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In Risk Legacy, there is a Bunker that always adds (+1 to the highest defense die, except when the high die is a 6).

Is it better to roll 1 or 2 defense dice when defending a bunkered location.

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up vote 7 down vote accepted

I ran a script to calculate probabilities of attacker losing two troops (D wins), defender losing two troops (A wins) and each losing one troop (Tie). The following table shows these probabilities, along with the difference from standard play in brackets. The final column shows the troop loss ratio per die.

Number of  | Win Probabilities (Difference due to bunker)            | Troop loss ratio
 Dice      |                                                         | (A loss : D loss)
-----------+---------------------------------------------------------+------------------
D: 1, A: 1 | D: 0.722 (+0.139), T: 0.000 (+0.000), A: 0.278 (-0.139) | 0.722 : 0.278
D: 2, A: 1 | D: 0.861 (+0.116), T: 0.000 (+0.000), A: 0.139 (-0.116) | 0.861 : 0.139
D: 1, A: 2 | D: 0.583 (+0.162), T: 0.000 (+0.000), A: 0.417 (-0.162) | 0.583 : 0.417
D: 2, A: 2 | D: 0.533 (+0.085), T: 0.320 (-0.004), A: 0.147 (-0.081) | 0.693 : 0.307
D: 1, A: 3 | D: 0.506 (+0.166), T: 0.000 (+0.000), A: 0.494 (-0.166) | 0.506 : 0.494
D: 2, A: 3 | D: 0.352 (+0.060), T: 0.408 (+0.073), A: 0.239 (-0.132) | 0.556 : 0.443

If you look at each pair of rows then you can compare the defender rolling one or two dice. In each case the defender's troop loss per die roll is decreased by rolling two dice, so it is always theoretically better to roll two dice.

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