The value of blockers

Hand 1
I should be seeing the last draw here. Tapirboy is a good player who recognises that I've probably improved to a strong three-card, so he'll happily reraise with any badugi. And the pot is easily big enough for me to peel.

Full Tilt Poker Game #25763106984: Table Vulgamore - $1/$2 - Limit Badugi - 01:42:11 ET - 2010/11/22
Seat 1: halcyon_phoenix ($18.15)
Seat 2: plutoman20 ($76.75)
Seat 3: Tapirboy ($49)
Seat 4: Raine1000 ($20)
Seat 5: Holdem_my_life ($60.50)
Seat 6: MacGeek ($40)
Seat 7: kawbloo75 ($108)
Seat 8: chight ($20)
plutoman20 posts the small blind of $0.50
Tapirboy posts the big blind of $1
5 seconds left to act
Time has expired
chight is sitting out
The button is in seat #1
*** HOLE CARDS ***
Dealt to plutoman20 [3s Ah 7h Js]
Holdem_my_life folds
MacGeek folds
kawbloo75 folds
halcyon_phoenix calls $1
plutoman20 calls $0.50
Tapirboy raises to $2
halcyon_phoenix calls $1
plutoman20 calls $1
*** FIRST DRAW *** (Pot: $6)
plutoman20 discards 2 cards [7h Js]
Tapirboy discards 1 card
halcyon_phoenix discards 1 card
Dealt to plutoman20 [3s Ah] [4c 3d]
Tapirboy is dealt 1 card
halcyon_phoenix is dealt 1 card
plutoman20 checks
Tapirboy bets $1
halcyon_phoenix calls $1
chight has returned
plutoman20 raises to $2
Tapirboy raises to $3
halcyon_phoenix calls $2
plutoman20 calls $1
*** SECOND DRAW *** (Pot: $15)
plutoman20 discards 1 card [3d]
Tapirboy stands pat
halcyon_phoenix discards 1 card
Dealt to plutoman20 [3s Ah 4c] [8h]
halcyon_phoenix is dealt 1 card
plutoman20 checks
Tapirboy bets $2
halcyon_phoenix calls $2
plutoman20 folds
*** THIRD DRAW *** (Pot: $19)
Tapirboy stands pat
halcyon_phoenix discards 1 card
halcyon_phoenix is dealt 1 card
Tapirboy checks
halcyon_phoenix checks
*** SHOW DOWN ***
Tapirboy shows [Qh 8d 3c 2s] a Badugi: Q, 8, 3, 2
halcyon_phoenix mucks
Tapirboy wins the pot ($18.25) with a Badugi: Q, 8, 3, 2
*** SUMMARY ***
Total pot $19 Rake $0.75
Seat 1: halcyon_phoenix (button) mucked [6c 5d 2h Qc] - a 3-Card: 6, 5, 2
Seat 2: plutoman20 (small blind) folded after the 2nd Draw
Seat 3: Tapirboy (big blind) showed [Qh 8d 3c 2s] and won ($18.25) with a Badugi: Q, 8, 3, 2
Seat 4: Raine1000 is sitting out
Seat 5: Holdem_my_life folded before the Draw (didn't bet)
Seat 6: MacGeek folded before the Draw (didn't bet)
Seat 7: kawbloo75 folded before the Draw (didn't bet)
Seat 8: chight is sitting out

Hand 2
I'm pretty sure Youfarted's hand stinks (I put him on a three-card seven or eight) so I think this was a good bluff.

Full Tilt Poker Game #25844044389: Table Codrington - $1/$2 - Limit Badugi - 00:55:54 ET - 2010/11/25
Seat 2: plutoman20 ($44.75)
Seat 3: MacGeek ($60)
Seat 6: Admiral Otomoto ($12.50)
Seat 7: meyus ($66)
Seat 8: YOUFARTED ($57.60)
YOUFARTED posts the small blind of $0.50
plutoman20 posts the big blind of $1
The button is in seat #7
*** HOLE CARDS ***
Dealt to plutoman20 [Kd 3d 5d 2c]
Admiral Otomoto folds
meyus folds
YOUFARTED raises to $2
plutoman20 calls $1
*** FIRST DRAW *** (Pot: $4)
YOUFARTED discards 1 card
plutoman20 discards 2 cards [Kd 5d]
YOUFARTED is dealt 1 card
Dealt to plutoman20 [3d 2c] [9s Tc]
YOUFARTED bets $1
plutoman20 calls $1
*** SECOND DRAW *** (Pot: $6)
YOUFARTED discards 1 card
plutoman20 discards 1 card [Tc]
YOUFARTED is dealt 1 card
Dealt to plutoman20 [3d 2c 9s] [7d]
YOUFARTED checks
plutoman20 checks
*** THIRD DRAW *** (Pot: $6)
YOUFARTED discards 1 card
plutoman20 discards 1 card [7d]
YOUFARTED is dealt 1 card
Dealt to plutoman20 [3d 2c 9s] [6d]
YOUFARTED checks
plutoman20 bets $2
YOUFARTED folds
Uncalled bet of $2 returned to plutoman20
plutoman20 mucks
plutoman20 wins the pot ($5.75)
*** SUMMARY ***
Total pot $6 Rake $0.25
Seat 2: plutoman20 (big blind) collected ($5.75), mucked
Seat 3: MacGeek is sitting out
Seat 6: Admiral Otomoto folded before the Draw (didn't bet)
Seat 7: meyus (button) folded before the Draw (didn't bet)
Seat 8: YOUFARTED (small blind) folded after the 3rd Draw

Hand 3
I think the most difficult spot in single draw is standing pat out of position with a rough hand against someone drawing one. Against this player, who bluffs a lot, it's even harder. As this session wore on, and I became aware of just how bluffy Bar_men is, I began to regret the way I played this hand. I should have bet seven or eight bucks post-draw; he'd have been less likely to bluff me. Who knows what he had. As it happens, I was in a similar situation tonight, with exactly the same hand, and bet it. My opponent folded.

PokerStars Game #53187757562: Single Draw 2-7 Lowball No Limit ($0.25/$0.50 USD) - 2010/11/24 3:22:09 ET
Table 'Kobresia' 7-max Seat #3 is the button
Seat 1: boongoo ($28.90 in chips)
Seat 2: andrey738 ($39.55 in chips)
Seat 3: frankpw ($36.35 in chips)
Seat 4: Elales ($19.50 in chips)
Seat 5: plutoman20 ($26.30 in chips)
Seat 6: John V1982 ($7.75 in chips)
Seat 7: bar_men_83 ($23.05 in chips)
Elales: posts small blind $0.25
plutoman20: posts big blind $0.50
*** DEALING HANDS ***
Dealt to plutoman20 [7c 3d 8s 9d 6d]
John V1982: folds
bar_men_83: raises $1.50 to $2
boongoo: folds
andrey738: folds
frankpw: folds
Elales: folds
plutoman20: raises $4 to $6
bar_men_83: calls $4
plutoman20: stands pat on [7c 3d 8s 9d 6d]
bar_men_83: discards 1 card
plutoman20: checks
bar_men_83: bets $17.05 and is all-in
plutoman20: folds
Uncalled bet ($17.05) returned to bar_men_83
bar_men_83 collected $11.65 from pot
*** SUMMARY ***
Total pot $12.25 Rake $0.60
Seat 1: boongoo folded before Flop (didn't bet)
Seat 2: andrey738 folded before Flop (didn't bet)
Seat 3: frankpw (button) folded before Flop (didn't bet)
Seat 4: Elales (small blind) folded before Flop
Seat 5: plutoman20 (big blind) folded on the Flop
Seat 6: John V1982 folded before Flop (didn't bet)
Seat 7: bar_men_83 collected ($11.65)

Hand 4
I don't break many 10-9's. Luckily this break worked out for me. I'm not sure whether it was the right play. I guess Popaionut could have had a worse 10-9 here.

PokerStars Game #53237858414: Single Draw 2-7 Lowball No Limit ($0.25/$0.50 USD) - 2010/11/25 2:57:04 ET
Table 'Bok IV' 7-max Seat #1 is the button
Seat 1: denuc G ($8.90 in chips)
Seat 2: mr_mcgee2 ($26.30 in chips)
Seat 3: sngonta ($28 in chips)
Seat 4: popaionut ($100.55 in chips)
Seat 5: plutoman20 ($32.90 in chips)
Seat 6: vladd0 ($57.05 in chips)
vladd0 said, "sorry"
mr_mcgee2: posts small blind $0.25
sngonta: posts big blind $0.50
*** DEALING HANDS ***
Dealt to plutoman20 [Ts 5d 6c 3s 9d]
popaionut: raises $1.50 to $2
plutoman20: raises $4 to $6
vladd0: folds
denuc G: raises $2.90 to $8.90 and is all-in
mr_mcgee2: folds
sngonta: folds
popaionut: calls $6.90
plutoman20: calls $2.90
popaionut: stands pat
plutoman20: discards 1 card [Ts]
Dealt to plutoman20 [5d 6c 3s 9d] [2d]
denuc G: discards 1 card
popaionut: checks
plutoman20: bets $11
popaionut: folds
Uncalled bet ($11) returned to plutoman20
*** SHOW DOWN ***
plutoman20: shows [2d 5d 6c 3s 9d] (Lo: 9,6,5,3,2)
denuc G: shows [Jh 8c 5c 2s 4s] (Lo: J,8,5,4,2)
plutoman20 collected $26.10 from pot
*** SUMMARY ***
Total pot $27.45 Rake $1.35
Seat 1: denuc G (button) showed [Jh 8c 5c 2s 4s] and lost with Lo: J,8,5,4,2
Seat 2: mr_mcgee2 (small blind) folded before Flop
Seat 3: sngonta (big blind) folded before Flop
Seat 4: popaionut folded on the Flop
Seat 5: plutoman20 showed [2d 5d 6c 3s 9d] and won ($26.10) with Lo: 9,6,5,3,2
Seat 6: vladd0 folded before Flop (didn't bet)

Hand 5
If you're going to shove, this would seem to be a particularly bad hand to do it with. This hand has enormous implied odds, and by going all-in you forfeit all of those. Then when he gets called, surely he should break here.

PokerStars Game #53188076258: Single Draw 2-7 Lowball No Limit ($0.25/$0.50 USD) - 2010/11/24 3:40:14 ET
Table 'Kobresia' 7-max Seat #7 is the button
Seat 1: boongoo ($12.65 in chips)
Seat 2: andrey738 ($36.05 in chips)
Seat 3: frankpw ($47.25 in chips)
Seat 4: Elales ($20.60 in chips)
Seat 5: plutoman20 ($24.25 in chips)
Seat 6: John V1982 ($5.10 in chips)
Seat 7: bar_men_83 ($26.20 in chips)
boongoo: posts small blind $0.25
andrey738: posts big blind $0.50
*** DEALING HANDS ***
Dealt to plutoman20 [Ks Ad Qd 6h 9h]
frankpw: folds
Elales: calls $0.50
plutoman20: folds
John V1982: folds
bar_men_83: folds
boongoo: raises $12.15 to $12.65 and is all-in
andrey738: calls $12.15
Elales: folds
boongoo: stands pat
andrey738: stands pat
*** SHOW DOWN ***
boongoo: shows [3c 6d 2h Jd 7d] (Lo: J,7,6,3,2)
andrey738: shows [6c 3d 5s 9d 4h] (Lo: 9,6,5,4,3)
andrey738 collected $24.55 from pot
*** SUMMARY ***
Total pot $25.80 Rake $1.25
Seat 1: boongoo (small blind) showed [3c 6d 2h Jd 7d] and lost with Lo: J,7,6,3,2
Seat 2: andrey738 (big blind) showed [6c 3d 5s 9d 4h] and won ($24.55) with Lo: 9,6,5,4,3
Seat 3: frankpw folded before Flop (didn't bet)
Seat 4: Elales folded before Flop
Seat 5: plutoman20 folded before Flop (didn't bet)
Seat 6: John V1982 folded before Flop (didn't bet)
Seat 7: bar_men_83 (button) folded before Flop (didn't bet)

Hand 6
The value of blockers in this game can at times be significant. When Andrey pats behind, I surrender, not that I ever expected to see a top-twenty hand (the chances of that kind of hand are very much reduced due to my holding). If I was him I would have four-bet pre-draw. At work today (yes it was a slow day) I calculated some card removal effects; I show the results of those at the end of this hand.

PokerStars Game #53188153634: Single Draw 2-7 Lowball No Limit ($0.25/$0.50 USD) - 2010/11/24 3:44:40 ET
Table 'Kobresia' 7-max Seat #4 is the button
Seat 1: boongoo ($29.75 in chips)
Seat 2: andrey738 ($49.55 in chips)
Seat 3: frankpw ($47 in chips)
Seat 4: Elales ($17.10 in chips)
Seat 5: plutoman20 ($23 in chips)
Seat 6: John V1982 ($12.80 in chips)
Seat 7: bar_men_83 ($30.50 in chips)
plutoman20: posts small blind $0.25
John V1982: posts big blind $0.50
*** DEALING HANDS ***
Dealt to plutoman20 [4s 3h 3d 4h 4c]
bar_men_83: folds
boongoo: folds
andrey738: raises $1.50 to $2
frankpw: calls $2
Elales: folds
plutoman20: raises $7 to $9
John V1982: folds
andrey738: calls $7
frankpw: folds
plutoman20: stands pat on [4s 3h 3d 4h 4c]
andrey738: stands pat
plutoman20: checks
andrey738: checks
*** SHOW DOWN ***
plutoman20: shows [4s 3h 3d 4h 4c] (Lo: a full house, Fours full of Threes)
andrey738: shows [4d 9d 6h 3s 2c] (Lo: 9,6,4,3,2)
andrey738 collected $19.50 from pot
*** SUMMARY ***
Total pot $20.50 Rake $1
Seat 1: boongoo folded before Flop (didn't bet)
Seat 2: andrey738 showed [4d 9d 6h 3s 2c] and won ($19.50) with Lo: 9,6,4,3,2
Seat 3: frankpw folded before Flop
Seat 4: Elales (button) folded before Flop (didn't bet)
Seat 5: plutoman20 (small blind) showed [4s 3h 3d 4h 4c] and lost with Lo: a full house, Fours full of Threes
Seat 6: John V1982 (big blind) folded before Flop
Seat 7: bar_men_83 folded before Flop (didn't bet)

The probability of being dealt the nuts in deuce-to-seven is one in 2548. A top-twenty hand is therefore a one-in-127 shot. But, given that I have 44433, the probability of any one player having a top-twenty hand (which Andrey did indeed have in the hand above) is one in 262, i.e. 51% less likely than without the card removal effect.

Probabilities for some other hands (the probability shown is the chance of any one player being dealt a top-20 hand given that you have that particular holding):
22227..........1 in 463............72% less likely compared with no card removal
22277..........1 in 286............56% less likely
22777..........1 in 251............49% less likely
27777..........1 in 273............53% less likely
96532..........1 in 170............25% less likely
Broadway......1 in 75..............69% more likely

Having done these calculations, the blocking value of paired low cards is greater than I first thought. Of course, if you happen to hold all four deuces, your opponents can't possibly have (or make) any of the top eight hands. In a deep game, it might be worth going to the mat with quad deuces, both times in your life that you get them.