P = (level/2 + 3*treasure hunter + 2*lucky ranks)/100
At level 20 the following table shows the probablity of your lockpick surviving
Table 1 - Base probability for a lockpick surviving Lucky hunter 0 1 2 3 4 5 0 0.10 0.12 0.14 0.16 0.18 0.20 1 0.13 0.15 0.17 0.19 0.21 0.23 2 0.16 0.18 0.20 0.22 0.24 0.26 3 0.19 0.21 0.23 0.25 0.27 0.29 4 0.22 0.24 0.26 0.28 0.30 0.32 5 0.25 0.27 0.29 0.31 0.33 0.35 6 0.28 0.30 0.32 0.34 0.36 0.38 7 0.31 0.33 0.35 0.37 0.39 0.41
C = sum(P^i)
This is a geometric series so as it approaches infinity, c can be generalised as
C = 1/(1-P)
and the net cost of a opening a chest (O) can be expressed as
O = 1500 (1-P)
So how can you use this information? Well with the addition of lockpicks, you can also use them on chests in normal mode. You receive a bonus(B) to P depending on the cost of the key (K), as shown below:
Table 2 - Bonus probability for a lockpick surviving Key cost Bonus 450 0.35 600 0.30 750 0.25 1250 0.10
K > 1500(1-P-B)
I know you're all lazy

Table 3 - Costs for using a lockpick on a normal mode chest Key Cost P 450 600 750 1250 0.10 825 900 975 1200 0.11 810 885 960 1185 0.12 795 870 945 1170 0.13 780 855 930 1155 0.14 765 840 915 1140 0.15 750 825 900 1125 0.16 735 810 885 1110 0.17 720 795 870 1095 0.18 705 780 855 1080 0.19 690 765 840 1065 0.20 675 750 825 1050 0.21 660 735 810 1035 0.22 645 720 795 1020 0.23 630 705 780 1005 0.24 615 690 765 990 0.25 600 675 750 975 0.26 585 660 735 960 0.27 570 645 720 945 0.28 555 630 705 930 0.29 540 615 690 915 0.30 525 600 675 900 0.31 510 585 660 885 0.32 495 570 645 870 0.33 480 555 630 855 0.34 465 540 615 840 0.35 450 525 600 825 0.36 435 510 585 810 0.37 420 495 570 795 0.38 405 480 555 780 0.39 390 465 540 765 0.40 375 450 525 750 0.41 360 435 510 735
But wait, there's more!
WIth the 26/04/2007 update a retaining a lockpick gives you 250 points to your unlucky title and breaking one gives you 25 points to your unlucky title.
Effect on the lucky title
Using the nine rings game as the base cost for title upgrades, each lucky point is worth 0.88g. We know from that each chest can be opened 1/(1-P-B), so if you include the increased lucky title as a cost offset, the new cost K' is
K' = Cost of opening - cost of rine rings per point* points per retain * retains per pick
K' = 1500(1-P-B) - 0.88 * 250 * (1/(1-P-B) -1)
K' = 1500(1-P-B) - 220.5(1/(1-P-B)-1)
Again, because you're lazy, the new cost has been included below.
Table 4 - Net cost for using a lockpick for opening a chest including offset for lucky title progression 50 80 300 450 600 750 1250 0.55 0.54 0.45 0.35 0.30 0.25 0.10 0.10 116.43 148.89 406.11 645.00 753.33 856.54 1145.00 0.11 81.97 115.50 379.36 622.17 731.77 835.97 1126.39 0.12 47.32 81.97 352.71 599.46 710.33 815.50 1107.81 0.13 11.44 47.32 325.50 576.46 688.66 794.85 1089.14 0.14 -25.79 11.44 297.70 553.15 666.75 774.02 1070.37 0.15 -64.50 -25.79 269.25 529.50 644.59 753.00 1051.50 0.16 -104.84 -64.50 240.12 505.50 622.17 731.77 1032.53 0.17 -147.00 -104.84 210.24 481.13 599.46 710.33 1013.45 0.18 -191.17 -147.00 179.55 456.35 576.46 688.66 994.25 0.19 -237.58 -191.17 148.00 431.15 553.15 666.75 974.94 0.20 -286.50 -237.58 115.50 405.50 529.50 644.59 955.50 0.21 -338.25 -286.50 81.97 379.36 505.50 622.17 935.93 0.22 -393.20 -338.25 47.32 352.71 481.13 599.46 916.24 0.23 -451.77 -393.20 11.44 325.50 456.35 576.46 896.40 0.24 -514.50 -451.77 -25.79 297.70 431.15 553.15 876.41 0.25 -582.00 -514.50 -64.50 269.25 405.50 529.50 856.27 0.26 -655.03 -582.00 -104.84 240.12 379.36 505.50 835.97 0.27 -734.50 -655.03 -147.00 210.24 352.71 481.13 815.50 0.28 -821.56 -734.50 -191.17 179.55 325.50 456.35 794.85 0.29 -917.63 -821.56 -237.58 148.00 297.70 431.15 774.02 0.30 -1024.5 -917.63 -286.50 115.50 269.25 405.50 753.00 0.31 -1144.5 -1024.5 -338.25 81.97 240.12 379.36 731.77 0.32 -1280.6 -1144.5 -393.20 47.32 210.24 352.71 710.33 0.33 -1437.0 -1280.6 -451.77 11.44 179.55 325.50 688.66 0.34 -1619.0 -1437.0 -514.50 -25.79 148.00 297.70 666.75 0.35 -1834.5 -1619.0 -582.00 -64.50 115.50 269.25 644.59 0.36 -2094.5 -1834.5 -655.03 -104.84 81.97 240.12 622.17 0.37 -2415.7 -2094.5 -734.50 -147.00 47.32 210.24 599.46 0.38 -2824.5 -2415.7 -821.56 -191.17 11.44 179.55 576.46 0.39 -3364.5 -2824.5 -917.63 -237.58 -25.79 148.00 553.15 0.40 -4114.5 -3364.5 -1024.5 -286.50 -64.50 115.50 529.50 0.41 -5232.0 -4114.5 -1144.5 -338.25 -104.84 81.97 505.50
A word to the wise
The cost offsets have been calculated for someone that is trying to achieve the lucky title and would have spent money on 9 rings to do it. The offset cost would be significantly smaller for someone who is getting the lucky title for the sole purpose of reducing the costs of using lockpicks. Calculating this would involve solving integrating a recursive function, and is well beyond the cobwebbed brain of an old fuddy duddy like me. If someone else wants to attempt to solve it, I can edit it into the first post (fully attributed of course!).