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Recently I started a solitaire game with the No-Bess option.

I declared war on Yugoslavia with Germany and a Neutral Italy on pulse 3 of the game, it generated two US Entry dice rolls. Surprised, I went back to a save and only declared war with Germany instead.

I thought when Both Italy and Germany declare war on Yugoslavia, it is supposed to be one die roll.

Is that correct?

Two rolls is correct, you only generate one roll for joint DoWs if the chart says so specifically. The notes under the chart are a bit ambiguous but under 13.3.3 in RAW it states: "20, 31 & 32 Major Power declares war on neutral minor - roll once for each major power declaring war on this minor this impulse."

If Italy were already Active, then it could be at war with Yugo too because Germany DoW'd, and Yugo aligns to a Major at war with Italy, but only the declaring powers get Surprise benefits.

It is a great idea to do this when you are keeping Italy neutral for a while. When you align Romania to Germany, the Italians lose the oil resource and end up with only 4 resources. Grabbing the two Yugoslavian resources with the Italians really helps their production when neutral. 6 resources X the .75 production multiple gives 4.5 rounding to 5 BPs. This is a decent level of production for Italy during 1940 while building up their forces.

I must admit it can be really tough keeping Italian units organized with only 1 saved oil for a long time...