Understand This

This is why poker works (for those who work at poker)

Imagine you and I were to play a gambling game where we flip a coin and wager on the result. Whenever the coin comes up heads I give you 50 cents, and when it comes up tails, you give me a dollar. Would you agree to play this game with me? No, of course not, but every day people play this game with me nonetheless, if just in a different form. Let's illustrate my point using 5 card draw poker - the kind of poker you see in all the movies:

I hold: A(hearts)A(clubs)X,X,X (three random and meaningless cards).

There is $10 in the pot (we each anti $5), and my one opponent and I each have $50 in front of us. There will be two betting rounds, one before the draw, and one after. No betting limit. I am first to act and bet $30 - so the pot has now grown to $40. My opponent looks at his cards:

2(spades)8(spades)5(spades)9(spades)K(clubs).

With the large bet i have made in relation to the size of the pot (i bet $30 to win $10) my experienced yet ignorant opponent guesses i have either a big pair, or some other good hand like three of a kind or a straight. He decides that if he draws to his flush (by calling my $30 bet, and discarding his king of clubs) and hits it, he will very likely win. He is correct in all of his thinking so far. However, what are the chances of his drawing to a flush? Well, there are 13 spades in total in the deck, and he has 4 of them, so that leaves 9 spades. He has 5 cards in his hand, so that leaves 47 unaccounted for cards. Of those 47 cards, 9 will help him(the spades) and 38 won't. So we are left with 38-9 or a little more than 4 to 1 (20%). So 1 times he will draw his spade and beat me (we are ignoring the possible full house i could draw to, to make this simpler), and 2,3,4,5 times he won't. Should he call the $30? No, the pot would have to be at least $120 in size for him to call(120 - 30 is 4-1) and the pot is only $40.

How is this like the coin flip? Well, if my opponent does call the $30 he will increase the pot to $70 and win that pot 20% of the time. Or, in other words, he stands to win 20% of $70 which is $14, less the $30 he paid to call, for a grand total of minus $16 whenever me makes this play.