JCT: I made a small in my last post: "1,2 Overcard 6,12-out
threat odds vectors"

>>
When you're facing one opponent, that 12% chance is 7:1. But
with more opponents, it eventually gets down top even money.
How many opponents are needed for it to be 50:50 that my
Tens are still good? With 23 outs being half the deck, I
rated hands of between 20 and 26 outs danger as even money
shots, hands of 17-19 outs as 2:1 shots for or against and
14-16 outs as 3:1 and the usual 10 outs for 4 and the rest
of the outs-odds array.

JCT: Actually, it's:

hands of 14-19 outs as 2:1 shots for or against and 11-13
outs as 3:1 and the usual 10 outs for 4 and the rest of the
outs-odds array.

A silly typo.

So here's the complete array of threat outs vectors:
(best viewed in txt mode)

Odds for Outs vs Opponents

Opponents
1 2 3 4 5 6 7 8
Outs
2 22 11 7 5 4 3 3 2
4 10 5 3 2 2 1 1 1
6 7 3 2 1 1 1 2 2
8 5 2 1 1 2 2 3 4

10 4 2 1 2 2 3 5 6
12 3 1 2 3 4 5 7 10
14 2 1 2 3 5 8 12 18
16 2 1 3 5 8 12 19

18 2 2 3 6 11 19
20 1 2 5 9 16
24 1 4 8 18
30 2 7

When the odds were greater than 22:1 of a 2 out hand, I
didn't include it.

Let's say that on the River, there's a 4 straight on board.
8 possible cards to beat you x 2 cards = 16 outs danger.

With 1 opponent, it's 2:1 against him having it.
With 2 opponents, it's 1:1 even money.
With 3 opponents, it's 3:1 against you being good.
With 4 opponents, it's 5:1 against you being good.
With 5 opponents, it's 8:1 against you being good.
With 6 opponents, it's 12:1 against you being good.
With 7 opponents, it's 19:1 against you being good.
With 8 opponents, it's over 22:1 against you.

The most important thing to do is to learn the even money
50-50 cut points. On the left, it's odds against opponents
having it, on the right, it's the odds against you being
good.

Let's say that you have boss set when the 4-straight hits.
If the odds of opponent having you beaten are less than the
money in the pot, you should probably call. If they are way
more than the money in the pot, you should probably fold.

Knowing this information is very useful in calling but as I
pointed out in my previous post, it's more useful in making
more money when you have a really good chance of winning
(40%) and didn't realize it.


--
Abolitionist Debt Slave Leader John C."The Banking Systems Engineer"
Turmel for UNILETS interest-free time-based currency in U.N. resolution
C6 to Governments in the http://www.un.org/millennium/declaration.htm
http://www.cyberclass.net/turmel USENET blog: alt.fan.john-turmel