2-7 Single Draw odds

Had never played it, but I think it depends on blockers. Not often but you could have for example 49%:
http://twodimes.net/h/?z=8047677
pokenum -l27 .....2d 3d 4s 7h vs.... qh/ - 2s 3s 4h 7d js
5-card Draw 2-7 Lowball: 42 enumerated outcomes
cards ............win %win lose %lose tie %tie EV
4s 3d 2d 7h ....20 47.62 19 45.24 3 7.14 0.512
Js 3s 2s 7d 4h 19 45.24 20 47.62 3 7.14 0.488

in 2-7 triple draw, if you get dealt trip deuces, along with 7,6 or 7,5, you can throw two (or even 3 to the 7,2) and you know that only one other player can possibly ever have a nut draw.

In Single draw, this isn't so powerful, since hands are often won by smooth 8s and 9s

I don't know why it has taken a month to answer -- I normally get notifications when someone replies

Cheers,
VS

Maybe this makes everything easier:

https://www.cardplayer.com/poker-tools/odds-calculator/deuce-to-seven

Hi CptJokerFish,
Thanks for thinking of this.

Note: I hid your post until I can find out whether the link to a competitor's website is acceptable.

I had a look, and the first hand I tried seems to give overly optimistic results:

The Example I chose was:
J♠:T♠:9♠:8♠:6♣: vs 7♥:4♥:3♥:2♦: | 2♣: <= tossed the deuce of clubs

So the worst J-lo, vs the best possible 1-card draw.
To make it even better, let's assume that the holder of the draw threw either a 7, 4, 3 or 2
thus there is one less card that can pair his hand.

In this case, from the point of view of the person drawing 1, there are 47 unknown cards.
When the J-lo stands pat, the drawing hand knows that 5 of his outs are missing -- it doesn't matter which ones.
(if the pat hand is J,7,4,3,2 the situation is even better for the drawing hand, since it is less likely he can pair.)

First, a pat J,T,9,8,6 vs 7,4,3,2 | 2 (threw the 2)
Outs:
3 Jacks
3 Tens
3 9s
4 8s
0 7s (pairs)
3 6s
4 5s
Thus there are 20 cards that give him the winning hand.
20/47 = 42.6%
The calculator gave the drawing hand 44%

In the situation where the pat hand is J,7,4,3,2 vs 7,4,3,2 | 2
The outs are:
2 Jacks (a Jack results in a tie)
4 Tens
4 9s
4 8s
0 7s
4 6s
4 5s
for 22 outs, 22/47 = 46.8%

mmmm, OK -- if you average those two, it's more-or-less 44%, but I did not specify the 2nd hand, only the first.

Also, in the calculator, if I mark the tossed deuce as "dead" then the drawing hand's chances improve slightly

I'd like to know the math behind that...

Adoraria aprender mais sobre esse jogo muito divertido, alguem aqui da coach dessa modalidade?

Originally posted by Afonso
Adoraria aprender mais sobre esse jogo muito divertido, alguem aqui da coach dessa modalidade?

translated by Google
I would love to learn more about this very fun game, someone here of the coach of this modality?

Hi Afonso,
welcome to the English Community forums.
Please use English to post here, since few of us know much Portugese.

If you don't know English, use https://translate.google.com/ to translate for you.

As for your question, we don't have coaches for 2-7 Single draw.
I've studied it, and I play it regularly on Pokerstars -- there is a $3.30 NL 2-7 Single draw PKO tournament each day at 20:03 UTC

I have been told that my calculations are off, but I haven't had time to re-do them.

All the best,
VS

Hey Afonso,

2-7 Draw games are not popular enough to justify having a coach, however SuperMod VorpalF2F plays it regularly.

You should check out his Twitch stream at https://www.twitch.tv/maugr1s

Regards

Laz

I did some calculations on the odds of making various hands when drawing 2 cards.

The assumptions:
 You are drawing to a smooth hand with no chance of hitting a straight. For example, if you are drawing two cards when holding 7,5,4 all the combos of (6,3) are poisoned outs since they make a straight.
 In each case, you hold the top card, and 3,2 The odds are the same no matter which two cards you hold, so long as you have no poisoned outs.
 If you hold 7,3,2 you can still hit an 8-, 9-, T-, or J-lo and the odds of doing so are the same as if you held that card. So the chance of hitting a 9-lo are 14.8% whether you hold 9,3,2 or 7,3,2

The primary table
              To hit:         7          8            9              T                J  
               #Outs:         3          4            5              6                7  
                Outs:     6,5,4    7,6,5,4    8,7,6,5,4    9,8,7,6,5,4    T,9,8,7,6,5,4  
               Cards:        12         16           20             25               30  
              Combos:        66        120          190            300              435  
        Remove pairs:        18         24           30             36               42  
     Combos that hit:        48         96          160            264              393  
       Unknown cards:        47         47           47             47               47  
       2-card combos:     1,081      1,081        1,081          1,081            1,081  
  Chances of success:      4.4%       8.9%        14.8%          24.4%            36.4%  
   Chance of failure:     95.6%      91.1%        85.2%          75.6%            63.6%  
                odds:    21.5:1     10.3:1        5.8:1          3.1:1            1.8:1  

The reason for going through this exercise is that I normally don't draw 2 cards at all, but I keep getting slaughtered by people doing exactly that.
In NL 2-7 Single draw, though there are very real implied odds, and in the bounty tournaments, the implied odds are even greater.

I will next revisit drawing 1, then I'll do drawing 3

All the best,
VS

Actually, we're more concerned with the chances of villain pairing his hand

If we are drawing 1, and villain is drawing 1, we need to know what are chances are if we draw an A or a K.
The assumptions:
 We are drawing 1 card, there are 47 unknowns (since we have seen 5 cards)
 Since we hold 4 cards of different ranks, there are 12 cards in the deck that will pair our hand

Therefore, we stand a 12/47 chance of making a pair or 25.5%
Stated another way the odds are 2.9:1 against making a pair.

Why do we care -- we don't want pairs!
We care because if we draw poorly, we can bluff-catch with some weaker made hands and villain bets out after having drawn 1.
Furthermore, if villain checks, we can bet ourselves -- bet/fold if we hit a reasonable hand.
We don't necessarily want to do this multi-way, though!

Cheers,
VS

Hmm I did a 1 draw simulation and this came back:

2-7 triple draw sim, 100000 trials, 1 draw:
Dead cards: 2♣

Hand 0: J♠ T♠ 9♠ 8♠ 6♣: EV 54.6% - WIN/LOSE/TIE %: 54.6/45.4/0.0
Hand 1: 7♥ 4♥ 3♥ 2♦ --: EV 45.4% - WIN/LOSE/TIE %: 45.4/54.6/0.0

I used the site Anykey44 recommended, and also one from cardplayer.com
The results are in the spoiler below.
Both agree at 54.75 to 45.25 in favour of the pat jack

Here are screenshots of the calculations on the two sites I used:
The equities are 54.75 and 45.25 in favour of the pat jack -- the slight differences are probably rounding errors

I am clearly missing something.
If I assume the drawing hand threw an Ace, then the odds are 54.78 to 45.22 in favour of the pat jack.

I can't see what I'm doing wrong.

[Edit: If we assume Hero's pat hand has no blockers to villains draw, then villain is drawing from a pool of 42 cards, and has 19 outs]

19/42 = 45.23% so hero has 54.76% chance of winning.

for every blocker Hero holds, his chances improve.

Regardless of nit-picking percentages, I did manage to bink the $3.30 NL 2-7 Single Draw PKO on Monday this week

Im not that much of a math freak so I dunno, sorry
PS: I use Troutulator for the sims

Originally posted by VorpalF2F
Regardless of nit-picking percentages, I did manage to bink the $3.30 NL 2-7 Single Draw PKO on Monday this week

Sweet
I recently binked $4.40 PL Badugi PKO

Nice -- I've cashed the Badugi, but never very deep.

I want to try to figure out the drawing odds for Badugi -- but I don't have lots of time these days

Not very likely, unless you have a lot of players behind you...

This table is only showing the chances of a player behind you having a better pat hand. There's nothing to stop any one of them from outdrawing you. We've previously looked at drawing odds...

The table shows each of the possible lowball hands in the first column, the number of combinations that make that hand in the 2nd column. In the third column is the total number of combinations of 5 cards that beat the given hand.
The remaining 6 columns show the chances (in %) that any one of that many players may have you beat.
Example: If you shove T5xxx UTG in a 7-handed game, there is a better than 10% chance one of the 6 players yet to act has it beat.

Note: to get all the columns to fit, widen your browser window to the max

The table: [1]
   Hand    Combos     Better        1        2        3        4        5        6  
  75xxx      1020          0                                                        
  76xxx      3060       1020     0.04     0.08     0.12     0.16     0.20     0.24  
  85xxx      1020       4080     0.16     0.31     0.47     0.63     0.78     0.94  
  86xxx      4080       5100     0.20     0.39     0.59     0.78     0.98     1.17  
  87xxx      9180       9180     0.35     0.71     1.06     1.41     1.75     2.10  
  95xxx      1020      18360     0.71     1.41     2.10     2.80     3.48     4.16  
  96xxx      4080      19380     0.75     1.49     2.22     2.95     3.67     4.39  
  97xxx     10200      23460     0.90     1.80     2.68     3.56     4.43     5.30  
  98xxx     19380      33660     1.30     2.57     3.84     5.08     6.31     7.52  
  T5xxx      1020      53040     2.04     4.04     6.00     7.92     9.80    11.64  
  T6xxx      4080      54060     2.08     4.12     6.11     8.06     9.98    11.85  
  T7xxx     10200      58140     2.24     4.42     6.56     8.65    10.70    12.69  
  T8xxx     20400      68340     2.63     5.19     7.68    10.11    12.47    14.78  
  T9xxx     34680      88740     3.41     6.71     9.90    12.97    15.95    18.82  
  J5xxx      1020     123420     4.75     9.27    13.58    17.68    21.59    25.32  
  J6xxx      4080     124440     4.79     9.35    13.69    17.82    21.75    25.50  
  J7xxx     10200     128520     4.95     9.65    14.11    18.36    22.40    26.24  
  J8xxx     20400     138720     5.34    10.39    15.17    19.70    23.99    28.04  
  J9xxx     35700     159120     6.12    11.87    17.27    22.33    27.09    31.55  
  JTxxx     56100     194820     7.50    14.43    20.84    26.78    32.27    37.34  
  Q5xxx      1020     250920     9.65    18.38    26.26    33.38    39.81    45.62  
  Q6xxx      4080     251940     9.69    18.45    26.35    33.49    39.94    45.76  
  Q7xxx     10200     256020     9.85    18.73    26.74    33.95    40.46    46.33  
  Q8xxx     20400     266220    10.24    19.44    27.69    35.10    41.74    47.71  
  Q9xxx     35700     286620    11.03    20.84    29.57    37.34    44.25    50.40  
  QTxxx     57120     322320    12.40    23.27    32.78    41.12    48.42    54.82  
  QJxxx     84660     379440    14.60    27.07    37.72    46.81    54.57    61.21  
  K5xxx      1020     464100    17.86    32.53    44.57    54.47    62.60    69.28  
  K6xxx      4080     465120    17.90    32.59    44.65    54.56    62.69    69.37  
  K7xxx     10200     469200    18.05    32.85    44.97    54.91    63.05    69.72  
  K8xxx     20400     479400    18.45    33.49    45.76    55.76    63.92    70.58  
  K9xxx     35700     499800    19.23    34.76    47.31    57.44    65.63    72.24  
  KTxxx     57120     535500    20.60    36.96    49.95    60.26    68.45    74.95  
  KJxxx     85680     592620    22.80    40.40    53.99    64.48    72.58    78.83  
  KQxxx    121380     678300    26.10    45.39    59.64    70.17    77.96    83.71  
  A5xxx      1020     799680    30.77    52.07    66.82    77.03    84.10    88.99  
  A6xxx      4080     800700    30.81    52.13    66.87    77.08    84.14    89.03  
  A7xxx     10200     804780    30.97    52.34    67.10    77.29    84.32    89.18  
  A8xxx     20400     814980    31.36    52.88    67.66    77.80    84.76    89.54  
  A9xxx     35700     835380    32.14    53.95    68.75    78.80    85.61    90.24  
  ATxxx     57120     871080    33.52    55.80    70.61    80.46    87.01    91.36  
  AJxxx     85680     928200    35.71    58.67    73.43    82.92    89.02    92.94  
  AQxxx    122400    1013880    39.01    62.80    77.31    86.16    91.56    94.85  
  AKxxx    167280    1136280    43.72    68.33    82.17    89.97    94.35    96.82  

[1] To keep the table size manageable, we're lumping together all hands with the same two top cards.
For example, 7,6,5,4,2 is lumped with 7,6,5,3,2 and 7,6,4,3,2. Clearly these hands are not the same, and if you shove 7,6,5,3,2 from the small blind there is a finite (but very small) chance that you will run into a better pat hand. I've busted out of a tournament in exactly that situation.

Also, If you jam 8,6,x,x,x with 6 players left to act pre-draw, there is a 1.17% chance that someone already has you beat, but don't despair, someone can draw to an 8,5,x,x,x and still beat you.

Comments?
VS