Need recommendations on learing how to calculate odds...

[Big Country]

It is this simple mainly because your two hole cards out of the deck leaves 50 cards, and each card in a 50 card deck has a 2 percent chance of showing. Thus, each out has a 2 percent chance of showing with each board card. Technically after the flop there are 4 unseen cards, but the difference in the math nedded is so minute that it is easier to consider each card 2% chance vs. the 2.13% chance that 1/47 really is

[AKQJ10]

FWIW i usually find myself rounding the 47 (or 46 on the turn) unseen cards to 45 or 48.

6 effective outs: probability roughly 6/48 or 1/8, you need about 7 to 1 odds.

5 effective outs: 5/45 or 1/9, you need 8 to 1.

4 effective outs: 4/48 or 1/12, you need 11 to 1.

3 effective outs: 3/45 or 1/15, you need 14 to 1

Note that most of the borderline draws, at least in low limits, fall in this neighborhood. I leave out strong draws like four-flushes and open-ended straights because at low limits they're almost always worth drawing to. But your more marginal draws are things like:

Two overcards -- starts with 6 outs but top pair is likely to not hold up, so discount to between 3 and 5.

Middle or bottom pair -- starts with 5 outs to two pair or trips, these hands hold up more often than just top pair so discount to 3 or 4.

Gutshot -- 4 outs, if to the nuts then there you go, 4 effective outs. If the gutshot isn't to the nuts then a straight is still a durable hand, so discount to 3 or 3.5.


(See SSH and this this recent thread for much more about discounting outs. This is perhaps THE most important topic in SSH.)

[Francis]

I won't debate the right outs, but as far as learning odds, I'd do the following

- select the odds for the most common situations (I made some cards based on ITH's odds chart, but I've seen some good ones on SSH threads around here too)
- put together flash cards for each situation, with the answer covered by your thumb.
- Now drill daily for 10 - 15 minutes, and within a week or so, you'll have 95% of all the situtions you'll ever need.

This is what I did when I was learning Blackjack deviation tables, and it works as well as it did when I was in 3rd grade learning multiplacaton tables... [img]/images/graemlins/smirk.gif[/img]

good luck!
Francis