Long shots odds math.

If you're the kind of player who's fond of inside straights and other long shot draws, consider this: you have four outs on the turn.  That's all.  And it's not much when you consider that 42 of the remaining cards won't help you at all, which means the chance of completing your hand is less than 9%.  If you prefer expressing that figure in odds, here's the bad news.  The odds against completing an inside straight draw our 10.5-to-1, and you'd need a pot that's more than 10 times the cost of your call in order to make it worthwhile.

This is an excerpt from Lou Krieger`s The Poker Player's Bible: Raise Your Game from Beginner to Winner - If you had two pair and knew for a fact that your opponent had a flush, you'd be in the same predicament, since only one of four cards will elevate two pair to a full house.  When can you play hands like this?  On two occasions.  The first occurs when you buy a winning lottery ticket, worth $90 million, and playing $20/$40 hold'em becomes the equivalent of playing for matchsticks.  The other occasion is in a game with complete maniacs whose collective motto is: "All bets called, all the time."  You would need to win more than 10 times the amount of your call to justify this kind of the draw.  But if you figure to win a $450 pot by calling a $40 bet with an inside straight draw, then go for it.

An easy method in calculating odds at the poker table involves multiplying your outs by two, then adding two to that sum.  The result is a rough percentage of the chance you'll make your hand on the next card.  Suppose you have a flush draw on the turn.  Since there are two suited cards in your hand and two more on the board, and a total of 13 cards of each suit in the deck, you have nine notes.  A quick calculation, 9 x 2 = 18 and 18 plus 2 equals 20, comes pretty close to the 19.6% chance you'd come up with if you worked out the answer mathematically. (Or if you were using a reliable poker calculator online).

If you want to estimate your chances on the flop of making your hand by the river, try this: if you have between 1 and 8 outs, quadruple them.  8 outs multiplied by four yields 32, while the precise answer is 31.5%.  With four outs to quadrupling method yields 16%, while the accurate answer 16.5%.