those odds i gave were from pokertips.
You're telling me that there are two hands that have a more even chance of winning than what i posted?
Are you looking for highest chances to tie, or most even chances to win?
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those odds i gave were from pokertips.
You're telling me that there are two hands that have a more even chance of winning than what i posted?
Are you looking for highest chances to tie, or most even chances to win?
The most even chances to win. I'm not sure if its the best answer, but I found one that is 49.58/ 49.54.
lol, that is closer by .02. that's gonna be a hell of a one to figure out though.
No what I was saying is that they make the same amount of straights and that the 23456 board case counts as part of 56s' straights and 67s' straights (because if 23456 is a variation of 345 then its also a variation of 234).
Explain it to me in terms of straights made using one of the hole cards (in other words there is no straight on the board).
According to me this would be the same number for 56s and 76s. Is this wrong?
Now if there is a straight on the board there is no case where 56 does better than 76.
So why is 56 the favourite?
Quote:
Originally Posted by Martini
I don't understand why the online simulation would be any more accurate than pokerstove, more likely it would be less accurate as it runs such a short time. I am using the Monte Carlo method on AQs v 22 for a good 15minutes now and the valuehas pretty much set to 50.0109% and its not changing anymore. Give me the hand you think is correct and I will run it a similar amount of time and don't tell me that the Monte Carlo algorithm used is not accurate because it is.
Check your math.Quote:
Originally posted by Cocco_Bill
Hmm, even if I use pokertips.org, the differense is 0,06 between AQs and 22, same as the one you found.
Does pokerstove account for ties? The simulator at pokertips does and it doesn't use an algorithm. It gives you the exact odds every time.
arkana it seems you are comparing 5,6 vs 6,7 vs A,A, istead of comparing 5,6 vs A,A and 6,7 vs A,A.
"No what I was saying is that they make the same amount of straights and that the 23456 board case counts as part of 56s' straights and 67s' straights (because if 23456 is a variation of 345 then its also a variation of 234). "
no, that last part is wrong. 23456 is not a variation of 234, because it creates a tie. However, it does not create a tie for 67, so it is a variation of 345 in that case.
When i was saying that all that matters is whether or not a hand is a variation of 234, or 345, etc., this was under the assumption that no tie is created. With 23456, there is a tie created for 56, breaking that assumption, so it is not just a variation of 234. Something is a variation of 234, or 345, etc., only when the other two cards do not change the outcome. The other two cards can either a. create a tie or b. create a loss. there is no need to record losses as they will be equal, so we must look at only ties. So, in this situation, for the hand 67, the board 23456 is a variation of 345, because it creates the winning straight of 34567, however for the hand 56, it is not a variation of 234, because it does not create the winning straight, 23456, it creates a tying straight.
What you are doing, is you are double counting. You are saying, ok 23456 forms a tie for 56, and a win for 67. so, 67 has one more win than 56. But that win for 67 has already been accounted for when we previously said that they will both win the same number of times. It is being counted twice.
And Im thinking you are counting 23456 as a win and a tie for 56, while you are thinking im counting 23456 as 2 wins for 76. :)
You probably have it figured out, I just cant quite follow your argument... I will have a think about it.
Just to make it more interesting here is what the the calculator at pokertips said:
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
As Ah 1315168 76.81 391637 22.87 5499 0.32 0.770
7d 6d 391637 22.87 1315168 76.81 5499 0.32 0.230
Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
As Ah 1314307 76.76 391582 22.87 6415 0.37 0.769
6d 5d 391582 22.87 1314307 76.76 6415 0.37 0.231
So you are right, 56s ties more often. But why does 76s win more often??? Does the fact that two Aces have been removed from the deck influence the possible straights? think A234 which would have given 56 a straight. (EDIT: ok the A isnt needed so I suppose it doesnt make a difference)
Anxiously awaiting your reply :)
6,7 doesn't win more often than 5,6. They both beat A,A the same amount of the time. A,A wins slightly more against 6,7 because of the one extra tie that 5,6 makes. That one extra tie takes away a win for A,A.
Nope that is not what its saying:Quote:
Originally Posted by Martini
The output is that out of the 1712304 boards
56 wins 391582 loses 1314307 and ties 6415 times (numbers sum to 1712304)
and
67 wins 391637 loses 1315168 and ties 5499 times (numbers sum to 1712304)
The rounded percentages are the same though.
Now you did it. I'll be thinking about this all day. :(
Okay, I got it.
5,6 beats A,A with this on board straight:
A,2,3,4,5
6,7 beats A,A with these on board straights:
A,2,3,4,5,
2,3,4,5,6
What makes it even worse is that there are only two Aces left in the deck for the A,2,3,4,5 straight.
so 67 both wins more and loses more than 56.
:shock:
6,7 wins more up against A,A than 5,6, but 5,6, wins and ties (and loses less) up against A,A more than 6,7 does, so, I would say that you are better off having 5,6.
i just read this post. Can someone give me back my 5 minutes please?
It looks like the hand that actually beats A,A the most times heads up is 7,8s (where the suit is different from the suit of the Aces).
well, now that we thoroughly understand the answer to what hand wins the most, wins + ties the most, etc. against aces, let's go on to another pointless question,
what's the closest heads up matchup that you found?
4,4 vs. j,t using all four suits.
I'm still waiting for someone to name the most lopsided head-up match.
I thought we did that? AA vs A6 or A9, where the 6 or 9 is the same suit as an ace
Not the right answer. Hint: neither of the hands is A,A
27 vs 77
not sure if i agree with that though, if that is it. The 7's actually win less in that situation than they do in aa vs a9, just 27 wins less but ties more.
i'm actually changing my answer. Kings vs. K2 suit overlapped
Yup, you got it.
78s is the most likely to win, but 56s has the best EV because it is more likely to tie (twodimes.net/poker).
All of the following boards make both 78 and 56 tie with AA (as long as there's no flush), but the boards marked with a * are more likely to fall if you have 56 than if you have 78:
AKQJT
QJT98 *
JT987 *
T9876 *
98765
87654
76543 and 65432 also give 56 a tie, but they give 78 a win. Also, if all 5 cards are the same suit as the hole cards, boards like AQJ95 make 78 win, whereas corresponding boards like AQJ97 make 56 tie.
- Nate
910 suited gives you the best odds against AA but I’m sure someone already said that... :lol: :wink:
just to add more fire to the mix...
have you guys considered the fact that with 65s, the aces are potentially taking 2 outs away from you if the board is 234, and with aces, the 65s is taking 1 out from you if the board is 234...
oh snap! what did i do now...
Odds of suited connectors beating AA when the suit does not overlay a suit of either Ace:
32s: 17.602%
43s: 19.626%
54s: 21.649%
65s: 23.056%
76s: 23.033%
87s: 23.021%
98s: 22.623%
T9s: 22.765%
JTs: 21.717%
QJs: 19.701%
KQs: 17.685%
AKs: 12.141%
The winner is 65s just barely clipping 76s.
Source: PokerStove, run in full evaluation mode so that it considers all possible 5 card flops. In this particular case,PokerStove reports that as 1,712,304 boards. That jives with the expected (48! / 43! ) / 5!.
Poker Stove is giving you incorrect results. Does Poker Stove account for ties? As I posted earlier, the simulator at pokertips.org gives you exact results the way a calculator does and accounts for ties. The simulator at twodimes.net works equally as well. They do not simulate thousands of hands.
65s will beat AA 391,582 times (22.8687% of the time) out of all the possible hands that can be dealt and 76s will beat AA 391,637 times (22.8719% of the time).
PokerStove accounts for ties splitting equity evenly between the winning hands in such a case. As I mentioned, PokerStove DOES NOT sample hands, it iterates through the entire set of 1,712,304 possible boards in that scenario and it reports as such.Quote:
Originally Posted by Martini
From the pokerstove website:Quote:
Originally posted by Pyroxene
As I mentioned, PokerStove DOES NOT sample hands, it iterates through the entire set of 1,712,304 possible boards in that scenario and it reports as such.
The simulators at pokertips.org and twodimes.net are superior, in that they will both give you the exact number of hands it is possible for each hand to win and tells you exactly how many ties there are. They don't average anything out over repeated trials. The hand that wiil actually beat A,A more than any other heads-up is 8,7s (where the suit is different from the suit of the Aces).Quote:
The values generated are all-in equity values. This is not the chance that a hand will win the pot. Rather it is the fraction of the pot that a hand will win on average over many repeated trials, including split pots.
PokerStove can be set to run in an average over repeated trials. But I have set it to run in full evaluation mode. As I have said, it iterated through all the possible board combinations and reported that number of board combinations through which it iterated. It's reported iteration count was 1,712,304 which is exactly the expected count of a 48_C_5 equation. The difference in expectation is brought about through the ties. To be specific, the utility that you mention at two dimes reports that 65s will win 391582 times and will tie 6415 times out of 1,712,304 possible boards. As there are two hands, ties provide 50% equity, yielding an effective equity of (391582 + 6415 * 0.5) / 1,712,304 or 23.056% which is exactly the equity that PokerStove gave, as listed in my first message. As to 76s, the two dimes utility reports 391637 wins and 5499 times. Again, ties yield a 50% equity so 76s would have an equity of (391637 + 5499 *0.5) / 1,712,304 or 23.033% which, again, is exactly the equity given by PokerStove in my first message. For completeness, the 87s numbers from twodimes yields an equity of 23.021, also matching PokerStove's measurement.Quote:
Originally Posted by Martini
The point of this being, 65s fairs better then 76s or 87s because of an increased number of ties and the 50% equity returned from such ties. Both PokerStove and the twodimes utility yield identical numbers bearing this out.
I already mentioned that 65s is the best hand to have heads-up against AA. As a side note, I posted that 78s actually beats AA more than any other hand heads-up.Quote:
Originally posted by Pyroxene
The point of this being, 65s fairs better then 76s or 87s because of an increased number of ties and the 50% equity returned from such ties. Both PokerStove and the twodimes utility yield identical numbers bearing this out.
Your quote:
It turns out that Pokerstove isn't incorrect, but you were incorrect stating that you were giving the odds of suited connectors beating AA. You were listing expected values. 87s has the best odds of beating AA.Quote:
Odds of suited connectors beating AA when the suit does not overlay a suit of either Ace:
32s: 17.602%
43s: 19.626%
54s: 21.649%
65s: 23.056%
76s: 23.033%
87s: 23.021%
98s: 22.623%
T9s: 22.765%
JTs: 21.717%
QJs: 19.701%
KQs: 17.685%
AKs: 12.141%
The winner is 65s just barely clipping 76s.
Ah, I see what you are saying now. I was speaking in terms of what hand other than the other AA has the best EV against pocket Aces. You were speaking in terms of actually beats. That being the case, yes I agree that 87s actually has a higher chance of beating AA; I should have been more clear that my numbers where EV%. I will note again, however, to those reading this that it still has a lower EV against AA due to ties.Quote:
Originally Posted by Martini