Fun Quiz:

Just some random questions I came up with. You can look up the answers to all of them, really, but what is the fun in cheating?

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts.

2) What is the lowest ranking hand preflop that can flop the stone cold nuts (unbeatable no matter what the turn and river are)

3) What hand has the greatest chance of beating AA preflop?

4) What non-pair hand has the greatest chance of beating 22 preflop?

5) What is the approximate % chance of top pair and a flush draw beating bottom 2 pair all in on the flop?

6) How much more often should you be dealt 72o than AKs?

7) What is the chance of being dealt AA If you were dealt AA on the last hand?

1. 62o
2. 62s
3. 67s
4. 67s
5. 50/50
6. (thinking) 3x more likely to have 72o
7. exactly the same as if you didn't have AA the hand before.

Close?

For 1) I don't mean preflop hand... i.e. 26 would make a 6 high straight, a 5 high straight is lower ranking. What is the lowest ranking 5-card hand that can be the nuts?

By the nuts, do you mean the nuts on a given board? Confuzzled.

A-5 straight?

1. 23 on an A459K board (or something similar)
2. 62s flopping a straight flush with 345s
3. I know it's a middle suited connector. Do 67s and 78s have different odds? I wouldn't think so.
4. Something middle and suited that the 2 doesn't interfere with the lower end of a possible straight? 67s?
5. No idea.
6. Almost exactly 3x more often (used a calculator)
7. The same as always 1/221

1) i think she means 7 high? (23457)
234567)
I have ADHD, I give up.

guessing...
2) 62s
3) some mid SC. 78s I think.
4) JTs
7) no difference (same probability)

I'm pretty sure 56s has the best chance against aces.

Wouldn't 89s, 87s, 76s, 65s, 54s all have the same chance since they can all make the most possible straights without being affected with the A?

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts.

Lowest possible nut hand is : QQQ78 (dealt QQ on a Q2378 board)

I think everyone got the rest:

2) 26s
3) 78s (different suits to the AA)
4) JTs (different suits again)
5) about 50%
6) 72s three times as often as AA.
7) The same - 220/1

I definitely know the answer to #3......it's 9-10s

It's definitely not.

I was wrong also, it's 56s

This makes sense if you think about it, because it rapes one of the ways AA can win, on a 2345 board.

Originally Posted by midas06

This makes sense if you think about it, because it rapes one of the ways AA can win, on a 2345 board.

That's smart, I didn't even think about that.

I actually had a 56 suited (spades) last night against AA. I knew he had a big pocket pair because of his big preflop bet. the flop was 4 8 10 with 2 spades. I called his 5 dollar bet. the turn was a 5 so I knew I had a crapload of outs. (15)I went all in w/ my last 11 bucks and of course the jack of clubs came down on the river. But man, good times....i was so close

Ok ill give these a go and then look down and see how wrong i am

Originally Posted by Demiparadigm

Just some random questions I came up with. You can look up the answers to all of them, really, but what is the fun in cheating?

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts.

QQ on a board of 2378Q

2) What is the lowest ranking hand preflop that can flop the stone cold nuts (unbeatable no matter what the turn and river are)

25s on a flop of A34s

3) What hand has the greatest chance of beating AA preflop?

Something like 67s

4) What non-pair hand has the greatest chance of beating 22 preflop?

something like 78s?

5) What is the approximate % chance of top pair and a flush draw beating bottom 2 pair all in on the flop?

45%? ish...


6) How much more often should you be dealt 72o than AKs?

72o can be delt in 12 ways. AKs can be delt in 4 ways.
3 times more common

7) What is the chance of being dealt AA If you were dealt AA on the last hand?
The same as if you werent. 4/52*3/51 = 12/2652 = 1/221

hmmm not too bad .

The 2nd one is not 25s. If the flop comes down A34s and the turn comes Ks, Qs, and the other person can have JTs to make a royal.

I'm late - but having not looked at the answers yet I'm taking a guess:

(1) Top Set on K J 8 5 2 rainbow board

(2) 56s straight flush flopped with 2 3 4 of the suit - cannot be beat

(3) 78s

(4) 9Ts

(5) 55%

(6) I dunno this one

(7) I dunno

56s, 67s, 78s all have the same (highest) chance of beating aces, but 56 > 67 > 78 when you look at ties.

1. the set of Qs

2. 26s Flop is 345 on suit.

3. 67s

4. 10Js

for Qs 3 and 4 I declined to look it up using software. My logic is that in Q3, we block the wheel straight. I can't see a difference between 56s and 67s. In question 4, the analogous choice would be 67s again to block the 1 card straight... but here high cards are valuable because they help to avoid having the board play (e.g. KKQQ8) would be a tie in the 67 case but not the J10 case

5. I'd say close to a flip. Depends how high is the highest pair of the 2 pair hand.

6. 3x more often

7. (4/52) * (3/51)

OK DEMI...
In a heads up game, what is the probability that one player will be dealt AK, and the other player is dealt 47?

Fun thread, let's see how bad I do.

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts. It would be top set on a board with no straight possibilities. 2378Q, set of queens.

2) What is the lowest ranking hand preflop that can flop the stone cold nuts (unbeatable no matter what the turn and river are) Obviously has to be the top end of a straightflush to take out the possibility of quads or someone else hitting a higher SF. 45s on A23 wouldn't work because of runner royal cards, So 56s on 234s flop.

3) What hand has the greatest chance of beating AA preflop? I think it's 67s or 78s, mid suited connectors I know.

4) What non-pair hand has the greatest chance of beating 22 preflop? Suited connecting overcards, the best of which is JTs.

5) What is the approximate % chance of top pair and a flush draw beating bottom 2 pair all in on the flop? Real rough math here...
9 outs to the flush, 3 outs to pair your 2nd hole card, 2 outs to pairing the turn card. 15 * 4 = 60%, minus the chance that he FHs which is 4 * 4 or 16%. ~45%

6) How much more often should you be dealt 72o than AKs? 4 ways to get AKs, 16 ways to get 72o, 4 times more.

7) What is the chance of being dealt AA If you were dealt AA on the last hand? 4/52 * 3/51 = 12/2652 = 1/221

After looking at other posts, looks like I got one wrong (#2.) Not bad. Oops, relooked and got #6 wrong too, that was a stupid mistake, you obviously can't get 72o after getting a 7 and 2 of the same suit. :[

For the last time.... 56s is the smallest dog against aces.

Jimmy Mac got them all right. Although I stand by 56s over 67 and 78s as the favourite over AA .... Mainly because Stove gives them like a .00something edge.

i was agreeing that 56 is the best against aces, i was just clarifying why. its because your odds of tying go up, which makes it more +EV. your chances of actually winning happen to be the same for 56-67-78. its just like a sidenote or pithy fact or whatever

can someone give an intuitive reason why 56s is preferred to 67s.

I agree with 78s is inferior, but since both the above choices block the wheel straight and I would have to think they are equivalent. Can someone give an intuitive explanation rather than "it's just so"?

1) 23os
2) 23s
3) T9s
4) T9s
5) 55/45
6) 3x
7) 1 in 221

Edit: I should have probably checked the bottom of the post before answering. I would have had 100% right then

Originally Posted by Demiparadigm

Just some random questions I came up with. You can look up the answers to all of them, really, but what is the fun in cheating?

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts.

2) What is the lowest ranking hand preflop that can flop the stone cold nuts (unbeatable no matter what the turn and river are)

3) What hand has the greatest chance of beating AA preflop?

4) What non-pair hand has the greatest chance of beating 22 preflop?

5) What is the approximate % chance of top pair and a flush draw beating bottom 2 pair all in on the flop?

6) How much more often should you be dealt 72o than AKs?

7) What is the chance of being dealt AA If you were dealt AA on the last hand?

Havn't looked at the thread at all. Some of these could be wrong.

1. A set on a non straight, non flush board. Set of Q's I believe. Board 2378Q. I don't really feel like thinking about it too much but I should know this.

2. Suited connected trash. It absolutely cannot be a big pair or big cards. SF/RF possiblities are always there. Even if you hold AA on AA7r board. 3s6s. Board 2s4s5s.

3. 67s I believe. The suited connectors that can't use an ace to make a straight are all pretty much the same.

4. Hrrrm. I'd say a high suited connector, something like a JTs or so. Definately something similar.

5. I'd say it's about a flip, probably with a slight edge for the tp + draw. Depends on the exact hands, but you gotta figure 5 tp/trips outs, 9 flush outs, and board pairing outs, say another out or two there. 2pr has 4 full house outs.. eh... A slight favorite to the top pair + flush draw combo.

6. 12 combos of 72o. 4 combos of AKs. 3x as likely.

7. Anyone who gets this wrong (assuming they know the probability of being dealt AA) should quit poker and anything related to mathematics. Events are independant of each other. Chances are still 1/221.

Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Ad 1315168 76.81 391637 22.87 5499 0.32 0.770
7s 6s 391637 22.87 1315168 76.81 5499 0.32 0.230

 Holdem Hi: 1712304 enumerated boards
cards win %win lose %lose tie %tie EV
Ac Ad 1314307 76.76 391582 22.87 6415 0.37 0.769
6s 5s 391582 22.87 1314307 76.76 6415 0.37 0.231

so, 76s actually flat out wins 55 more times, but 56s ties 916 more times.

Can someone confirm (reject) that the winning % for 56s against AA is identical to 67s past 2 decimal places?

Originally Posted by Lukie

Can someone confirm (reject) that the winning % for 56s against AA is identical to 67s past 2 decimal places?

Were gunna have to do some maths on this for a proof.

I think its too close for Pokerstove which just conducts trials as far as im aware so there is the same varience you would expect in a real game.

it is simple, assuming their hands won is correct, then 67s flat out wins 0.228719316% of the time, and 56s flat out wins 0.228687196% of the time

as said before, the EV for 56s is higher though.

as for why any of that is, its too complicated for me to figure out. trying to determine 900 out of 1.7 million hands is too hard

Code:

pokenum  -h ah ad  - 7s 8s 
Holdem Hi: 1712304 enumerated boards
cards      win   %win     lose  %lose   tie  %tie     EV
Ad Ah  1315602  76.83   391672  22.87  5030  0.29  0.770
8s 7s   391672  22.87  1315602  76.83  5030  0.29  0.230

pokenum  -h ah ad  - 6s 7s 
Holdem Hi: 1712304 enumerated boards
cards      win   %win     lose  %lose   tie  %tie     EV
Ad Ah  1315168  76.81   391637  22.87  5499  0.32  0.770
7s 6s   391637  22.87  1315168  76.81  5499  0.32  0.230

pokenum  -h ah ad  - 5s 6s 
Holdem Hi: 1712304 enumerated boards
cards      win   %win     lose  %lose   tie  %tie     EV
Ad Ah  1314307  76.76   391582  22.87  6415  0.37  0.769
6s 5s   391582  22.87  1314307  76.76  6415  0.37  0.231

67s wins a few more times against AA then 56s because if the board is 23456 ... 67 would win..

if it was AA vs 56 on this board it would be a tie..
56s shares alot more straights boards with AA then 67s does

56s and 67s lose a few extra hands against AA because if the board was 2/3/4/5 all the same suit of either ace, the ace would have a straight flush.. so thats 2 hands that 56s & 67s make straighst and still lose that 78s wouldn't because 78s is completely out of range for any straight AA could make.
Since the order of the cards doesnt matter, those 2 straight flushes actually generate 100s of hands that 56s & 67s loses against AA that 78s doesnt.

Example
Ah Ad VS 5s 6s (or 6s 7s)

Boards
2h 3h 4h 5h 9c
2h 3h 4h 5h 9d
2h 3h 4h 5h 9s
2h 3h 4h 5h 9h
2h 3h 5h 4h 9h
etc, etc

67s and 78s are VERY close (winwise).. much closer then 56s and 67s..
this is because 67s shares very little straights with AA.. its just the one situation where 67s would lose to the A to 5 straight flush..78s cant possibly lose a hand where it makes a straight to a straight flush because its not in range of any straights that have an ace.

6/7s wins a few more hands then 5/6s because of the one situation where the board is 23456.. but as I said before since the order doesnt matter that generates 100s of boards where 67s wins and 56s ties
7/8s has the least amount of ties because it is completely out of range of any straight AA could possibly make... but as stated has a greater EV against AA..

but since the question was
"3) What hand has the greatest chance of beating AA preflop? "
7/8s is the correct answer

Note: I already knew the answer, didnt look it up, just posted the stats because everyone seems to be confused about the situation.. I was also very tired when I typed this, so it might be hard to understand, ill reread it tomorrow...

4) What non-pair hand has the greatest chance of beating 22 preflop?

I see alot of people put 9Ts.. but I believe TJs is the correct answer.. TJs would win a few more hands that 9Ts would tie.

9Ts can end up tieing its low straights if another card comes down tomake the board a higher straight.. example

board TJQK if a 9 or Ace comes down itll be a tie
this happens to TJs alot less because it makes the top straights, so its lowest straight is broadway..
so the worst that could happen to TJ is if the board was JQKA.. a Ten could come down to make it a tie..

which is why TJs would win a few more times against 22 then 9Ts would

It seems that many of you think that the differences between 65s/76s/87s against AA in some way related to them blocking or dominating the possibilities for AA to make the wheel (or straight-flush versions thereof). This is actually completely wrong.
Story time: A few months back I decided to write my own poker number-crunching programs. I used AA vs 76s as a test case while debugging. In my first drafts I didn't bother including the extra lines of code necessary to allow A to play low in a straight. When I did add the code I at first thought I had got it wrong: the output for AA vs 76s did not change at all!
But when you think about it it makes perfect sense: there really is no way that AA will beat 76s with a straight (or straight flush) it it could not also beat it with a pair of aces (or a flush). If we changed the rules so that you cannot play an A at the low end of a straight the win/tie/lose probabilities for AA vs 76s would stay exactly the same. So the wheel really is not the issue here.
What's actually behind the differences in win/tie/lose probabilities between 65s/76s/87s against AA is that the lower ones are more likely to have their straights counter-feited by board straights, so they are slightly less likely to win. On the other hand it is more likely that there will be some board straight, so they are more likely to tie.

Originally Posted by Bailey

which is why TJs would win a few more times against 22 then 9Ts would

There's also good ol' high card power. JTs is more likely to play its kicker on a two pair or quad board, less likely to have boats counter-feited etc.

1) What is the lowest ranking hand that can be the nuts on the river?
EDIT: *NOT* pre flop hand... lowest ranking 5 card hand that can be the nuts. Set of queens

2) What is the lowest ranking hand preflop that can flop the stone cold nuts (unbeatable no matter what the turn and river are)? JTs

3) What hand has the greatest chance of beating AA preflop? 78s

4) What non-pair hand has the greatest chance of beating 22 preflop? 78s

5) What is the approximate % chance of top pair and a flush draw beating bottom 2 pair all in on the flop? 40%

6) How much more often should you be dealt 72o than AKs? Even

7) What is the chance of being dealt AA If you were dealt AA on the last hand? Same odds as being dealt any other pocket pair (not sure what exactly). Odds of getting AA twice in a row? That would be the AA dealt % squared.

67s

2345x
345xx
348xx
489xx
89Txx
89TJx


78s

4567x
456xx
569xx
69Txx
9TJxx
9TJQx

Okay.. now I am confusing myself, prior to using that calculator on twodimes I always thought 67s was the best against AA.. and logically it should be.. because 78s can lose alot of low end straights to ace high straights.. ie

9TJ flop.. turn Q river K .. if that was 67 in this situation itd be a tie rather then a lose.

Krimson you were right about the straight flush thing because under those same circumstances that could happen to any hand on their straight board, but it would just be a flush.

So, how is 78s slightly better then 67s?

Blah I give up.. the %s are so close for all of them it doesnt matter !

Originally Posted by krimson

It seems that many of you think that the differences between 65s/76s/87s against AA in some way related to them blocking or dominating the possibilities for AA to make the wheel (or straight-flush versions thereof). This is actually completely wrong.
Story time: A few months back I decided to write my own poker number-crunching programs. I used AA vs 76s as a test case while debugging. In my first drafts I didn't bother including the extra lines of code necessary to allow A to play low in a straight. When I did add the code I at first thought I had got it wrong: the output for AA vs 76s did not change at all!
But when you think about it it makes perfect sense: there really is no way that AA will beat 76s with a straight (or straight flush) it it could not also beat it with a pair of aces (or a flush). If we changed the rules so that you cannot play an A at the low end of a straight the win/tie/lose probabilities for AA vs 76s would stay exactly the same. So the wheel really is not the issue here.
What's actually behind the differences in win/tie/lose probabilities between 65s/76s/87s against AA is that the lower ones are more likely to have their straights counter-feited by board straights, so they are slightly less likely to win. On the other hand it is more likely that there will be some board straight, so they are more likely to tie.

Originally Posted by Bailey

which is why TJs would win a few more times against 22 then 9Ts would

There's also good ol' high card power. JTs is more likely to play its kicker on a two pair or quad board, less likely to have boats counter-feited etc.

Great post. I didn't think of this myself. I think I've finally cracked this puzzle.

1. 56s is more likely to tie than 67s than 78s. This is because more central cards (7s and 8s) remain in the deck and therefore more board straights available. 67s is the second most likely to tie, and 78s the least likely out of all three.

2. 87s is more likely to win than 67s than 56s. This is not because of straights being counterfeited (that makes no sense). The reason is because of *flushes* being counterfeited. If you hold 87s, then the only board flush and tie by coming AKQJ10, AKQJ9, and AKQ109 (all in the suit of the connector). Any other possibility gives the 78s a straight flush. But as you go down to 76s and 65s, there are a lot more ways (like AQ1097 spades coming down then you hold 65s is a tie, not a win for 65s.

3. 87s is more likely to lose than 67s or 56s. This is because one of the straight boards made by 87s is actually a loss (9 10 J Q K).

So there you go. Mystery solved.

Also, can someone verify that the lowest pre flop hand that can be the stone cold nuts on the flop is indeed 26s and not any of the other answers given?

Also, can someone verify that the lowest pre flop hand that can be the stone cold nuts on the flop is indeed 26s and not any of the other answers given?

We need to flop a straight flush for the stone cold nuts, as quads on the flop is vulnerable (to higher quads or a straight flush). We can't have the ace on the flop, as then we are vulnerable to a runner runner royal.

23s cant make the nut straight flush without an A on the flop.
24s is vulnerable on a 356s flop
25s is vulnerable on a 346s flop
26s - flop 345s no higher straight flush is possible (as we hold the 6)