View Full Version : basic probability

09-12-2005, 04:48 AM
I just read TOP and HOH, I've always been a gut player, but I do well at mental math, and need to expand the mathematical sector of my game. I need to start at the basics, where do I go for that? Things like converting percentages to odds, and the second and third level probabilities (adding in other possibilities, mathematically considering implied and expected odds).

could we get a sticky or faq? is there a good book for this?

thanks for the help, I look forward to this incredibly improving my game.

09-12-2005, 08:47 AM
Search for basic combinatorics functions (permutations/combinations). Percentages to odds: [(1/percentage) - 1]:1.

Define 2nd and 3rd level probabilities.

09-12-2005, 02:42 PM
what I mean by permutation "levels" is this:

anyone can pretty much figure out what their odds are of catching the flush on the river, or of filling your two pair..

but when you add in implied odds, expected odds, add up the percentage chance you think he's bluffing to the outs you think he has (HOH),then the thinking starts to hurt my head.

I'll try another search, and if that fails, Im just gonna pull out a paper and pencil and do the problems till they become easy.

09-12-2005, 03:05 PM
It really seems like the two things that keep coming up are:
1. How many hands beat me.
2. How likely am I to make my draw.

The second question is typically adressed with the 'outs' shorthand -
the number of cards that you need in order to make your hand. Slansky
apparently suggests that a runner-runner straight is worth one out, so
we can figure that for two-card draws, it's 32 to an out.

Practically speaking, there are only up to 47 outs, which is small enough to memorize, and, in fact, you really don't care beyond 23 - you should probably wory about making the pot bigger there.

(I'm not sure how you can do better than an oustside straight flush draw with top pair& overcard against a pocket over pair which would give you: 2 straight flush outs, 6 straight outs, 7 flush outs, 3 two-pair outs, and 2 three of a kind outs for a total of 20 outs.)

Working out how likely your opponent is to beat you involves profiling
which makes it more complicated.

For your convenience the number of outs, followed by the probability in one or two cards.
1 out 1/47 on the turn, 46/1081 on the river
2 out 2/47 on the turn, 91/1081 on the river
3 out 3/47 on the turn, 135/1081 on the river
4 out 4/47 on the turn, 178/1081 on the river
5 out 5/47 on the turn, 220/1081 on the river
6 out 6/47 on the turn, 261/1081 on the river
7 out 7/47 on the turn, 301/1081 on the river
8 out 8/47 on the turn, 340/1081 on the river
9 out 9/47 on the turn, 378/1081 on the river
10 outs 10/47 on the turn, 415/1081 on the river
11 outs 11/47 on the turn, 451/1081 on the river
12 outs 12/47 on the turn, 486/1081 on the river
13 outs 13/47 on the turn, 520/1081 on the river
14 outs 14/47 on the turn, 553/1081 on the river * +EV for raising on the turn

Leaving it here for a moment, we have that the average out is worth roughly 40 possibilities - or about 1 in 27 or a bit more, since, most of the time, you'll be looking at fewer than 14 outs, and the earlier ones are worth more.

Runner runner flush draws are 72 possibilities (which is almost 2 outs) and double-sided runner runner straights are 48 possibilities - which is a bit more than one out.