Originally Posted by Four Dogs
Sorry Jesus, I didn't invent the rule of 4. It is a formula that works quite well with 2 cards to come. It WILL give you a very good idea of your chances of picking up your out card after the flop. Not on the next card. The Rule of 4 is for Poker, not coins. Here's the math. Lets say your on an open ended straight draw. There are 8 cards left in the deck that can help you. Outs. On the next card, the Turn, you have an 8/47 chance of a pickup = 17% or .1702. You have an 83% chance of missing or .8298. This is the important number. Assuming You do miss, your chance of the pickup on the river is now slightly greater. .1739. But once again, we work with the chance of missing, not hitting which is .8261.
So .8298x.8261=.6855 is the chance of not filling your outs with 2 cards to come. 1.6855=.3145 is your chance of catching your dream card. Thats about 31%. Remember the rule of 4? Number of outs 8, multiplied by the magic number 4 = 32%. Pretty darn close.
But that's not the end of the story. There's another step which for the sake of brevity, and because it seemed to obvious to bother with. Lets look at our straight draw again, assuming you don't question my math. You have a 31% chance of filling the out after the flop, by the numbers. A 32% chance using the rule of 4. For the sake of ease, lets just call it 33%. That means there's a 66% of missing right? 2:1. Pot Odds. Done! Unless your trapping with a flush, you don't want to give your opponent better odds than that to call. A bet of slightly larger than the pot will play on his optimism while, in the long run, turning you a profit.
Here's where you made your mistake with your funny coin. In your analogy you added your 2 chances thus arriving at a 100% chance of getting heads. It's bad math. Pot or coin odds are calculated by multiplying one chance against the next not adding them. Your coin has a 75% chance of turning heads with 2 tries.
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Doggy, doggy, doggy...where can i start....ok, let´s go:
I know you didn´t invented the rule of 4. Clonie Gowen told it on a mail and Phil Gordon told it chatting on FTP. I know that the formula works quite well with 2 cards to come. I know that it will give you a very good idea of your chances of picking up your out card after the flop. Not on the next card. I know all that. Actually, i use that rule. But when do i use it? When i want a general idea of where i´m standing on the hand. For example, it helps to know that if i have an inside straight draw i probably don´t have to chase it, because 4 x 4 = 16% and that´s very low, but if i have a flush
draw with two overcards probably i should be raising, because 15 x 4 = 60%, and that´s very high.
That rule works pretty well to calculate the total hand odds. And it´s very useful.
But where it´s useless? When you are calculating the pot odds. Why?...i already said the reason, but i´m going to repeat it until you finally understand it.
To calculate pot odds you need a pot and a bet. And that factors are variable. The only case where you should use the rule of 4 after the flop to calculate pot odds is if you know that on the turn your opponent will check. But if not, you don´t know how much is he gonna be the bet, so that´s why you must calculate the pot odds on each card, not both at the same time. The right odds you can calculate with the rule of 4, but the pot odds no.
You can calculate the turn and river odds of making your hand, but you can´t calculate the pot odds in advance if you don´t know what the bet is going to be.
If you don´t believe, search for information or ask to a pro (you play at FTP) is your pot odds for catching a flush should be 2:1 as you say or 4:1 as i say. I´m 100% sure that they are going to say you that if you have a flush draw after the flop, your pot odds are 4:1. If you call with a flush draw after the flop with 2:1, in the long run you aren´t going to have a profit.
Remember: you should use the rule of 4 after the flop to calculate your pot odds
ONLY if you are 100% sure that there is not going to be a bet on the turn.
Look at this example:
You hold: flush draw
Flop: $10 Pot + $10 bet
You call: $10 (getting 2 to 1 odds)
Turn: $30 pot + $10 bet
You call: $10 (getting 4 to 1 odds)
If you are right Dogs that play should make you a profit in the long run (i chose 100 hands to make it more exact).
Let´s see if you are right:
Cost to play = 100 Hands x ($10 flop call + $10 turn call) = $2,000
Total won = 100 hands x 35% chance to win x $50 pot = $1,750
You paid $2000 to win $1750....a profit? I don´t think so.
Now let´s play as i say:
You hold: flush draw
Flop: $30 pot + $10 bet
You call: $10 (getting 4 to 1 odds)
Turn: $50 pot + $16 bet
You call: $16 (getting about 4 to 1 odds)
Again let´s see in the long run of 100 hands:
Cost to play = 100 hands x ($10 flop call + $16 turn call) = $2,600
Total won = 100 hands x 35% chance to win * $82 pot = $2,870
You paid $2600 to win $2870.....a profit? Of course.
If you realize on the first example i used 2:1 pot odds because i used the rule of 4, but in my second example, where it exist a profit, i just multiplied the outs by 2 (after the flop).
Again, if you calculate the pot odds using the rule of 4 after the flop, you´re assuming that there will not be a bet on the turn.
Now let´s go with the funny coin: I know it´s bad math to add the two 50% to make a 100%. I told it was bad math. Why i told that? Because even if you don´t believe that analogy works to explain the same thing of pot odds that i explained before. If you use the rule of 4 to calculate pot odds after the flop, you´re adding up the turn and river odds. And as i said before, unless it´s going to be a certain check on the turn, adding the turn and river is incorrect. I also know that the coin has really 75% of getting head at least one time. 1  (1/2 x 1/2) = 1  (1/4) = 3/4 = 75%.
Here in
Chile the schools are bad, but at least i know something of probabilities.
Now, ANYONE ELSE WANT A PIECE OF ME! lol