Interesting you should bring the Eastern Europe battle up. Let’s take a look at that battle, and compare the possible low luck outcomes versus the possible ADS outcomes.
The battle involves 17 inf, 3 arm, 2 ftr (RUS) vs 9 inf 7 arm (GER).
Here is the table of possible outcomes (assuming the battle is fought to completion and no one retreats), with the winner on the left, the amount of units remaining, and the probabilities for that outcome under ADS and LowLuck (LL) on the right. Let’s also assume that the attacker kills off fighters before losing his last armor.
| Winner | Inf | Arm | Ftr | ADS | LL |
| DEF | 6 | 7 | 0 | <1% | 0% |
| DEF | 5 | 7 | 0 | <1% | 0% |
| DEF | 4 | 7 | 0 | <1% | 0% |
| DEF | 3 | 7 | 0 | <1% | 0% |
| DEF | 2 | 7 | 0 | <1% | 0% |
| DEF | 1 | 7 | 0 | <1% | 0% |
| DEF | 0 | 7 | 0 | <1% | 0% |
| DEF | 0 | 6 | 0 | <1% | 0% |
| DEF | 0 | 5 | 0 | <1% | 0% |
| DEF | 0 | 4 | 0 | <1% | 0% |
| DEF | 0 | 3 | 0 | <1% | 0% |
| DEF | 0 | 2 | 0 | <1% | 0% |
| DEF | 0 | 1 | 0 | <1% | 0% |
| DEF | 0 | 0 | 0 | <1% | 0% |
| ATT | 0 | 1 | 0 | <1% | 0% |
| ATT | 0 | 1 | 1 | 1% | 0% |
| ATT | 0 | 1 | 2 | 2% | 0% |
| ATT | 0 | 2 | 2 | 3% | 0% |
| ATT | 0 | 3 | 2 | 4% | 0% |
| ATT | 1 | 3 | 2 | 5% | <1% |
| ATT | 2 | 3 | 2 | 6% | <1% |
| ATT | 3 | 3 | 2 | 8% | 4% *** |
| ATT | 4 | 3 | 2 | 9% | 19% |
| ATT | 5 | 3 | 2 | 10% | 38% |
| ATT | 6 | 3 | 2 | 10% | 26% |
| ATT | 7 | 3 | 2 | 10% | 10% |
| ATT | 8 | 3 | 2 | 9% | 2% |
| ATT | 9 | 3 | 2 | 7% | 0% |
| ATT | 10 | 3 | 2 | 5% | 0% |
| ATT | 11 | 3 | 2 | 3% | 0% |
| ATT | 12 | 3 | 2 | 2% | 0% |
| ATT | 13 | 3 | 2 | <1% | 0% |
| ATT | 14 | 3 | 2 | <1% | 0% |
| ATT | 15 | 3 | 2 | <1% | 0% |
| ATT | 16 | 3 | 2 | <1% | 0% |
| ATT | 17 | 3 | 2 | <1% | 0% |
*** - actual result of battle in your game
As we see, the actual result in your game was statistically unlikely in either ADS or LowLuck, but possible in both. DarthMaximus in either dice system should have expected a more favorable result. In both dice systems, the median result (5-6 infantry alive for the attacker) is the same, and there are a quite a range of possibilities outside that median result. However, it’s curious that in ADS, it is actually more likely that DarthMaximus would have rolled worse than the exact outcome that was achieved. This is because although the odds of getting that result is more likely in ADS, the variance (or standard deviation) of results is much greater in ADS than LowLuck. This is the reason I like LowLuck: the “unlikely” scenarios of ADS are still possible in LowLuck, which makes every game different and forces players to adapt to dynamic changes in balance, but at the same time rules out the “extreme” circumstances of say, DarthMaximus actually losing that battle with your full armor regiment intact. While any individual “extreme” outcome is in ADS so insigificant to consider alone, when you consider the number of these outcomes it makes it so that you really cannot always expect to win such a decicisive battle, if you play enough. Someone recently posted the idea that any given player can expect to only win 80% of his games because of strategy and the remaining 20% would be affected by bad dice; this makes it so those proportions are more reasonably tilted towards strategy.
If I wanted to play a game where the dice can easily make a huge difference, I would play Risk, because the majority of the fun in that is the social interaction. And I play that on a somewhat regular basis. There is a good deal of “potential” strategy in that game, but the dice can make or break any valid one, and yet it is still often fun because you really don’t expect to win the majority of the time, because it’s pretty clear from the get-go that this isn’t too much of a strategic game: it’s more luck and politics than actual strategy. I’ve often won huge swatches of territories because I happened to be rolling well despite being the weakest player on the board at the start of my turn, and on the other end of the spectrum, I can recall at least one game where I was the strongest player on the board, and the next strongest attacked me on a whim with a moderate sized army only to win without taking any casualties, so he kept up the process until he had completely eliminated me from the game without loss to himself, destroying at least 30 infantry and taking over more than a continent, with only around 15 or so of his own infantry to start with. Statistically unlikely sure, and I walked away from that game somewhat disappointed, but more amused than anything else  because with a dice system like Risk’s, you expect these oddities to happen once in a while.
Axis and Allies on the other hand, is designed to be a more strategic game. I have very rarely played a game of Axis and Allies with more than one player controlling a side. In those cases, the social interaction did indeed add to the fun, but when I play online, that simply does not translate for me across the web. Unfortunately, the way the dice is set up according to the box, it actually has the potential to be more random than Risk. Good players are aware of this and deliberately conduct battles only when they can be more certain of results - not throwing away their armies in a 50/50 crapshoot unless they are already behind and are open to the possible but unlikely event of good dice swinging a decisive battle to their favor. However, the desired guarantor is hard to pin down because of the “extreme” outcomes discussed above. In every ADS game I have observed in the last year or so (since I started playing LowLuck), and every game I remember playing before then, one player or another will inevitably get some horrible dice within the first couple turns. Now if this player was a significantly inferior player to begin with, this makes little difference. Conversely if this player is a significantly superior player to begin with as well, this player is usually able to overcome this disadvantage until the dice inevitably land in his favor again. I’ve seen both these outcomes happen particularly when I would play others who are new to the game - if I get bad dice, I actually kind of like it then, because it gives my opponent some support and hope, and at least stretches out the game a bit so it doesn’t seem like I decimated them. Â However if both players are roughly equally matched, then an early blow is often crippling: I can usually predict the outcome of the game from that point unless another extreme dice result occurs in a way that is significant to alter the balance. After reading through most of the latest threads on the Games forum here, I can say that that seems definitely to be the case - except where the player with the good luck is gracious enough to offer to his opponent the ability to “revise” the dice to a more reasonable result. In this case, why bother playing with ADS anyway, since it seems you’re not willing to deal with its consequences? For instance, we have the G1 attack in your latest game on the North sea, where the outcome you got was actually not that unlikely even - it had a high chance of being the outcome even had you been playing LowLuck (I think it would have been about 20% in LowLuck, the second most likely outcome). But DarthMaximus, being extremely gracious to you since I suspect he rightly considered your overall position and strategy to be significantly inferior, offered to give you a fighter or two back for free. Well, consistent with what your gaming philosophy appears, you rejected his offer. I suspect that if you had lost all your airforce without having killed any of his units, you would still have rejected a similar offer. Well, I’m sorry, but that’s playing a game that’s significantly different from the game I play. If your only goal is having fun, that’s great, because a person can have fun no matter what happens. You can still potentially have fun if you were imprisoned and being tortured, so of course you can still have fun by knowingly playing out a losing game. I play not purely because of the fun itself, but because I derive having fun from developing my strategy further and seeing it successful if it is superior to my opponent’s, or seeing it fail if it is inferior. Currently I started playing a (LowLuck) game after seeing that you were not interested in playing, and I don’t think I’m doing as well as my opponent is, but it’s hard to tell even though we’re in round three. There have been some statistically unlikely events that have happened, that have affected both our strategies, such as my inability to kill Germany’s navy in R1 while losing the Russian navy completely, but because there has been nothing gamebreaking, it has been a match of my strategy against my opponents. A majority of the games I play end up being 10 rounds or more because unless one of us is significantly weaker, our strategies cannot count on waiting for a good dice result and then taking advantage of that; rather, there is a depth of play that is present but rare in ADS games in my opinion with the constant struggle of well matched forces.
So anyway, regarding the “simulations” you present in this thread, I say they are irrelevent to your support. My entire critique of your strategy was based on a simulated game I played based on expected results, and you remained unconvinced. I remain certain that by exchanging the German air force for the combined navies of the UK and the US, you open the possibility of direct and relatively unsupported invasion from Russia. These statistics you bring up in this thread have nothing to do with Russia’s stack that is growing steadily as you expend most of your energy making pre-emptive attacks against the west. (By the way, in the original thread where you brought up this discussion, you had assumed that Germany would buy 1 fighter per turn for the first couple turns, which I don’t see discussed anymore - did you give up on that?) So if you are unwilling to accept my simulation, all I can do is say that by playing an actual game where the dice don’t determine the balance of the game (granted it’s possible for this to happen in an ADS game, I’m just not really interested in taking the time to play one when the possibility is reasonable that it won’t), Â I am sure you will find that your strategy may have seemed just as good in your head as the Sea Lion Scare, only to find that it does not work in practice.