What do you think about the scenarios? Do they cover enough to teach us something?
Yes, I think it is useful to work out how profitable it is to call flop bets with draws in various scenarios.
In NLHE, in practice:
- Your opponent can bet, or check, on any street
- His bets can be of any size (assuming both players are deep stacked)
- You also have the option to bet, or raise, on any street. This will often be the most profitable choice.
- Your bets or raises can be of any size
- Your opponent can fold, call, or re-raise in response to any bet you make.
That's a lot of variables.
If you know your opponent, or know the way typical opponents play in your game, you can estimate what actions he is likely to take, and how likely he is to take those actions.
I don't find it practical to work out a mathematical effective odds figure at the table. But working out the math for scenarios in advance helps make decisions on the table easier.
My actual thinking at the table regarding effective odds for the example hand in NLHE is more like:
This player completed from the SB. He didn't raise, although he raises unopened pots in late position about 40% of the time. So he probably doesn't have an Ace, a pair, or suited connectors, although maybe he is being sneaky.
He bet half pot on the flop. He's pretty tight and passive post-flop, so his bet on the flop probably represents a real hand - maybe a 7, a 2, or a flush draw, although occasionally he will
bluff.
If I call, he'll probably check the turn if his hand does not improve, although occasionally he will bluff. If his hand does improve on the turn, he'll probably bet half-pot or more, and I'll need to fold.
He's not a calling station post-flop. So I can probably get to the river at no additional cost, but I probably won't win a large pot if I hit my flush. If I make my flush on either street, he'll probably pay off one half-pot bet about half the time.
Since his hand is probably weak, and he is not a calling station, I think he will fold about half the time if I bet 3/4 pot on the turn (if he checks the turn).
Sometimes I'll win 4 BB by betting the turn, sometimes I'll win 4 BB by making my flush, sometimes I'll win 6 BB by making my flush, and sometimes I'll lose 1 BB, sometimes I'll lose 6 or more BB if I make my flush and my opponent makes a better flush or a full house. I can't assign an exact probability to any of those outcomes. But I think the price is low enough, and the chances of winning are high enough, that I should call this flop.
You can see that there are many things we can change about the opponent that might change the effective odds.
The opponent might bet bigger on the flop. He might be passive pre-flop, increasing the chances that he has an A or another good hand that would pay off a bigger bet post-flop.
He might be more aggressive post-flop, or a calling station. He might raise pre-flop, and his usual range for raising might be wide or narrow, etc.
TL;DR, it's not practical to come up with an exact estimate at the table, and there are many factors to consider, but it is helpful to run some numbers away from the table.
In Limit Hold'Em - 2 handed (with equal stacks, no one in danger of all-in) when Hero hits 4 to a flush on the flop and faces a bet from Villain calling is NOT correct mathematically UNLESS Hero believes that Villain will call a bet on the river when the flush comes.