I am really puzzled by your reaction the comment that history is decided by rolls of a dice. I understand that there were no dice on the bridge of the Bismark

, and the events of 31May41 were determined by a whole sequence of events. However, a game has to model things. Take 15" German shells; I do not have a clue what the fraction of them that would fail to expload was, but a number would. This would be due to:
- design errors in the fuse (say a critical element wasn't strong enough in certain circumstances, like ,in the extreme case, the US Mk 14 torpedo when hitting square on would distort the fuse and render in inoperable),
- non-conformance in the fuse or shell (a part made wrong so the thing doesn't work)
- something peculiar in the shell/armour engagement geometry (for example the shell that hit PoW - may not have exploaded because it tumbled on hitting the sea
- etc etc etc.
How are you going to game this: your arguements (to me) seem to imply that the detailed fuse tolerances of every shell fired should be generated some how (presumably by modelling the machine tools that made them, and the operator, since you don't like dice), the shell tracked though the firing process, and flight, on to the target. The target then has to be modelled to determine the fuse initiation parameters, and then you 'know' whether the shell will expload, and what damage it will do.
Now, getting real, this same sequence is modelled by a table of probablilty, and a random number: AKA a roll of the dice.
Tristanjohn wrote:But Bismarck didn't sink Hood by means of a "fluke" but by means of any number of easily computable factors of the battle:
I dispute that any of your factors are 'easily computable'!
1) Hood was forced to advance head on to Bismarck in an attempt to close range as quickly as possible in order to mitigate against her very certain vulnerability to Bismarck's plunging fire,
No one forced anything: Holland CHOSE to deal with the issue that way. Why? Would he have made the same decision the day before, or after? Would any external factors have altered his choice? Cloud/visibilty? Exact time of sighting (rel sun rise)? Exact bearing of sighting? And so on.
2) Admiral Holland decided unwisely to lead with Hood instead of Prince of Wales,
Explain please how this changes anything (in terms of assessing whether Hood blows up - but don't get me wrong, I would probably have lead with PoW, but then I would have split the two ships anyway, and that is a different story)? Bismark may well have engaged the lead ship initially, but given PoW's fire control and turret problems she would have likely wanted to change target to Hood to attempt to hinder her. Would Hood still have been in the critical range window? Depends. PoW could have taken some hits early and suffered damage (Bismark's early salvos were very accurate - no reason to suppose that would change in PoW was leading). All somewhat difficult to assess?
3) Bismarck had distinctly superior fire control solutions than did Hood, and while PoW had theoretically better fire control than Hood her batteries were masked to open the action and in any event this ship was spanking new, hadn't even completed her initial workups, her crew was green, it turned out her quadruple turrets were inherently compromised in critical respects, etc.
4) Holland turned to port rather severely at speed at the wrong instant in time, thereby presenting a larger flushed-deck profile to incoming German rounds, 6) Hood in any other more favorable circumstance was not a match for Bismarck or in fact a match for any capital ship of that era with 14" rifles or greater . . . and on and on and on.
Exactly how did these issues (particularly you point 4) affect things? There is dispute as to whether Hood had actually started, or how far round the turn she was. All that can be said IIRC, is that some witnesses thought she was turning, and her rudders were found to Port. Whether the turn, and any heel affected the shell impact point is moot, and insoluble.
It was not a "roll of the dice" but rather much more like a foregone conclusion that Hood was not in for an especially good day, Mogami.
It was most definately not a forgone conclusion that Hood would blow up. Hood was going to be damaged, but then so (probably) was Bismark. It would depend on how many hits Bismark landed before taking significant damage herself, and whether Holland pulled off as soon as her was sure Bismark was slowed/damaged. If he didn't pull off, or didn't get the necessary damage, Hood would not have stood up well in all probablity. I hope you do not really think that any game of the Denmark Straits should blow Hood up every time?.
As for the damage done to Bismarck: that wasn't a "fluke" either and in fact the damage inflicted on her by a torpedo launched from an RN Swordfish could well have been much worse given that the first RN strike had expended itself uselessly (and dangerously) in a mistaken attack on one of its own ships.
It was also not a "fluke" that Bismarck should have been caught in mid-ocean alone instead of accompanied by her consort Prinz Eugen but rather due to the commanding German admiral's decision not to top off Bismarck's oil bunkers prior to weighing out of Norway.
See discussion of Hollands decisions above. Do you know why the refuelling was not done? What might affect that?
Neither was it a "fluke" that a round from a PoW salvo hit Bismarck forward on her port side and ruptured one of those bunkers, thus causing her to lose yet more precious fuel, which lead directly to the German admiral's decision to send Prinz Eugen on her convoy-raiding way and return alone with Bismarck to France in order to affect repairs.
Here I really struggle. Lets define some terms: fluke=low likelihood of success that actually comes off. Now, the geometry of the engagement was such that the shell hit where it did. But where was the effectlive mean point of aim (or the centre of the CEP if you prefer?) What is the shape and size of the CEP of the 14" on PoW projected on to the Bismark at the point of impact? If you go the maths (impossible in reality) I suspect there is a very small chance of getting the shell where it was EVEN GIVEN THE EXACT SAME mean shell trajectory. I may be wrong, but in my book, the hit was a fluke. You could land a 14" in many places on the Bismark and not have the same effect on the voyage.
The encounter had nothing to do with "rolling the dice." It had a lot to do with hard decisions made by men of flesh and blood in the unforgiving cauldron of battle.
Indeed, there were few if any dice at sea that day, but 'rolling the dice' is a reasonable way of thinking about history, and the only way to model it in a game.
[edit to tidy up]