re: Poker & Working out poker odds
I copied this from a rival forum, if you want the link to it, send me a PM and I will give it to you.
Pot Odds, Calculating Outs and the Rule of 2 and 4:
This question is asked quite a bit on this forum so I thought it would be useful to have the oft repeated information in one post.
The most sited example is the 4 to a flush, so I will be lazy and use it here as well. You have two cards of one suit, and there are 2 cards of your suit on the board. Another card of that suit would give you the nut flush and the winning hand. What are your odds to draw to the flush? Furthermore, should you draw to the flush (are you getting proper odds)? You have:
and the board is:
Q[image: http://forumserver.twoplustwo.com/images/smilies/diamond.gif] A[image: http://forumserver.twoplustwo.com/images/smilies/spade.gif] 2[image: http://forumserver.twoplustwo.com/images/smilies/spade.gif]
There is $80 in the pot. The bet to you is $20.
The first part, determining the pot odds, is easy. There is $100 in the pot ($80 pot + Villain's $20 bet) and it will cost you $20 to make the call. Dividing the total pot by the price to call ($100 / $20) gives you pot odds of 5 - 1.
Now what about our card odds? Assuming only the flush will give you the winning had (in this example let's say your opponent has at least a pair of aces so we cannot count the three Kings as outs), you have 9 outs to improve, since there are 13 spades in the deck, 13 minus 2 on the board minus 2 in your hand = 9. How do we determine what our odds are of making the nut flush on the flop? Here is the equation:
P is the percentage, UC is the number of unseen cards, which in this case is 47. (52 total cards minus 2 cards in our hand minus 3 cards on the board). Our chances of making the nut flush on the turn are therefore:
1 - (47-9)/47 = 19.15%
Then we turn this into a ratio to compare it to pot odds with:
R = (1/19.15)*100-1 = 4.22 – 1 dog
So, we’re getting 5-1 on our money by calling the bet to us, and we only need 4.22-1 to make the call profitable, so we call.
But what if we’re facing an all in bet on the flop? Villain bets $20, we raise to $60, and Villain shoves in his remaining $140. The pot is now $300 and it costs us $80 to call. So the pot is giving us an immediate 3.75-1 odds ($300/$80). But what are our odds of making the flush? We will see two cards, the turn and the river. So we need to multiply our turn and river odds together using the following equation:
Chug away at that and we get a 34.97% chance to make our flush, or 1.86-1 odds. Our pot odds are 3.75-1 so we call.
Ok, ok. Wait! How do I possibly do all this complex math in my head, you ask? This is where the Rule of 2 and 4 comes in. The Rule of 2 and 4 will give us a good estimate (but not exact) of the percentage chance of making our hand. Keep that last point in mind. These are the odds for making your hand, not winning the pot!
So, to use the Rule of 2 and 4, we multiply our outs by 4 on the flop, or by 2 on the turn and we will get a rough estimate of the percentage of making our hand. On the flop, we had 9 outs. 9 x 4 = 36%, which is roughly the same as the actual percantage of 34.97%. On the turn, we multiply our outs by 2 and get 18%, which is roughly the same as the actual 19.57%. Keep in mind that you can misapply this rule if you are not in an all in situation on the flop but still use the rule of 4 to determine your odds. This is because you will most likely be facing another bet on the turn and, therefore, will not be using the correct pot odds to make your flop decision. Also, the rule of 2 and 4 is not very accurate in situations where you have lots of outs. As you can see, if we had 18 outs on the flop, 18*4 = 72%, where actually you only have 62.44%. But with so many outs, all that really matters is you're a huge favorite in the hand.
Another way to keep these odds straight is to just print out a list like the one below and keep it next to your computer for a handy reference: