11-16-04, LearnTexasHoldem:

Odds 2/4 Shortcut Question

Question: My question is how accurate is the 4/2 rule.

Suppose you are at a full table with 9 other players. 20 cards are dealt, 1 is burned and the flop 3 is dealt. You have A K the flop is K 9 2. You have 5 out ( A,A, A K K) According to the 4/2 rule this would be a possibility of 20% (4 x 5) for the turn and 10% (2 x 5) for the river if I understand correctly. Don't you have to somehow take in consideration that 24 cards were initially dealt? I would think the 4/2 rule would not be entirely accurate.

Thanks

Pat

Top 3 Beginner Rooms

Answer: Let me start off by refreshing the readers memory regarding what the 2/4 rule is. When you are in the heat of battle and you can't remember the odds for a given situation, instead of trying to figure out all the math in your head, you can use the 2/4 rule to give you a pretty close odds answer. The rule basically is if you are seeing both the turn and river to catch then you multiply your outs by 4. If you are using only the turn card or the river card but not both then you multiply your outs by 2. The number that you get will be about right.

For example, if we have a garden variety flush draw with a hand like 7s8s and the flop is As - Ks - 2 then we have 9 spades left to make the flush. The chance of hitting it on the turn would be 2 x 9 = 18% and the chance of hitting in on the river would be 4 x 9 = 36%. That's pretty close to what the actual number is which is 35% to hit one spade on the turn or river or 39% if you count a win if you hit both the turn and river spades. You then use this information to determine whether drawing is a good investment (I'm not going to get into pot odds in this reply, you can read the section on pot odds if you are interested).

Your question was basically stating that since other cards are dealt, how can we calculate odds on unseen cards. Take the spade draw example above, what if all 9 spades were already dealt, our chance or catching one of them would be zero. The reason we can use odds to estimate our chances on unseen cards is because there is no difference in the likelihood of an unseen card being one thing or another; in other words it is the same chance that the 24 cards dealt are spades as anything else.

Take an example of dealing two hands. Is there any better chance of the cards dealt not helping us then those still in the deck? Hopefully there is no difference or someone is cheating. The cards dealt should be random and if they are random then there is no greater chance of one of the ones in the deck being what we need versus one in someone's hand. Right now you may be thinking, well what about when all 9 spade cards are already dealt out of the deck like you mentioned above?

The answer is that sure, I may be screwed on this one hand and have no chance of catching a spade but it is just as likely that all the other nonspade cards were dealt out and I have even a greater chance of hitting my draw. So the bottom line is because all cards have equal chances of being in the deck or being dealt we treat "unseen" cards the same way -- no card is given more weight.

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