[Orpheus]

The following shows some of the inaccuracies in the 2/4 rule It'll be long. Please skip it if you don't care.

In short strokes, the 2% rule is reasonably accurate, if you understand why it works. At various stages in various games (Hold-em, Omaha , etc.) you will have a "known number of unknown cards" (i.e. 52 - # cards in your hand - # cards showing on the board) You should simply *know* these numbers for the game you are playing.

IN HE, there are 47 and 46 unknown cards before the river and turn, respectively. In Omaha, there are 45 and 44.

Each of these numbers is pretty darn close to 50. your chance og getting 1 card (1 out) from 50 unknown cards would be exactly 2% (1/50). 1/45 or 1/48 are pretty close, so you get a good estimate for the turn OR river

HOWEVER, the "4% rule" (for turn AND river together)is much less accurate. You can't simply add the results of the 2% rule for the tuen and river separately to get the correct total result. Why? Because the outcome on the turn will alter the probability on the river -- and you need to understand how this effect works for the draw you want to make

Lets say you have pocket jacks, and flop rags. What are your chances of getting a jack on the turn? 1/47 (4.26%) On the River? 1/46 (4.35%) -- 2%/out is 'close enough'.

If you have a flush draw after the turn. Your odds of making it on the river are 9/47 (19.57% -- almost 20% instead of 18%) That's because the slight difference between 1/46 and 150 adds up, the more outs you have. In some situations, this make a difference in calculating pot odds.

Example: JoeAces raised preflop from the SB, which you (savvy reader that you are) know he ONLY does if he has AA. You called with T9s, and because you live a pure life, the flop came 789 rainbow. You have 19 outs to win (4 6s, 3 7s, 3 8s 2 9s 3 Ts, 4 Js) but that also means 19x the error.

In this example, in a multiway pot, you wouldn't fold if you missed the turn, because you'd be 19/46 = 41.3% to make the river. But if it's heads-up at the final table of a tournament, you might want to know your exact postflop pot odds to size your raise. the 4% rule says 76% BUT that's an overestimate. It doublecounts the cases where you draw an "out" on both the turn and river, and we all know you don't get extra credit for making your straight twice, drawing three pairs vs two pairs, etc.

A more accurate postflop estimate of your chances of beating JoeAces would be Pt + (1-Pt)*(Pr) where Pt is your chances of drawing an out on the turn, and Pr is your chances of drawing an out on the river. This result (65%) doesn't count the "overkill" situations. (An even more accurate esitmate would factor in JoeAce's chances of making his set of aces, which would kill many of your outs, but that's beyond the scope of this example)

This is much more important in Omaha, where you can be drawing to [e.g.] two different flushes with one hand, but you should understand it in TXHE -- though it'll rarely change your decisions in actual play, Since the difference will, at worse, turn a slight +EV decision into a slight -EV in uncommon situations, using the 4% rule can only be a small leak, and the time/energy it saves can make it +EV overall, by letting you focus on your opponent.