How reliable is poker math?

Red Chipper Posts: 2 ✭✭
The question is simple, and might have been asked before. How reliable is poker math?

Let's say I'm on a nut flush draw, on the flop, in a 9 handed no limit Hold'em game. I would like to think that I have 9 outs and I need atleast 4:1 to make a call. However I have no way of knowing how many of my nine outs have already been dealt to and folded by some of the other 8 players (not to forget the burn card). So how reliable is this math really? and what can we do?

• Las VegasRed Chipper Posts: 96 ✭✭
edited July 9
The math is not taking into consideration the actual cards that the players are holding because this is unknown. The math you are talking about is based purely on the facts that we do know.

In your example the facts that we do know are as follows:

1. There are 9 players at the table with 2 cards each. This means that there are a total of 16 cards not including your own that have been used.
2. There was a burn card and a flop, this means 4 more cards were used
3. Based on the previous 2 facts we know that there are 30 cards in the deck left
4. There are 2 cards of our suit on the flop and 2 in our hand, leaving us with 9 possible cards that match our suit in the deck.
5. Based on our outs we know that roughly 1/3 of the deck could favor us or 4*9=36

The thing to keep in mind about poker math is that its not meant to be exact because we have incomplete information and doing probability math in your head is not easy. Its meant to get you close enough so you can make an educated decision on what to do next. Keep in mind that just because you are a huge favorite mathematically does not mean that you are are automatically entitled to win. It means that the more often you find yourself in that scenario the more likely you will win over a longer period of time.

Another example of what the math represents is taking a basketball shot from the free throw line. Lets assume that your average is 80%. This doesn't mean that you will always make the shot 8 out of 10 or 80 out of 100, it just means that over the course of time you will most likely make the shot 80% of the time each time you step up to the line.
• Las VegasPosts: 4,960 -
Knowing the probability of cards coming is completely exact. Whether they're in the stub or not is irrelevant. The tricky part is identifying clean outs.
Moderation In Moderation
• Red Chipper Posts: 82 ✭✭
Think of it this way. If you shuffle a deck of cards and then look at the top one, how often will it be an ace? Hopefully you know it's 1/13, and any trial experiment you do will show this to be true in the long run (even if it takes a while to get there).

Now shuffle the same deck, then count out 20 cards, and set them aside. Look at the top card of the remaining 32. How often will that be an ace? Well, it's also 1/13. Sure, sometimes all 4 aces are in the 20 you set aside, but that doesn't matter. At the end all we are doing is looking at one random card out of 52. Whether we pull from the top, middle, or bottom doesn't really matter. It's the same with drawing to a flush. Sometimes all of your outs are still in the deck. Sometimes they have all been folded and burnt. But on the average, when you flop a flush draw, the odds of you hitting the turn are 9/47.