I recently played the stand-alone game "Plane and Tower Defense" and found that its numerical system is actually quite interesting. The surface is synthesis + idle, and the core is a simple exponential growth model. I spent some time sorting out the basic data of all aircraft (based on the current version) and directly talked about the conclusions and derivation process.
Let's first look at the synthetic revenue curve of the aircraft. All aircraft in the game are divided into 5 levels (white → green → blue → purple → gold). Each time they are combined, the firepower is doubled, but the gold coins consumed also increase exponentially. Actual measurement data: The basic attack of a whiteboard aircraft is 100. To synthesize it into green requires 2 whiteboards + 500 gold coins, and the green attack is 200; the blue aircraft requires 2 green aircraft + 2000 gold coins, and the attack is 400. By analogy, for each level up, the firepower is ×2 and the gold coin consumption is ×4. This multiplier relationship means that if you stay at a low level for too long, the synthetic benefits will be eaten up by the marginal cost of gold coins.
To give a specific example: You have a blue plane (attack 400) in your hand. If you use it to kill monsters directly, it will produce about 1,000 gold coins per minute. But what if you make it purple? It requires another blue +8000 gold coins, and the gold coins consumed is equivalent to 8 minutes of output, while the purple attacks 800, the output efficiency is doubled, and the payback time only takes 8 minutes. In other words, as long as you can guarantee not to exit the game within 8 minutes, the synthesis will be a positive income. The same applies to offline time. Offline revenue is calculated based on 60% of online efficiency. Therefore, 8 minutes offline is equivalent to 4.8 minutes of online revenue, and the synthetic return period will be extended to about 13 minutes.
The optimal strategy is actually very clear: give priority to synthesizing a level that allows you to stably repay your investment within the next hour. Specific operation: First manually synthesize the aircraft to blue (the most cost-effective, because the synthesis below blue consumes too few gold coins, but blue to purple is the first watershed). Then turn on offline hang-up, wait until the gold coins are accumulated to the next level of synthesis, and then go online to synthesize. Be careful not to blindly pursue gold, because gold synthesis consumes 40,000 gold coins and has 1,600 firepower, but the payback period exceeds 40 minutes. Unless you are prepared to be offline for a long time, the income from the blue + purple mix is smoother.
In addition, the gift pack dropping mechanism is also worth calculating: randomly dropped gift packs have a probability of opening a gold coin treasure chest, and the value is equal to 3 times your current online output per minute. Therefore, if you have a gift bag before going offline, it is recommended not to pick it up yet, because the gift bag will not disappear during the offline period, but the offline income is low. If you pick it up after going online, you can directly get the highest proportion of gold coins. This small detail can earn 8-10% more daily income.
Summary: Although the values of this game are simple, if you grasp the timing of synthesis and offline connection, the daily income can vary by more than 30%. It is recommended that newcomers manually synthesize the blue aircraft for the first two hours, and then hang up fully automatically, and go online every half hour to synthesize it. In the long run, it is worthwhile to prioritize the synthesis of golden aircraft when they have been offline for more than 2 hours, otherwise the massive blue stack will be more stable.