Rank of 2-Card Hands

[peak_007]

i posted this on the General Section but see that the "Theory" Section may be a better location:

I have read from a few differerent sources on the strength of two-card hands. Using Groups 1,2,3 from Sklansky, using point based systems, A=16pts, K=14pts, Q=13pts, with points for pairs, suited cards, and cards which can be part of a straight.

My question: Is there an empirical monte carlo work on the exact strength of two card hands (meaning probability that the hand leads to the best 7 card hand).

And secondly, if someone could provide not only rank of hands but the actual probability of winning so it can be determined which hands are marginably better than others and which are materially better than others.

If you could rank the first 2 cards you are dealt...how would you rank the following hands:

Here is my ranking but I haven't done a full Monte Carlo and not sure if my results are even in the correct order (in order of best hand to be dealt):

1) A,A
2) K,K
3) A,K (suited)
4) Q,Q
5) A,Q (suited)
6) J,J
7) K,Q (suited)
8) A,J (suited)
9) A,K (any)
10) K,J (suited)
11) Q,J (suited)
12) 10,10
13) A,10 (suited)
14) A,Q (any)
15) J,T (suited)
16) 9,9

Do others agree with my ranking of these 16 hands and how much better (or worse) mathematically is it to be dealt one versus the other off the first two cards?

Sorry this is long-winded.
Best Regards, /forums/images/icons/diamond.gif /forums/images/icons/confused.gif

[Bozeman]

The problem is the results depend on your assumptions.

The easiest is to assume that everyone will stay to the river, which yields aa,kk,qq,aks,jj,aqs,kqs,ajs,kjs,tt for a 10 player game.

http://www.worldzone.net/company/elpasochance/nf001020.html

If you want to take into account folding, you have to model the other players, and the results are sensitive to these model parameters. For example, abdul's site yields aa,kk,qq,jj,aks,ak,tt,aqs,ajs,99,aq,ats,kqs, ... for UTG with particular player models in TurboTexasHoldEm.
http://www.posev.com/poker/holdem/sim/utg10ta03b-1600.gif

Can you specify the properties of the game you would like to see simulated?

Craig

[peak_007]

/forums/images/icons/cool.gif
That makes sense. Of course it will be dependent upon number in to the river. So I suppose a general rule of thumb will be that the hands with straight-flush potential will be stronger the more players.

I am just trying to understand (quantitatively) how each of the powerful two-card hands tends to lead to the best hand, ultimately, by the time all 7 cards are down.

How much more frequently does AA lead to the best hand if you are dealt the AA and stay till the end versus KK and you stay until the end. I'm not talking about A,A vs K,K I'm talking about A,A winning vs. all others with no other info vs K,K winning vs all others with no other info known.

Anything empirically needs assumptions. So yea. For a 10 player game if you assumed all stayed until the end what % of the pots do AA's take. Of course garbage hands which will be folded will be played in the emprical study but I'm not interested in the number of pots AA's wins when all cards are drawn......but how well it does RELATIVE to say K/K or Q/Q. Understanding the relative strngth in hands is a key aspect to higher-level play.....(which I need to work on) regardless of whether you have 2 players vs 10 players.

Another example:
In straight up play:
how does 9,9 hold up vs JT (suited) vs AJ (unsuited). On a relative basis.

I am not articulating this well at all. But the essence of my question is getting to a better quantitive understanding of how many more times will a certain 2-card combo end up generating the best 7 card hand vs other 2-card combos. On a relative basis. /forums/images/icons/confused.gif

will check out the sites you posted
Peak

[Ed Miller]

Check out Two Dimes... http://www.twodimes.net/poker/

[Bozeman]

In a 10 player game, AA wins 31% and KK wins 26%.

Heads up against a random hand, AA wins 85%, KK wins 82%.

In a regular game, the difference between AA and KK is much greater. In abdul's simulation, AA won $56 while KK won $37 on average in $10-20 limit.

9d9h returns 51% against TsJs and 56% against AsJc.

These results come from the links I cited earlier, and "HoldEm Showdown" (twodimes could be used instead).

Craig

[AmericanAirlines]

Hey Peek-007,
Try these sites. The tables are no-foldem winning percentages per number of opponents.

Take a look at say, JJ. It ranks higher among its peer hands against 1 opponent (looks to be about 4th) than against 9 (looks to be about 6th). Picks up 2 places as your number of opponents goes down.

http://mentorms.best.vwh.net/poker/HE_Val_Sort.htm
http://mentorms.best.vwh.net/poker/HE_Value.htm

Sincerely,
AA