C.A.T.S.Crunchy Automated Tactical System

The Engine

3d6 exploding, roll-over. Why three dice, and what a modifier point is actually worth.

Chance to succeed

Roll-over: meet or beat the Target Number. Exploding dice push totals upward, so high must be good — under a roll-under system a lucky 6 would drive you toward failure.

0%27%54%81%108%2610141822261d6 — 2: 83%1d6 — 3: 67%1d6 — 4: 50%1d6 — 5: 33%1d6 — 6: 17%1d6 — 7: 17%1d6 — 8: 14%1d6 — 9: 11%1d6 — 10: 8%1d6 — 11: 6%1d6 — 12: 3%1d6 — 13: 3%1d6 — 14: 2%1d6 — 15: 2%1d6 — 16: 1%1d6 — 17: 1%1d6 — 18: 0%1d6 — 19: 0%1d6 — 20: 0%1d6 — 21: 0%1d6 — 22: 0%1d6 — 23: 0%1d6 — 24: 0%1d6 — 25: 0%1d6 — 26: 0%1d62d6 — 2: 100%2d6 — 3: 97%2d6 — 4: 92%2d6 — 5: 83%2d6 — 6: 72%2d6 — 7: 58%2d6 — 8: 47%2d6 — 9: 38%2d6 — 10: 31%2d6 — 11: 25%2d6 — 12: 21%2d6 — 13: 17%2d6 — 14: 13%2d6 — 15: 10%2d6 — 16: 8%2d6 — 17: 6%2d6 — 18: 5%2d6 — 19: 4%2d6 — 20: 3%2d6 — 21: 2%2d6 — 22: 2%2d6 — 23: 1%2d6 — 24: 1%2d6 — 25: 1%2d6 — 26: 1%2d63d6 — 2: 100%3d6 — 3: 100%3d6 — 4: 100%3d6 — 5: 98%3d6 — 6: 95%3d6 — 7: 91%3d6 — 8: 84%3d6 — 9: 75%3d6 — 10: 66%3d6 — 11: 57%3d6 — 12: 49%3d6 — 13: 42%3d6 — 14: 36%3d6 — 15: 30%3d6 — 16: 25%3d6 — 17: 21%3d6 — 18: 17%3d6 — 19: 14%3d6 — 20: 11%3d6 — 21: 9%3d6 — 22: 8%3d6 — 23: 6%3d6 — 24: 5%3d6 — 25: 4%3d6 — 26: 3%3d6chance to succeedTarget Number

Three dice were chosen for the shape of that curve. One die is too coarse; four explode too often, and re-rolling on nearly half of all rolls fights the pace of play.

What one point is worth

This is the most important chart in the system. Every environmental effect — wind, range, target size, evasion — is converted into modifier points, so the value of a point sets the whole design grid.

0%3%5%8%10%3711151923+1 worth — 3: 0%+1 worth — 4: 1%+1 worth — 5: 3%+1 worth — 6: 5%+1 worth — 7: 7%+1 worth — 8: 8%+1 worth — 9: 9%+1 worth — 10: 9%+1 worth — 11: 8%+1 worth — 12: 7%+1 worth — 13: 6%+1 worth — 14: 6%+1 worth — 15: 5%+1 worth — 16: 4%+1 worth — 17: 4%+1 worth — 18: 3%+1 worth — 19: 3%+1 worth — 20: 2%+1 worth — 21: 2%+1 worth — 22: 1%+1 worth — 23: 1%+1 worth — 24: 1%+1 worth — 25: 1%+1 worth — 26: 1%+1 worth — 27: 0%+1 worthpercentage points bought by +1Target Number

The engine cannot express a 5% effect

One modifier point is worth about 8.3 percentage points near the median, falling to 4.9 at TN 15 and 2.1 at TN 20. The smallest unit the system has is bigger than 5%, so every model is built on a grid of roughly 8-point bands. The design rule "never go finer than 5%" is satisfied structurally — it is impossible to violate.

Master table

Target NumberChance to succeed+1 worth
3100.0%0.5 pts
499.5%1.4 pts
598.1%2.8 pts
695.4%4.6 pts
790.7%6.9 pts
883.8%8.3 pts
975.5%9.0 pts
1066.4%9.0 pts
1157.4%8.3 pts
1249.1%6.9 pts
1342.1%6.3 pts
1435.9%5.6 pts
1530.3%4.9 pts
1625.4%4.4 pts
1721.0%3.9 pts
1817.1%3.1 pts
1914.0%2.5 pts
2011.4%2.1 pts
219.3%1.7 pts
227.6%1.5 pts
236.2%1.3 pts
244.9%1.0 pts
253.9%0.8 pts
263.1%0.6 pts