Hidden Outs Revisited

1.
Win 3xK, 2xA = 5
Chop 3×9 = 3

2.
win 3×2 = 3
Chop 3xJ, 3×9, 3×3 = 9

3.
Win 4×5, 3×2 = 7
Chop 3×3, 3×4 = 6

4.
Win 3xQ, 3xT, 3x, 1xA = 10
Chop 6c, 8c, 9c, Jc, Kc = 5

5.
Win 3xA 3xQ 3XJ = 9
Chop 3×8 = 3

6.
Win 3×4 = 3
Chop 2xK 2×2 = 4

7.
Win 1×3 2×9 = 3
Chop

8.
Win 4xA, 4×6, 3×3 = 11
Chop 3×2, 3×5 = 6

9.
Win 3×3 = 3
Chop 3xT 3×4 4xK 4xQ 4xJ = 18

10.
Win 2×2 = 2
Chop 2xA, 2xJ, 4xK, 4xQ, 4xT, 4×9, 4×8, 4×7, 4×6, 4×5, 4×4 = 40

Here’s my count of the outs:

1. Win: 5 outs (2 aces, 3 kings). Chop: 3 outs (3 nines).

2. Win: 3 outs (3 twos). Chop: 10 outs (1 ace, 3 jacks, 3 nines, 3 threes).

3. Win: 3 outs (3 twos). Chop: 6 outs (3 fours, 3 threes).

4. Win: 10 outs (1 ace, 3 queens, 3 tens, 3 sevens). Chop: 5 outs (Kc, Jc, 9c, 8c, 6c).

5. Win: 16 outs (3 aces, 4 kings, 3 queens, 3 jacks, 3 eights). Chop: 0 outs.

6. Win: 3 outs (3 fours). Chop: 19 outs (4 aces, 1 king, 4 queens, 4 jacks, 4 tens, 2 twos).

7. Win: 3 outs (2 nines, 1 three). Chop: 0 outs.

8. Win: 11 outs (4 aces, 4 sixes, 3 threes). Chop: 6 outs (3 fives, 3 twos).

9. Win: 3 outs (3 threes). Chop: 18 outs (4 kings, 4 queens, 4 jacks, 3 tens, 3 fours).

10. Win: 2 outs (2 twos). Chop: 42 outs (everything else).

Corrections:

3. Win: 7 outs (4 fives, 3 twos). Chop: 6 outs (3 fours, 3 threes). (I missed the straight outs.)

5. Win: 13 outs (3 aces, 4 kings, 3 queens, 3 jacks). Chop: 3 outs (3 eights). (The eight outs only tie, not win, because of the ace on the board.)

OK, just for the hell of it:

1. Two aces and three kings for a win; three nines for a chop. (7.5 outs)
2. Three deuces for a win; three jacks, three nines, and three threes for a chop. (7.5 outs)
3. Three deuces and four fives for a win; three fours and three threes for a chop. (10 outs)
4. Three queens, three tens, and three sevens for a win; KJ986 of clubs for a chop. (11.5 outs)
5. Three aces, four kings, three queens, three jacks, and four nines for a win; three eights for a chop. (18.5 outs)
6. Three fours for a win; two kings and two deuces for a chop. (5 outs)
7. Two nines and one three for a win. (3 outs)
8. Four aces, four sixes, and three threes for a win; three fives and three deuces for a chop. (14 outs)
9. Three threes for a win; three tens and three fours for a chop. (6 outs)
10. This hand is backwards; A3 cannot win the hand. A2 has two deuce outs to a win, all other cards result in a chop.

I missed the case ace on #2 and a bunch of kickers on #6 and #9. Oh well.

1.
Win: (5) 2 aces, 3 K’s
Chop: (3) 3 nines

2.
Win: (3) 3 deuces
Chop: (22) 1 Ace, 4 K’s, 4 Q’s, 3 J’s, 4 Tens, 3 nines, 3 threes

3.
Win: (7) 4 fives, 3 deuces
Chop: (6) 3 fours, 3 threes

4.
Win: (9) 3 Q’s, 3 tens, 3 sevens
Chop: (5) Kc, Jc, 9c, 8c, 6c

5.
Win: (17) 3 aces, 4 K’s, 3 Q’s, 3 J’s, 4 nines
Chop: (3) 3 eights

6.
Win: (3) 3 fours
Chop: (19) 4 aces, 1 K, 4 Q’s, 4 J’s, 4 tens, 2 deuces

7.
Win: (3) 2 nines, 1 three
Chop: (0)

8.
Win: (11) 4 aces, 4 sixes, 3 threes
Chop: (6) 3 fives, 3 deuces

9.
Win: (3) 3 threes
Chop: (18) 4 K’s, 4 Q’s, 4 J’s, 3 Tens, 3 fours

10,
Win: (2) 2 deuces
Chop: Every other card in the deck.

That smiley for number 9. is just supposed to say eighteen cards for the chop.

1. 5 to win, 3 to chop
2. 3 to win, 22 to chop
3. 7 to win, 6 to chop
4. 9 to win, 5 to chop
5. 13 to win, 3 to chop
6. 3 to win, 19 to chop
7. 3 to win
8. 11 to win, 6 to chop
9. 3 to win, 18 to chop
10. 2 to win, many to chop

1. 2 Aces (W), 3 Kings (W), 3 Nines (T)
2. 3 Deuces (W), 3 Jacks (T), 3 Nines (T), 3 Threes (T)
3. 3 Deuces (W), 3 Fours (T), 3 Threes (T)
4. 3 Queens (W), 3 Tens (W), 3 Sevens (W), 5 clubs tie (K, J, 9, 8, 6)
5. 4 Kings (W), 4 Nines (W), 3 Queens (W), 3 Jacks (W), 3 Aces (W), 3 Eights (T)
6. 3 Fours (W), 2 Kings (T), 2 Deuces (T), 4 Tens (T), 4 Jacks (T), 4 Queens (T), 4 Aces (T)
7. 2 Nines (W), 1 Three (W)
8. 3 Threes (W), 4 Aces (W), 4 Sixes(W), 3 Fives (T), 3 Dueces (T),
9. 3 Threes (W), 3 Fours (T), 3 Tens (T), 4 Jacks (T), 4 Queens (T), 4 Kings (T)
10. 2 Deuces (W), every other card is a tie!

And my corrections:

2: Missed: 1 Ace (T)
3: Missed: 4 each: KQT9
6: 1 King, not 2 – duh.

I got 5/10 correct.

If anyone wants more practice, you might try this:

http://www.castrovalva.com/~la/countem.htm

1. 5 to win 3 to chop.
2. 3 to win 21 to chop
3. 7 to win 6 to chop.
4. 9 to win 5 clubs chop it.
5. 17 to win 3 eights to chop.
6. 3 to win 3 to chop.
7. 3 to win.
8. 11 to win 20 to chop.
9. 3 to win 26 to chop.
10. 2 to win 42 to chop.

Hand #1

3 kings win
3 nines split

Hand #2

3 2′s win
3 Jacks Split
3 3′s split
3 9’2 spilt

Hand #3

3 2′s win
3 Jacks split
3 3′s split
3 4′s spilt

Hand #4

3 Queen’s win
3 Ten’s win
3 7′s win
Kc splits
Jc spilts
9c splits
8c spilts

Hand #5

3 queens win
3 jacks win
3 8′s spilt

Hand #6

3 4′s win
2 2′s split
1 King splits

Hand #7

2 9′s win
1 3 wins

Hand #8

3 3′s win
4 Aces win
4 6′s win

Hand #9

3 3′s win
3 Tens split
3 4′s split

Hand #10

3 2′s win
1 Ace splits
2 Jacks split

My question to you Ed is, What is the practicality of this excerise? (not that I mind the exersises. Oh no siree! If anything, I say make MORE exercises!)

But, is this just a way of learning that “we have more outs than we think” so when we are on a marginal call we may just go for it since we probally haven’t though of some hidden outs like when a river card will counterfeit an opponents hand?

Thanks Ed

1: An ace or king to win (5 Outs), 3 9s to a chop

2: 3 Deuces to win, every trey and every card 9 or higher to a chop, which makes 22 outs.

3: A Deuce or 5 to win (7 outs), a four or trey to a chop (6 outs)

4: A paired board to win (9 outs), every club 6 or higher to a chop (5 Outs)

5: An eight, nine or everything J or higher to win (20 Outs), no outs to a chop

6: A four to win (3 outs), a deuce and everything T or higher to a chop (19 outs)

7: A nine or trey to win (3 Outs), no way to chop

8: A trey, six or ace to win (11 Outs), deuce or five to chop (6 outs)

9: 3 treys to win, a four or anything ten or higher to chop (18 outs)

10: The remaining two deuces to win, everything but a deuce or trey to chop (39 outs)

1. 5 wins – 3 chops
2. 3 wins – 22 chops
3. 7 wins – 6 chops
4. 9 wins – 5 chops
5. 17 wins- 3 chops
6. 3 wins – 19 chops
7. 3 wins – 0 chops
8. 11 wins- 6 chops
9. 3 wins – 18 chops
10. 2 wins- 42 chops

1- 5 win 3 chop
2- 3 win 22 chop
3- 7 win 6 chop
4- 9 win 5 chop
5- 17 win 3 chop
6- 3 win 19 chop
7- 3 win 0 chop
8- 11 win 6 chop
9- 3 win 18 chop
10- 2 win 42 chop

1. win 3xK = 3
chop 2xA, 3×9 = 5

2. win 3×2 = 3
chop 1xA, 4xK, 4xQ, 3xJ, 4xT, 3×9 = 19

3. win 3×2, 4×5 = 7
chop 3×4, 3×3 = 6

4. win 3xQ, 3xT, 3×7 = 9
chop K,J,8,9,6C = 5

5. win 3xA, 4xK, 3xQ, 3xJ = 13
chop 3×8 = 3

6. win 3×4 = 3
chop 1xK, 4xQ, 4xJ, 4xT, 2×2 = 13

7. win 2×9, 1×3 = 3
chop 0

8. win 4×6, 4xA, 3×3 = 11
chop 3×5, 3×2 = 6

9. win 3×3 = 3
chop 4xK, 4xQ, 4xJ, 3xT, 3×4 = 18

10. win 2×2 = 2
chop 1xA, 2xJ, 4xQ, 4xJ, 4xT, 4×9, 4×8, 4×7, 4×6, 4×5, 4×4, 3×3 = 38

Haven’t looked at other’s answers yet:

1. 2 A, 3 K To Win (TW) – 5
3 9s To Tie (TT) – 3

2. 3 2 TW – 3 Total
1 A, 4 K, 4 Q, 3 J, 4 T, 3 9s, 3 3s TT – 22

3. 4 5s, 3 2s TW – 7
3 4s, 3 3s TT – 6

4. 3 Q, 3 J, 3 7s TW – 9
Kc Jc 9c 8c 6c TT – 5

5. 4 K, 3 Q, 3J, 3 A TW – 13
3 8s TT – 3

6. 3 4s TW – 3
1 K, 2 2s TT – 3

7. 2 9s, 1 3 TW – 3
none to tie – 0

8. 3 3s, 4 As, 4 6s TW – 11
3 5s, 3 2s TT – 6

9. 3 3s TW – 3
3 4s TT – 3

10. 2 2s TW – 2
1 A, 2 J, 4 K, 4 Q, 4 T, 4 9s, 4 8s, 4 7s, 4 6s, 4 5s, 4 4s 3 3s TT – 42

correction on 10.

4xK not 2xJ = 44 not 38

Ignore that IT IS 2xJ but equals 42, getting confused now

Did these kind of quick, but relatively easy, so here goes:

1) 5-3
2) 3-18
3) 7-6
4) 9-5
5) 14-6
6) 3-3
7) 3-0
11-6
9) 3-3
10)2-39

Thanks Ed — I’m an emerging lurker taking part in the quiz here:

1. 8 outs
2. 3 outs to win, 11 outs to tie
3. 3 outs to win, 6 outs to tie
4. 10 outs
5. 20 outs
6. 3 outs to win, 17 outs to tie
7. 3 outs
8. 11 outs to win, 6 outs to tie
9. 3 outs to win, 18 outs to tie
10. He’s not really “trailing” — 2 outs to win, 42 outs to tie (any other card)

Whoa, I did awful! And here I thought I knew this stuff…

Hopefully this will come out correctly:

#win,#chop outs to win outs to chop
———————————————
5,3 3xK, 2xA 3×9
3,8 3×2 3×9,3xJ,2xA
7,0 4×5,3×2 0
9,5 3xQ,3xT,3×7 5xclub
13,3 3xA,3xQ,3xJ,4xK 3×8
3,18 3×4 2xK,4xA,4xQ,4xJ,4xT
3 1×3,2×9 0
11,6 3×3,4xA,4×6 3×5,3×2
3,18 3×3 4xK,4xQ,4xJ,3xT,3×4
2,39 2×2 1xA,2xJ,9*4 (everything above 3)

ugh, retry:

#win,#chop outs to win outs to chop
---------------------------------------------
5,3 3xK, 2xA 3x9
3,8 3x2 3x9,3xJ,2xA
7,0 4x5,3x2 0
9,5 3xQ,3xT,3x7 5xclub
13,3 3xA,3xQ,3xJ,4xK 3x8
3,18 3x4 2xK,4xA,4xQ,4xJ,4xT
3 1x3,2x9 0
11,6 3x3,4xA,4x6 3x5,3x2
3,18 3x3 4xK,4xQ,4xJ,3xT,3x4
2,39 2x2 1xA,2xJ,9*4 (everything above 3)


Last try (made some corrections, I made about two errors I think)

1.
5 wins: 3xK,2xA
3 chops: 3×9

2.
3 wins: 3×2
10 chops: 3×9,3xJ,1xA,3×3

3.
7 wins: 4×5,3×2
6 chops: 3×4,3×3

4.
9 wins: 3xQ,3xT,3×7
5 chops: 5xclub

5.
13 wins: 3xA,3xQ,3xJ,4xK
3 chops: 3×8

6.
3 wins: 3×4
18 chops: 2xK,4xA,4xQ,4xJ,4xT

7.
3 wins: 1×3,2×9
0 chops:

8.
11 wins: 3×3,4xA,4×6
6 chops: 3×5,3×2

9.
3 wins: 3×3
18 chops: 4xK,4xQ,4xJ,3xT,3×4

10.
2 wins: 2×2
39 chops: 1xA,2xJ,9*4 (everything above 3)

PS. I don’t want to play with Todd, when he has an Ace in his hand, it seems to come from up his sleeve…

hmmm, there do seem to be 5 there. doh!

I would look at it this way, Jeroen. As I understand it casinos are pretty good at spotting the straightforward card counter playing black jack. If they decide that the counter is counting cards badly, they will let the player play on as he is still at a disadvantage to the house. The would be counter plays off his money thinking he has an advantage.

If you found yourself at a table with me and spotted me the extra A, I think you would come to the same conclusion as the casino…. play on….

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1. win 3XK 2XA
tie 2X5 3X9
2. win 3X2
tie 3X9 4XT 3XJ 4XQ 4XK 1XA
3. win 3X2 4X5
4. tie 6,8,9,J,K clubs
5. win 4X9 3XJ 3XQ 3XA
tie 3X8
6. win 3X4
tie 2X2 4XT 4XJ 4XQ 2XK 4XA
7. win 1X3 2X9
8. win 4XA 3X3 4X6
tie 3X2 3X5
9. win 3X3
tie 3X4 3XT 4XJ 4XQ 4XK
10. win 2X2
tie 4X4 4X5 4X6 4X7 4X8 4X9 4XT 2XJ 4XQ 4XK 1XA

win – tie

1. 5 – 3
2. 3 – 22
3. 7 – 6
4. 9 – 5
5. 17 – 3
6. 3 – 19
7. 3 – 0
8. 11 – 6
9. 3 – 18
10. 2 – 42

I got most or all of them right first try – it just took me longer than I would like too. Sitting at the table I will need to do this faster. Sometimes I miss a most likely split pot and fold.

Good exercise. That is an advantage a much younger person has.

Correction – I missed more than I though after checking Ed’s answers. Here is my answer for the record – oops – not as easy as I thought.

I missed the FH outs on #4 – Donkey! – Live it is easier but still not that easy.

1) 5 outs (A,K) to win and 3 outs (9) to chop.
2) 3 outs (2) to win, 21 to chop (3 A, 3Ks, 3 Qs, 3 Js, 3s, 3 9’s, 3 3’s)
3) 7 outs (2’s and 4 5’s to a win) – 6 outs ( 3 4’s and 3 3’s) to a chop
4) 5 outs (6,8,9,J,K clubs) to chop.
5) 16 outs to win (Q, J, K or A) 3 outs to chop (8)
6) 3 outs to win (4) and 15 outs to chop (A,K,Q,J,T,2)
7) 3 outs to win (9,3) – no chop here
8)11 outs to win (A,2,6), 6 outs to a chop (2,5)
9)3 outs to win (3), 18 to chop
10)2 out to win (2) – everything else chops.