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In Axis & Allies (2nd Edition Rules), is it every a smart move to spend IPCs to research weapons development?
I usually forego doing any weapons development, but I play with others who spend 5 IPC every turn or who will turn to researching weapons development when their cause looks close to hopeless.
Ok, so I asked a question over at math.stackexchange.com to get some advise on how to analyze the various weapon development options (see How to analyze risk vs. reward for spending on research and development work). Mike Spivey suggested using a decision tree, which I had some familiarity with from past classes in probability and statistics. In short, the decision tree calculates the expected value for spending 0 through 30 IPC on a turn for weapons development research.
To construct this decision tree (see below), I made some assumptions:
Here is the decision tree I constructed to compute the expected values for spending 0 to 30 IPC in a turn, meaning paying for 0 to 6 rolls of the die.
The expected value of one of the rolls is computed by adding together the value (the amount in the bottommost boxes) times the probability of getting there for a particular branch in the tree. I presume the player has a purse of 30 IPC at the start of their turn.
For instance, if you do zero rolls (the far left branch) then you have an expected outcome of 100% * 30, or 30 IPC. In other words, you'll always end up with a purse of 30 IPC after the rolls. However, if you decide to spend money to do one roll then you have a ~2.75% chance of getting Heavy Bombers (1/36). Doing so yields a purse of 25 + X, where X is the "worth" of having heavy bombers. There is ~97.25% chance that you will not get heavy bombers, in which case you have a purse of 25 IPC. So the expected value of one roll is 2.75% * (25 + X) + 97.25% * 25. Of course, the actual hard number depends on X, which is what heavy bombers is worth to you.
I created a very simple Excel spreadsheet that calculated all seven expected values for a given value of X, where X was a number in a particular cell. Using this spreadsheet I could play with X to see at what point it actually makes sense to roll for weapons development.
The chart below shows how the expected value changes as the value of X grows. The X-axis shows the expected outcome for zero to six rolls. The series show how the expected value changes as the value of the heavy bombers tech (X) increases. Here I show the expected value for six different values: 45, 90, 135, 180, 225, and 270.
Note how at a "worth" of 180, heavy bombers have the same expected value regardless of how many times you roll the die. If the value is lower, however, it makes sense to abstain from weapons development altogether; if its higher to you, spend every last penny you have on development!
Personally, I think heavy bombers are not worth this much. 180 IPC is the combined budget of 5-10 turns. It is equivalent to purchasing 12 standard bombers. Forgoing any sort of unit procurement for that many turns, just to get heavy bombers, is a suicidal thought.
In closing, keep in mind that this is a very simple model. It presumes heavy bombers are the only worthwhile tech. It does not factor in that if you discover other technologies, that the odds of discovering heavy bombers actually increase since if you roll an initial 6 you get to keep rolling for your discovered tech until you discover a new one. Also, the analysis presumes the player is in a vacuum of sorts and does not factor in that he must spend certain amounts of IPCs to hold his territories from the enemy, not to mention the monies needed to go on the offensive.
Edit - The question was originally asked about the Revised edition, which is what this answer is based off of. For 2nd Edition rules I agree with the above answers, in that it is not worth it. I'll leave this answer up in case anyone wants an opinion on the Revised edition.
Yes...but it is dependent on the situation. Speaking in terms of long range aircraft and heavy bombers(I haven't used the others before), I can think of several advantages to use them(non-tournament rules).
Long Range Aircraft - Researching this means you need less planes to do the same amount. They could be used to attack Russia in one turn and then a fleet in the Atlantic in the next. This is especially beneficial for America since this allows them to bring their planes into action much earlier after being built.
Heavy Bombers - In addition to the obvious benefit of bombers increased firepower, another benefit is that needing less planes for the same firepower means less chances of being shot down by anti-aircraft and thus saves IPCs.
Regarding the accepted answer(I don't have the rep to comment), the math you used is based off rules in the Classic edition. In the Revised edition, the odds of getting your technology with a single dice is 1 in 6 and not 1 in 36.
Also, I think it is best not to expect a concrete answer on this. The math on weapons development is never going to be very good because it is impossible to accurately gauge its benefit.
I should note that when I actually research a weapon, I always use 4-8 dice. You may get lucky with one or two but I research it only when I think it is necessary.
Anecdote of when I lost a major battle due to research:
I was playing Axis(2-person game) and Japan had its original territories plus a few in USSR. It was the 5 or 6 turn and the Japan mainland only contained 6 bombers and a few fighters. America had a fairly large fleet off the Western U.S. coast whose purpose was to invade the Japanese mainland. I had a few carriers(with a couple planes) south of Japan but no other real naval force. My plan was that since the American fleet would require two moves to launch the invasion, I would concentrate on attacking China until the U.S. made its move. When that happens, I would throw 30 IPCs at Heavy Bombers(a calculated risk), then launch an air attack against the fleet(using the fighters as fodder and the carriers to land them on). I don't remember the exact configuration of forces but I remember that I expected to destroy the fleet with at least 3 or 4 bombers left over.
What my opponent did was during the turn where the American fleet made the move, she successfully researched long range aircraft. She then sent fighters from China and fighters from her carriers in the Pacific and attacked the Japanese mainland. She easily destroyed the fighters and all 6 bombers while taking light losses. This was my entire air force(and my then my navy was mostly gone) so I didn't have much chance of repelling the next turn's invasion.
After she triumphantly ended her turn and started playing USSR, I pointed to my German transport off of the western coast of Algeria, the infantry in Algeria and the undefended Eastern U.S. As it turned out, the only ground units in North America were infantry in the Western U.S.(and Britain couldn't come to the rescue) thus making the U.S. unable to take back its capitol. At this point my very peeved girlfriend conceded.
Tech Development is a gamble with very bad odds. The only Tech that wins is Heavy Bombers. On average you will have to spent 21 dice (105 IPC) to get it. In statistical terms in fact you should use the median which is 19 dice (95 IPC) because the data is not normally distributed. For ease we go with average.
So on average even the US will need 4 turns to develop heavy bombers, and then you still have to buy bombers. Even if the Allies should generally win, against any reasonable opponent this much delay is going to loose you the game.
In my opinion no other nation can afford this kind of investment and be serious about winning. Lets assume we find it decisive if you develop Heavy Bombers within 2 turns (60 IPC, 12 dice). This has a 35% chance. Hence you throw away two/third of the games if you go for Tech. I welcome a player who plays this way, but probably not for long because it is no contest. Keep in mind that this is an average, so it could be a lot more. In 50% of the cases you will need more than 105 IPC!
Of course, later in the game, when decisive advantage has been achieved it can quicken the win. But as an overall starting strategy....
Short answer - No.
I used to try research when I first learned the game, but now I see no point in it. I have seen players who still insist on researching for the off-chance of getting long-range heavy bombers, and then going the whole game without getting it. That seems like a complete waste to me.
If your cause looks close to hopeless, you're probably out of luck anyways. I guess you could research weapons development as a way to speed up the game and get closer to finishing, instead of buying units, but I rather fight to the finish.
You can get an armor for 5 IPC every turn -- I would much prefer that. Over a few turns, that significantly adds up.
The value of R&D varies with the country played.
R&D is most valuable to the U.S. player because it has the most IPCs to spare for a gamble, and because it (initially) has the least impact on the game. Two oceans on either side means that the U.S. is easy to defend, but has a hard time as an attacker.
Most tech has to do with airpower, which is to say, the best U.S. means of projecting power. Especially if players can't choose which tech to try for, the U.S. clearly benefits most from longer range aircraft, heavy bombers, rockets (from an anti-aircraft gun to be landed in Algeria), and jet fighters. Economic relief is also helpful, super subs, perhaps the least of all.
Britain might benefit from developing tech if she chooses not to buy factories on land and uses an airborne strategy instead. Most techs improve airpower.
Germany and Japan probably shouldn't invest in tech until e.g. a midgame stalemate. In most games, they will either win early or not at all. In that event, they should maximize military units for blitzing their enemies. They get only small benefits from long range aircraft, or jet fighters. The greatest benefits are from heavy bombers (I use a "lighter"version), and economic relief is worth more to them than the Allies. but that requires "boxcars" or 6-5, only two chances out of 36.
Russia shouldn't roll for tech early on, because she has few planes and little use for them (compared to infantry).
Personally, I find that a wise investment is in Rockets. Germany has 3 rocket launch sites that can really strangle the Russian and British economy. I only invest in rockets when I am Germany however, because Russia, Germany and Britain have very few launch sites. Other than that, I stay away from upgrades. Jet Fighters and Long Range Aircraft are investments that I am willing to make, but I avoid buying those. Combined Bombardment and Super Submarines are useless. Heavy Bombers I haven't really used much, but you all have valid points. I generally only use Rockets, and if I don't get the tech on the 2nd try, I give up considering it doesn't have too much influence on the outcome of the game. I am only willing to invest about 30 or so IPC's on tech, and I tend to get lucky with technology. That's just my opinion though.
