No Limit Hold'em Poker Odds & Tourney Blind questions...

[CJD2011]

When computing outs & odds, I realize why you start with looking only at the cards you see (your two hole cards and those on the board) and most books recommend subtracting your outs from 46 and then getting your odds against ratio but was recently asked by one of our newer weekly players why you wouldn't count the other hole cards dealt out as well since those are no longer in the deck? He thought odds, if counted this way, would then actually increase as you go from 10 Handed down to Two Handed, mathematically anyway reasoning you would use a number less than 46 depending on how many players were dealt in. Told him since you don't know what those cards are they remain random and therefore remain part of the 'deck' and are not further subtracted from 46. Any thoughts here on how better to explain? Clearly I'm not a statistician!

This question started when three of our 10 players at the table had not yet arrived and we were dealing them in and blinding them off. Another player asked why we bothered doing this and one person said because it changed the odds if we didn't (effectively playing 7 Handed vs 10 Handed). Most of us however agreed that it had to do with the fact that it was a tourney (vs. cash) and would be unfair to let those present and posting blinds to allow those not present to get a free pass until they arrived. Again, any thoughts here on how to better explain?

Thx!

[Martini]

If your friend feels better to calculate odds based on how many players there are in the hand then why would you want to convince him otherwise?

[Dr. Neau]

This question started when three of our 10 players at the table had not yet arrived and we were dealing them in and blinding them off. Another player asked why we bothered doing this and one person said because it changed the odds if we didn't (effectively playing 7 Handed vs 10 Handed).

  

[BigPair88]

Make it simple, tell them that after the flop with the turn still to come, take their number of outs and multiply it by 4. That will roughly give them their percentage of making their hand ( add 2% and it may be a lil more accurate).  After the turn with the river still to come, take their number of outs and multiply it by 2. That will roughly give them their percentage of now making their hand ( add 1% and it may be a lil more accurate).

For example... if after the flop you have four to a flush ( you need one more to make your flush) there are 9 more of that suit to make your flush.
9 X 4 = 36
You are roughly 36% (or possibly 38%) to make your flush.
Lets continue with hand and assume ( Yeah yeah, I know what happens when you assume) the turn is a brick and you still have four to a flush.You still have 9 outs.
9 X 2 = 18
You are roughly 18% ( or possibly 19%) to make your flush.
There are probably much more accurate ways of calculating your odds and outs but this one is simple and it works for simple people like myself. 

My momma always says to use the KISS method....Keep It Simple Stupid

[stooks99]

First of all, in a tournament, if there is a stack, it gets a hand and it pays for being there.

The idea that it "changes the odds" depending on how many people get dealt in is ridiculous, UNLESS everyones cards are face up all the time.  If you have 2 cards and there are 3 board cards, that leaves 47 cards that you don't know anything about.  It doesn't matter if they are in the deck, in the muck, burn cards, or in someone's hand. 

[FLUX_13]

You either win the hand or lose the hand. The correct odds are 50/50.

Please don't take that too seriously.... just laugh.

[William]

That's not true, there's also a possibility for a split. So it's actually 1 in 3 that you'll win.

[Martini]

Or the hand could be nullified so it's more like 1 in 4.

[Milo]

Yeah but in a misdeal, you deal the same hand out all over again, so doesn't that double your chances?

[William]

That's right, then it's like 2 in 8, which is twice as good as 1 in 4.

[FSL009]

so effectively your trying to work out the chance of certain cards coming from the deck with very incomplete information.

this is done by a fraction which has a numerator and a denominator.

so if you understate the denominator you get the wrong answer.

if you overstate the numberator then you get the wrong answer.

ie if your looking for 2 more cards to get trips its 2 over 46 (if at the river).

2/44 = 4.5%  2x2 = 4% the 4 and 2 rule of thumb are good.

now lets assume your playing 9 other people so that is 18 cards. 

remove 18 from the denominator you would have 2/28 = 7% which is just crap cause its not the right answer cause you now dont know if the 2 are actually available gone, or whatever.  your both likely to be overstating the N and understating the D in this calc.

so the most accurate calc you can make is to leave the 18 in and hope like hell that you actually have the two cards in the deck and actually have better odds than that.

incomplete information means you have to make good assumptions and the assumptions are best made that of the remaining unknown cards you have a certain chance that the second one of the deck will be the card you need.