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FOUR SCORE Position with Feisty 52

Posted By: Nack Ballard
Date: Sunday, 3 December 2017, at 2:57 a.m.

Thanks to mamabear, Karol and ah_clem for their insightful comments, and for their patience! (Finishing my rollouts took longer than anticipated.) The original posting is here.

Correct answers: One of these three respondents chose H for money, one chose B at DMP, none chose D at Gammon Save, two chose K at Gammon Go, one chose H (tied) at Gammon sad, and one chose P at Gammon glad. That 33% is actually commendable, considering the number of close and plausible-looking candidate plays.

Other respondents didn't commit, but Casper predicted there would be six different best plays (almost!) and Barry rightly pointed out that he got clickbaited by "fake news! -- sad."

In the list-all-plausible plays category, Karol identified (and even gave names/descriptions to) eight moves, all of which are in the top dozen for Money or closer at other scores. Meanwhile, ah_clem looked even harder, finding thirteen plays, though four of them are illegal. (If 22/16 11/9 were legal, it would be best at all scores.)

To compensate all of you for tolerating my little deception (in the original subject header), I offer two anagrams of President Donald Trump:

.....Stupid man, pretend lord
.....Splendid undreamt port

Notice the careful selection of one anti-Trump and one pro-Trump, achieving a balance that will hopefully offend no one (or at least offend equally).

Below is a nacbracs summary of the rollouts (one line for each score). Rollout results on the left are 3-ply; on the right are 4-ply.

.........m[H P6 B16 D23 K30 X78 z95 x104 Z121] "<=343*41 12 5.....m[H P9] ^42
..........d[B H7 P8 D16 K29 X38 z41 x46 N49 Z51 @61] <55**5..........d[B H7 P9] ^23*10
..........s[D B12 H14 z20 P24 Z39 K58 X73] <31*20 5...........................s[D B12] ^10
..........g[K P9 H12 D47 B54 X55 x64] <257*72 5.................................g[K P8 H12] ^107*5+

.......c4 [H=B=D P12 z22 K38 Z40] <14*9 5.......................................c4 [B H3 D3] ^14
.......4c [P H3 K7 B21 D32 X42 x53] <71*15 5...................................4c [P H4 K7] ^38*25

Key:..@ (anchor) = 23/16, B (Both) = 23/18 11/9, D = (Down) = 16/9, H (Hit) = 11/9 8/3*, K (Kill) = 8/3*/1*, N (Near) = 11/9 6/1*, P = (Point) = 9/4 6/4, X (hit and split) = 24/22 8/3*, x = 22/20 8/3*, Z (reverse split) = 24/22 16/11, z = 22/20 16/11.
Nactation tutorial ....nacbracs explanation

Each of the four main scores has a different best play. In fact, this is not only a T4 (technical four-score position). It is also an "R4" (real four-score position), meaning that for each of money, DMP, gammon save and gammon go, the best play clears its respective .010, .0045, .007 and .007 "tied" margin (compared to any play that is best at one of the other three scores).

In addition, there is a fifth different best play at Gammon glad, specified as "4c" (–4–1, Crawford) above, which enhances this particular R4 to also an "R4+T1."

Finally, just above the Gammon glad row, I've included the result for Gammon sad, specified as "c4" (–1–4, Crawford), because it remarkably yielded a three-way dead heat (between H, B and D). [The 4-ply rollout of the same length had B .003 ahead of H and D.]

For definitions of "Gammon sad" and "Gammon glad," click here (then scroll down).

The power rating for this R4 is [sqrt 16 + sqrt 7*20/9 + sqrt 12*10/7 + sqrt 12*10/7] = 16.22. To compare to the power ratings of other R4's, click on the Jan. 2016 Consolidation (scroll to the bottom). Since then, R4's with the following rolls have been added in separate posts: 41, 43, 64, 44, 65, 21 and 54.

Detailed 3-ply rollout results follow. (I can post 4-ply on request.)

Nack

Money





White is Player 2

score: 0
pip: 176
Unlimited Game
Jacoby Beaver
pip: 181
score: 0

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:0:0:3:0:10

.65R-32S-42P-61U-634-53S-21H-43H-21H-65K-54-21K-
-22K-31-51K-31-32S-65P-41P-52S-61R-62X-43H-62H-F-52
..Perfectly played money sequence.............Nactation tutorial


1.Rollout111/9 8/3* eq: -0.030
Player:
Opponent:		49.70% (G:15.80% B:1.29%)
50.30% (G:17.41% B:1.42%)		Conf.: ± 0.001 (-0.031...-0.028) - [100.0%]
Duration: 4 days 00 hour 40 minutes
2.Rollout19/4 6/4eq: -0.035 (-0.006)
Player:
Opponent:		49.75% (G:16.00% B:1.21%)
50.25% (G:17.85% B:1.52%)		Conf.: ± 0.001 (-0.037...-0.034) - [0.0%]
Duration: 3 days 18 hours 09 minutes
3.Rollout223/18 11/9eq: -0.046 (-0.016)
Player:
Opponent:		50.11% (G:13.51% B:0.79%)
49.89% (G:17.55% B:1.37%)		Conf.: ± 0.003 (-0.049...-0.042) - [0.0%]
Duration: 15 hours 25 minutes
4.Rollout316/9eq: -0.052 (-0.022)
Player:
Opponent:		49.29% (G:14.01% B:0.87%)
50.71% (G:16.38% B:1.11%)		Conf.: ± 0.007 (-0.059...-0.045) - [0.0%]
Duration: 5 hours 21 minutes
5.Rollout48/3* 3/1* eq: -0.059 (-0.029)
Player:
Opponent:		48.56% (G:17.28% B:1.05%)
51.44% (G:18.30% B:1.70%)		Conf.: ± 0.011 (-0.070...-0.048) - [0.0%]
Duration: 2 hours 13 minutes
6.Rollout424/22 8/3* eq: -0.107 (-0.077)
Player:
Opponent:		48.10% (G:15.14% B:1.25%)
51.90% (G:18.96% B:1.28%)		Conf.: ± 0.012 (-0.119...-0.096) - [0.0%]
Duration: 2 hours 20 minutes
7.Rollout422/20 16/11eq: -0.124 (-0.095)
Player:
Opponent:		47.72% (G:12.61% B:0.64%)
52.28% (G:16.32% B:1.09%)		Conf.: ± 0.010 (-0.134...-0.114) - [0.0%]
Duration: 2 hours 09 minutes
8.Rollout422/20 8/3* eq: -0.133 (-0.103)
Player:
Opponent:		47.65% (G:15.05% B:1.26%)
52.35% (G:20.18% B:2.42%)		Conf.: ± 0.012 (-0.145...-0.121) - [0.0%]
Duration: 2 hours 07 minutes
9.Rollout424/22 16/11eq: -0.151 (-0.121)
Player:
Opponent:		47.07% (G:12.63% B:0.73%)
52.93% (G:16.78% B:0.91%)		Conf.: ± 0.010 (-0.160...-0.141) - [0.0%]
Duration: 2 hours 16 minutes
10.Rollout511/9 6/1* eq: -0.169 (-0.139)
Player:
Opponent:		47.14% (G:13.15% B:0.62%)
52.86% (G:18.75% B:1.46%)		Conf.: ± 0.011 (-0.180...-0.158) - [0.0%]
Duration: 31 minutes 07 seconds
11.Rollout513/11 8/3* eq: -0.184 (-0.155)
Player:
Opponent:		46.58% (G:15.11% B:1.36%)
53.42% (G:21.10% B:2.44%)		Conf.: ± 0.011 (-0.195...-0.173) - [0.0%]
Duration: 28 minutes 46 seconds
12.Rollout523/16eq: -0.201 (-0.171)
Player:
Opponent:		46.72% (G:12.27% B:0.70%)
53.28% (G:19.02% B:1.45%)		Conf.: ± 0.012 (-0.212...-0.189) - [0.0%]
Duration: 32 minutes 50 seconds
1 343440 Games rolled with Variance Reduction.
Dice Seed: 37887372
Moves: 3-ply, cube decisions: XG Roller

2 51840 Games rolled with Variance Reduction.
Dice Seed: 37887372
Moves: 3-ply, cube decisions: XG Roller

3 12960 Games rolled with Variance Reduction.
Dice Seed: 37887372
Moves: 3-ply, cube decisions: XG Roller

4 5184 Games rolled with Variance Reduction.
Dice Seed: 37887372
Moves: 3-ply, cube decisions: XG Roller

5 5184 Games rolled with Variance Reduction.
Dice Seed: 88888888
Moves: 3-ply, cube decisions: XG Roller

DMP





White is Player 2

score: 0
pip: 176
1 point match
pip: 181
score: 0

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:0:0:0:1:10

Blue to play 52 at DMP


1.Rollout123/18 11/9eq: +0.003
Player:
Opponent:		50.13% (G:15.55% B:2.39%)
49.87% (G:20.16% B:4.45%)		Conf.: ± 0.001 (+0.001...+0.004) - [100.0%]
Duration: 15 hours 18 minutes
2.Rollout111/9 8/3* eq: -0.004 (-0.007)
Player:
Opponent:		49.79% (G:17.84% B:4.03%)
50.21% (G:19.94% B:4.42%)		Conf.: ± 0.001 (-0.005...-0.003) - [0.0%]
Duration: 15 hours 30 minutes
3.Rollout19/4 6/4eq: -0.005 (-0.008)
Player:
Opponent:		49.75% (G:18.32% B:3.89%)
50.25% (G:20.68% B:4.93%)		Conf.: ± 0.001 (-0.006...-0.004) - [0.0%]
Duration: 16 hours 55 minutes
4.Rollout216/9eq: -0.013 (-0.016)
Player:
Opponent:		49.33% (G:15.95% B:2.47%)
50.67% (G:19.71% B:3.87%)		Conf.: ± 0.004 (-0.017...-0.010) - [0.0%]
Duration: 58 minutes 04 seconds
5.Rollout28/3* 3/1* eq: -0.026 (-0.029)
Player:
Opponent:		48.68% (G:19.32% B:2.53%)
51.32% (G:21.19% B:4.97%)		Conf.: ± 0.004 (-0.031...-0.022) - [0.0%]
Duration: 1 hour 35 minutes
6.Rollout224/22 8/3* eq: -0.035 (-0.038)
Player:
Opponent:		48.24% (G:17.04% B:4.16%)
51.76% (G:22.11% B:4.72%)		Conf.: ± 0.004 (-0.039...-0.031) - [0.0%]
Duration: 1 hour 38 minutes
7.Rollout222/20 16/11eq: -0.038 (-0.041)
Player:
Opponent:		48.09% (G:14.31% B:1.68%)
51.91% (G:20.04% B:3.62%)		Conf.: ± 0.004 (-0.042...-0.035) - [0.0%]
Duration: 1 hour 33 minutes
8.Rollout222/20 8/3* eq: -0.043 (-0.046)
Player:
Opponent:		47.83% (G:16.65% B:4.16%)
52.17% (G:23.66% B:6.56%)		Conf.: ± 0.004 (-0.048...-0.039) - [0.0%]
Duration: 1 hour 41 minutes
9.Rollout211/9 6/1* eq: -0.047 (-0.049)
Player:
Opponent:		47.66% (G:14.35% B:1.77%)
52.34% (G:21.94% B:5.06%)		Conf.: ± 0.004 (-0.051...-0.043) - [0.0%]
Duration: 1 hour 43 minutes
10.Rollout224/22 16/11eq: -0.048 (-0.051)
Player:
Opponent:		47.59% (G:13.92% B:2.37%)
52.41% (G:20.78% B:3.29%)		Conf.: ± 0.004 (-0.052...-0.044) - [0.0%]
Duration: 1 hour 37 minutes
11.Rollout223/16eq: -0.058 (-0.061)
Player:
Opponent:		47.10% (G:13.35% B:2.15%)
52.90% (G:22.19% B:4.66%)		Conf.: ± 0.004 (-0.062...-0.054) - [0.0%]
Duration: 1 hour 46 minutes
1 55728 Games rolled with Variance Reduction.
Dice Seed: 36091569
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 36091569
Moves: 3-ply, cube decisions: XG Roller

Gammon Save





White is Player 2

score: 0
pip: 176
1 point match
pip: 181
score: 0

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:0:0:0:1:10

Blue to play 52 at Gammon Save


1.Rollout123/18 11/9eq: +0.003
Player:
Opponent:		50.13% (G:15.55% B:2.39%)
49.87% (G:20.16% B:4.45%)		Conf.: ± 0.001 (+0.001...+0.004) - [100.0%]
Duration: 15 hours 18 minutes
2.Rollout111/9 8/3* eq: -0.004 (-0.007)
Player:
Opponent:		49.79% (G:17.84% B:4.03%)
50.21% (G:19.94% B:4.42%)		Conf.: ± 0.001 (-0.005...-0.003) - [0.0%]
Duration: 15 hours 30 minutes
3.Rollout19/4 6/4eq: -0.005 (-0.008)
Player:
Opponent:		49.75% (G:18.32% B:3.89%)
50.25% (G:20.68% B:4.93%)		Conf.: ± 0.001 (-0.006...-0.004) - [0.0%]
Duration: 16 hours 55 minutes
4.Rollout216/9eq: -0.013 (-0.016)
Player:
Opponent:		49.33% (G:15.95% B:2.47%)
50.67% (G:19.71% B:3.87%)		Conf.: ± 0.004 (-0.017...-0.010) - [0.0%]
Duration: 58 minutes 04 seconds
5.Rollout28/3* 3/1* eq: -0.026 (-0.029)
Player:
Opponent:		48.68% (G:19.32% B:2.53%)
51.32% (G:21.19% B:4.97%)		Conf.: ± 0.004 (-0.031...-0.022) - [0.0%]
Duration: 1 hour 35 minutes
6.Rollout224/22 8/3* eq: -0.035 (-0.038)
Player:
Opponent:		48.24% (G:17.04% B:4.16%)
51.76% (G:22.11% B:4.72%)		Conf.: ± 0.004 (-0.039...-0.031) - [0.0%]
Duration: 1 hour 38 minutes
7.Rollout222/20 16/11eq: -0.038 (-0.041)
Player:
Opponent:		48.09% (G:14.31% B:1.68%)
51.91% (G:20.04% B:3.62%)		Conf.: ± 0.004 (-0.042...-0.035) - [0.0%]
Duration: 1 hour 33 minutes
8.Rollout222/20 8/3* eq: -0.043 (-0.046)
Player:
Opponent:		47.83% (G:16.65% B:4.16%)
52.17% (G:23.66% B:6.56%)		Conf.: ± 0.004 (-0.048...-0.039) - [0.0%]
Duration: 1 hour 41 minutes
9.Rollout211/9 6/1* eq: -0.047 (-0.049)
Player:
Opponent:		47.66% (G:14.35% B:1.77%)
52.34% (G:21.94% B:5.06%)		Conf.: ± 0.004 (-0.051...-0.043) - [0.0%]
Duration: 1 hour 43 minutes
10.Rollout224/22 16/11eq: -0.048 (-0.051)
Player:
Opponent:		47.59% (G:13.92% B:2.37%)
52.41% (G:20.78% B:3.29%)		Conf.: ± 0.004 (-0.052...-0.044) - [0.0%]
Duration: 1 hour 37 minutes
11.Rollout223/16eq: -0.058 (-0.061)
Player:
Opponent:		47.10% (G:13.35% B:2.15%)
52.90% (G:22.19% B:4.66%)		Conf.: ± 0.004 (-0.062...-0.054) - [0.0%]
Duration: 1 hour 46 minutes
1 55728 Games rolled with Variance Reduction.
Dice Seed: 36091569
Moves: 3-ply, cube decisions: XG Roller

2 5184 Games rolled with Variance Reduction.
Dice Seed: 36091569
Moves: 3-ply, cube decisions: XG Roller

Gammon Go





White is Player 2

score: 1
pip: 176
2 point match
Crawford
pip: 181
score: 0

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:0:1:1:2:10

Blue to play 52 at Gammon Go


1.Rollout18/3* 3/1* eq: +0.325
Player:
Opponent:		49.15% (G:17.12% B:3.07%)
50.85% (G:21.49% B:5.36%)		Conf.: ± 0.001 (+0.325...+0.326) - [100.0%]
Duration: 2 days 16 hours 42 minutes
2.Rollout19/4 6/4eq: +0.317 (-0.009)
Player:
Opponent:		50.39% (G:15.45% B:3.21%)
49.61% (G:20.50% B:4.60%)		Conf.: ± 0.001 (+0.316...+0.318) - [0.0%]
Duration: 2 days 10 hours 45 minutes
3.Rollout211/9 8/3* eq: +0.315 (-0.010)
Player:
Opponent:		50.32% (G:15.44% B:3.44%)
49.68% (G:20.20% B:4.53%)		Conf.: ± 0.001 (+0.314...+0.317) - [0.0%]
Duration: 16 hours 16 minutes
4.Rollout316/9eq: +0.279 (-0.047)
Player:
Opponent:		49.97% (G:13.96% B:2.28%)
50.03% (G:20.03% B:3.81%)		Conf.: ± 0.005 (+0.273...+0.284) - [0.0%]
Duration: 1 hour 13 minutes
5.Rollout323/18 11/9eq: +0.272 (-0.054)
Player:
Opponent:		50.67% (G:12.92% B:1.83%)
49.33% (G:19.97% B:4.30%)		Conf.: ± 0.005 (+0.267...+0.277) - [0.0%]
Duration: 1 hour 13 minutes
6.Rollout324/22 8/3* eq: +0.270 (-0.055)
Player:
Opponent:		48.75% (G:14.77% B:3.34%)
51.25% (G:22.70% B:4.76%)		Conf.: ± 0.006 (+0.264...+0.277) - [0.0%]
Duration: 1 hour 21 minutes
7.Rollout322/20 8/3* eq: +0.262 (-0.064)
Player:
Opponent:		48.24% (G:14.84% B:3.01%)
51.76% (G:23.60% B:6.67%)		Conf.: ± 0.006 (+0.256...+0.268) - [0.0%]
Duration: 1 hour 21 minutes
1 257904 Games rolled with Variance Reduction.
Dice Seed: 52466768
Moves: 3-ply, cube decisions: XG Roller

2 72576 Games rolled with Variance Reduction.
Dice Seed: 52466768
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 52466768
Moves: 3-ply, cube decisions: XG Roller

Gammon sad




White is Player 2

score: 1
pip: 176
5 point match
Crawford
pip: 181
score: 4

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:4:1:1:5:10

Blue to play 52 at Gammon sad


1.Rollout111/9 8/3* eq: -0.190
Player:
Opponent:		49.31% (G:17.92% B:3.93%)
50.69% (G:17.01% B:2.64%)		Conf.: ± 0.003 (-0.193...-0.187) - [16.9%]
Duration: 3 hours 28 minutes
2.Rollout123/18 11/9eq: -0.190 (0.000)
Player:
Opponent:		49.71% (G:16.19% B:2.68%)
50.29% (G:17.78% B:2.95%)		Conf.: ± 0.003 (-0.193...-0.188) - [15.9%]
Duration: 3 hours 32 minutes
3.Rollout116/9eq: -0.190 (0.000)
Player:
Opponent:		48.89% (G:15.95% B:2.53%)
51.11% (G:16.23% B:2.20%)		Conf.: ± 0.003 (-0.193...-0.188) - [13.6%]
Duration: 3 hours 26 minutes
4.Rollout29/4 6/4eq: -0.194 (-0.004)
Player:
Opponent:		49.66% (G:18.46% B:4.58%)
50.34% (G:18.17% B:1.34%)		Conf.: ± 0.040 (-0.234...-0.154) - [37.1%]
Duration: 41.5 seconds
5.Rollout38/3* 3/1* eq: -0.211 (-0.021)
Player:
Opponent:		48.68% (G:18.51% B:2.66%)
51.32% (G:17.80% B:3.09%)		Conf.: ± 0.038 (-0.250...-0.173) - [9.2%]
Duration: 1 minute 01 second
6.Rollout422/20 16/11eq: -0.213 (-0.022)
Player:
Opponent:		46.93% (G:10.20% B:0.74%)
53.07% (G:14.61% B:1.90%)		Conf.: ± 0.034 (-0.247...-0.178) - [6.0%]
Duration: 31.6 seconds
7.Rollout524/22 16/11eq: -0.231 (-0.041)
Player:
Opponent:		46.41% (G:17.84% B:4.60%)
53.59% (G:15.40% B:2.53%)		Conf.: ± 0.040 (-0.272...-0.191) - [1.2%]
Duration: 34.8 seconds
1 14256 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

2 59 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

3 71 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

4 52 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

5 51 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

Gammon glad





White is Player 2

score: 4
pip: 176
5 point match
Crawford
pip: 181
score: 1

Blue is Player 1
XGID=aa-a--C-DAbAaBb-Ab-b-cAAA-:0:0:1:52:1:4:1:5:10

Blue to play 52 at Gammon glad


1.Rollout19/4 6/4eq: +0.167
Player:
Opponent:		50.16% (G:15.78% B:2.30%)
49.84% (G:20.34% B:4.60%)		Conf.: ± 0.001 (+0.166...+0.168) - [100.0%]
Duration: 16 hours 20 minutes
2.Rollout111/9 8/3* eq: +0.164 (-0.003)
Player:
Opponent:		49.99% (G:15.79% B:2.60%)
50.01% (G:20.03% B:4.47%)		Conf.: ± 0.001 (+0.162...+0.165) - [0.0%]
Duration: 17 hours 23 minutes
3.Rollout28/3* 3/1* eq: +0.159 (-0.007)
Player:
Opponent:		48.93% (G:17.51% B:1.75%)
51.07% (G:21.44% B:5.46%)		Conf.: ± 0.003 (+0.157...+0.162) - [0.0%]
Duration: 4 hours 09 minutes
4.Rollout323/18 11/9eq: +0.145 (-0.021)
Player:
Opponent:		50.44% (G:13.21% B:1.37%)
49.56% (G:19.77% B:4.50%)		Conf.: ± 0.004 (+0.141...+0.150) - [0.0%]
Duration: 36 minutes 24 seconds
5.Rollout316/9eq: +0.134 (-0.032)
Player:
Opponent:		49.51% (G:13.97% B:1.45%)
50.49% (G:19.85% B:3.85%)		Conf.: ± 0.004 (+0.130...+0.139) - [0.0%]
Duration: 32 minutes 12 seconds
6.Rollout324/22 8/3* eq: +0.125 (-0.042)
Player:
Opponent:		48.40% (G:15.10% B:2.70%)
51.60% (G:22.15% B:4.31%)		Conf.: ± 0.005 (+0.120...+0.130) - [0.0%]
Duration: 35 minutes 04 seconds
7.Rollout322/20 8/3* eq: +0.113 (-0.053)
Player:
Opponent:		47.84% (G:15.08% B:2.74%)
52.16% (G:23.95% B:6.95%)		Conf.: ± 0.005 (+0.108...+0.118) - [0.0%]
Duration: 35 minutes 27 seconds
1 71280 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

2 15552 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

3 5184 Games rolled with Variance Reduction.
Dice Seed: 82605212
Moves: 3-ply, cube decisions: XG Roller

 

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