odds are 5-1 and you can call.
If there is still money behind then it is a little more complex. Assume you are still facing the bet of $50 but your opponent has $100 left. Now there is $150 in the pot and a potential $100 to be gained on the river if you hit. Against a decent player who will figure out you are chasing the flush, you can't include that money in the calculation because he won't pay you off. Against a weaker player that you put on a reasonable hand, you might decide he will pay you off that $100 if you hit. If you add that $100 to the $150 in the pot, then you stand to win $250 and it costs you $50 to call, so you are getting implied odds of 5-1. Of course, it's difficult to assume 100% he will pay you off so you might reduce those odds a little. If you thought there was a 75% chance of him paying you off, you could add $100 x 75% to the odds calculation, which means a potential win of $225 for your $50, which is 4.25-1 and worth a call. Another thing you might consider is the player's tendency to tilt. If you know he understands odds and you know he hates it when people make bad calls and win and you know he has more money in his pocket, you might make a slightly bad call because you know you might get some or all of the money in his pocket if you hit and he tilts. if you don't have the nut flush draw, you also have to consider that he may be betting a flush draw and hitting might be a really bad outcome so you need to build that into the calculation as well.
It obviously gets a lot more complex with deeper stacks and bets on the flop but in a deep stack game you can call with much worse odds on the flop because of the potential payoffs if you have an unexpected hand.
Steve
