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My Problem with OUTS
I have read quite a few inspirational poker books by the Great Masters in my life. There have always been several things in most of these books that have bothered me. The one I am going to talk to you about today is OUTS in Holdem poker.
OUTS are the odds of hitting the card or cards that you need to improve your hand after the flop or turn. Say for instance you have J10 in your hand and the board is AK4, all you need is a Queen to complete your straight. There are four queens in the deck, so that is four OUTS. A simple conventional calculation states that you know five cards: two in your hand and three on the board. There are 52 cards in the deck. You subtract the number of cards you know from 52 (52-5=47) then you divide the four OUTS by that number. So four OUTS / 47 cards means you have an 8.5% chance of hitting a Queen on the turn. After the turn you know 6 cards so 52 -6 = 46 cards. Again 4/46 = 8.7% chance of hitting your queen on the river. To calculate from the flop to the river for the two cards to come gets more complex. I don’t know about you but I would have a hard time doing this math in my head, so the Great Masters have came up with the 2/ 4 rule. You take your OUTS starting from the flop multiply by two for the Turn and by four for the river. If we take the 4 OUTS after the flop and multiply by 2 we get an 8% chance on the turn then we multiply by four to get a 16 % chance by the river. I have read in different forums questioning if this is accurate enough. With a large number of OUTS there may actually be an error of a couple of percent.
But there is something that has always bothered me. If we go back to that “simple conventional” calculation (52 - 5 = 47 cards), I have a problem with the number 47. If you are playing at a 9 player table, like most online games, there are 8 other players with 2 cards each, or 16 cards, you have no way of hitting. The books tell us that since we do not know what these cards are we can ignore those 16 cards and add them to our chances.
So we are supposedly calculating chances down to a hundredth of a percent but ignoring 16 cards? That is 52 minus 5 we know, minus 16 we do not have available minus one burn card which only leaves 30 cards left in the deck. We now can calculate that 42% of the deck is gone. The 16 cards represent 34% of the 47 cards. OK, so I am supposed to just ignore 34% of the deck. I may not be a great statistician, but an error of 34% is not something you just ignore.
I propose a small change to the 2/4 rule. I have done some math utilizing the number of players. This now requires you to do the math as the number of players changes. The new calculation is: with 9 players you can use the rule of 1/ 2. Now 4 outs would be 4 times 1 = 4 % by the turn and 4 times 2 = 8% by the river. As the number of players decreases the percentage will increase back towards the original 16% of the 2/4 rule. This is on the conservative side and is not perfect but it may give a more realistic expectation of hitting your outs.
I may be way off on this idea but the more information one has leads to a more enriched life, on the Green Felt.
Now let us pray.
Church of the Green Felt