Synthesis Stone

In the recent event, we get a synthesis stone 1 daily.
One wonder what that is worth, and when it is best to use it.
Again, many of the computation will be based on my previous post :
http://sislandec.blogspot.com/2010/08/value-of-scrolls-and-ashes.html

Level 1 to Level 2 Synthesis
This is a 60% chance without the synthesis stone, and 50% chance when using the stone.
Each attempt saves you 10% from losing 3 level 1 ash and 1 synthesis rune. Since level 1 ash is worth nothing, the saving is 0.1 synthesis rune.

Level 2 to Level 3 Synthesis
You save 10% of losing 3 level 2 ash and 1 synthesis rune. Since each level 2 ash is worth 1.67 synthesis rune, you save 0.6 synthesis runes (0.1 * (3*1.67 + 1)).

Level 3 to Level 4 Synthesis
The saving is 0.1 * (3*13.67+1) = 4.2 synthesis runes.

Level 4 to Level 5 Synthesis
At this level, you stand to lose 2 level 4 ashes and one synthesis rune 2.
Each level 4 ash is worth 118.67 synthesis rune 1, so the total savings here is :
23.73 synthesis rune 1 + 0.1 synthesis rune 2.

For synthesis stone 2 and synthesis stone 3, multiple the value above by 2 and 3 respectively.

If you are buying, each synthesis rune 1 cost 1 diamonds, but each synthesis stone 1 cost 5 diamonds. It is not worth using the stones for Level 3 to 4 synthesis (only 4.2 in value), but definitely worth buying the stone for Level 4 to 5 synthesis.
Synthesis stone 2 cost 8 diamonds, so it is worthwhile at level 3 to 4 synthesis (saves 8.4 synthesis stone 1 and cost only 8 diamonds).
Synthesis stone 3 cost 12 diamonds (1.5 times that of stone 2) and will save you 1.5 times that of stone 2.

Conclusion : Save the stones for higher level synthesis. If you are buying, buy synthesis stone 2 or 3, but not 1, and use them for synthesizing level 4 or higher scrolls.