Sterno’s playkit #2. Number Cruncher, part one (number of opponents matter a lot)

[SternSwiss]

Hi all.


I like poker numbers.

They are very useful, since the games rely largely on understanding them, avoiding mistakes and pushing others to make some consistently over a huge number of hands.


So, I am intending to compile some of my personal documents (ie: notes, charts and other things gathered here or there) and to discuss them here, before embarking on other theory discussions as a kind of reference to discuss matters meanigfully.




This first thread is perhaps a bit abstract but I find it very useful and informative, especially for here.

The next ones will be shorter, and with more concrete examples discuss (or so is the plan).



The tables I discuss here describes ALL the possible combinations taking as a starting point any pre-flop hand, and then the chances of winnings if the hand is played until the river, depending on the numbers of opponents.

The full charts are posted below this blurb.


I find it extremely useful to understand different points, such as the barrenness of slow playing bullets or any top pair or even worse, unpaired premium, preflop.

What these figures show, for example, is that as soon as you have 5 people calling, you have more chances to loose with your AA than to win (though a close call), with KK & QQ it is 4 people, with JJ it is 3, with AK unsuited it is only 2 etc.



More widely, and this is what gets me on the whole the most desperate and leaving tournaments (either just leaving or playing carelessly) is the high number number of callers, even with steep raises because it makes any strategic play impossible.


There is often this argument voiced in the forum when people complain about games quality, saying that patience, patience, time will pay you off if you play sensibly. I never agreed to that point of view.

Of course one calling station is a blessing, two can be as well at times; but as soon as they add-up: there is no way to play any kind of meaningful game. And if you play with the “patience, patience” motto on the long run you will simply be loosing.




In more concrete terms. Imagine a situation we have all experienced I guess (I did so many bloody f-word times):

Early multitable tournament. You get QQ after a long-low-streak (and a few missed cheap calls) that started with your first hand 25 minutes ago.

Finally something chunky: "the ladies":

Hand Rank: 3 of 169 (Top 1.35%)
Deal Probability: 0.45%


Blinds are 25/50. You are in mid position; full table of ten. You get one limper in front of you, so the pot is now 125.

Nobody else has called and it is your turn to speak. Conscious of the loose callling tendencies you produce a steep raise to 350. Pot is 475.

The person after you calls, s/he is just a calling station and thinks his/her Q9 suited is worth being played..

The pot is now 825.

Nobody else calls until the small blind, who is a good player. S/he has a decent stack and an A10 suited. He calls. The move is legit with a chance taken on implied odds, so debatable.

The pot is now 1150 (25 were already paid by the sb).

The big blind doesn’t like his blinds raised and start to see what s/he regard are good pot odds: 300 to add, for odds of almost 1 / 4 and likely 1 / 5, if the last person calls. Playing an average hand is a possible move here, if one has a big enough M (say big stack).
Say s/he has K 10 suited and calls

The pot is now 1450, and the initial limper thinks that his 22 could very well make a huge hit if trips fall on flop, though odds are actually not in favour of calling (1/8th approx chances to hit trips on flop while pot odds are approx 1/5th)


S0 we end up with 5 players out of ten on flop. It is simply a disaster.

Ok: chances of winning this hand are thus:

You (QQ) = 37.9%

The calling station (Q9 suited) = 22.5%

The small blind (A10s) = 26.7%

The big blind (K10 suited) = 25.8%

The initial limper (pocket 2’s) = 15.5%

Sure, you are the favorite. Play in this configuration (approx independently of the specific hands of each) a thousand hands, you will loose 621 times.


Patience doesn’t pay at all.

The game becomes much more luck than skill and looses for me all interest if this repeats. Which it does not that rarely (and often which much worse hands).


And I think this is a crucial point for our beloved OP66 tables.


Notes on the example

1) The percentages exceed 100% when added (128,4%). Such percentages are always calculated perspective-based: in the shoes of the holder one of these pre-flop hands not knowing yet anything else. Just as when one is counting "outs", one can only take into account one's own hand and the community cards on table and not what others hold (Queens, 10's and suits interfere, as well as the proportion of high cards blocking some possible str8's)

For concrete examples and "third omniscient eye" figures adding to 100%, scroll below. 2 examples are discussed (changing the suits a tad to compare)


2) Of course, there is a fallacy in the example given since each hand won't be played until river: some people will fold. But it is more likely than not that you are already beaten on flop:

Chances of overcards hitting pair on flop is approx 15 % for each. There are two of those = 30%. Chances that the pair of 2's hit trips is 12%. Chances for the other players to hit a double pair is 2% each = 8%.
Chances of hitting flush directly when two suited cards = a bit less than 1% (so a total of 3%). Chances that others get trips by getting the same card on flop twice is 1.35 % (5.40% in total, for the 4 other players), then there are the possibilities of hitting striaghts for 3 players or, much less likely yet (but adding up), bigger nuts-monsters, etc., etc.

The total exceeds 50% anyway just on flop independently of any further play.

Now, you might tell that me is a good thing. Say say 43% percent chances to be ahead on flop (a guess, here: didn't compile all the possible combinations and smaller figures that add-up) with 1/5 preflop pot odds. Mathematically, yes. Besides, the fact that you'll likely have draws and all (which could be good for you too). Thing is you manage to get this figure with the 3rd ever best preflop hand. With the rest it of course fares much less. And callers substitute one for another hand after hand for draws, etc, you end up playing a much too random game (to my taste), even if you do make it through and win the hand.

And if you don't, which is more likely than the reverse, well, you will find yourself (in the scenario proposed) with a yellow-orange M, and little options to develop your game further.




Some other things you can see through these tables are:

1) Obviously the weight of having good cards preflop and of playing them well, in terms of raises.

2) The first column (one opponent) is useful to consider for heads-up

3) Meditating on all kind of concrete scenarios looking up these figures is very telling. Especially for end games or low M play (your low M or other player's).


I hope you will find this as interesting as I did. It is a good first base, I think.

.

[funkieskunky]

tht was alot to read but im not gonna lie...tht was extremely hepful....u know how u learn something new everday....i thyink im 20 days in advance now LOL...thanks for this stern

[zsazsaz]

Enjoying the threads Stern. Your personal style breaks up what could be a monotonous read. Nicely done sir

[CaptainSandy]

Very good and informative post Stern.
The only thing that puzzling is that in the original example we have 5 callers:
You (QQ) = 37.9%
The calling station (Q9 suited) = 22.5%
The small blind (A10s) = 26.7%
The big blind (K10 suited) = 25.8%
The initial limper (pocket 2’s) = 15.5%

This adds up to 128.4%.
I believe this is due to the percentage of the individual hand without knowing what the others hold.
As we know what each hand is, it would be interesting too see what the true percentages are for this senario (adding up to 100% - inc SP).
Unfortunately my brain is unable to do this hopefully someone can oblige.
Cheers.

[SternSwiss]

Originally Posted by CaptainSandy

Very good and informative post Stern.
The only thing that puzzling is that in the original example we have 5 callers:
You (QQ) = 37.9%
The calling station (Q9 suited) = 22.5%
The small blind (A10s) = 26.7%
The big blind (K10 suited) = 25.8%
The initial limper (pocket 2’s) = 15.5%

This adds up to 128.4%.
I believe this is due to the percentage of the individual hand without knowing what the others hold.
As we know what each hand is, it would be interesting too see what the true percentages are for this senario (adding up to 100% - inc SP).
Unfortunately my brain is unable to do this hopefully someone can oblige.
Cheers.

Thanks for your comments, all.


Yes, Sandy. It is exactly the reason why all add up to more than 100%.

Such percentages are calculated from the perspective of the holder one of these pre-flop hands. Just as when one is counting "outs", one can only take into account one's own hand and the community cards on table and not what others hold.

Here there are queens and tens entering into the picture (held by 2 diff players), as well as the repsective suits, which I didn't specifiy in my example as well as str8 draws conflation.

I crunched info into OP66's calculator and it gives this:

Scenario one:

Q Q = 25,9%

Q 9 = 13,0%

K 10 = 18,1%

2 2 = 20,2%

A10 = 22,9%


Total: 100,1%
Note the revalorisation of the poker 2's which gets correct actual odds by a millimiter (1/5). It gets this revalorization because lots of str8 possibilities are blocked for high cards due to respective holdings.



Of course suits will greatly affect the outcome...

If we make a tiny change:

QQ is now Q and Q and the Q9 is in

Rest remains the same.

Now the results are:

QQ = 30.3%
Q9 = 4.3%
K10 = 20,7%
22 = 18%
A10 = 26,6%

Note the huge drop for Q9 and the increase for QQ and A10s.



Thanks for the remark, I will add a comment on the OP so others do not get puzzled by the numbers.

[CaptainSandy]

Thanks for that, it's appreciated.
I'm amazed that the pair of twos has a 20% chance of winning as it needs to hit another 2 to win; also hope that no Q, straight or flush pops up.
Very interesting, ty.