There are various factors dependent on the Farm Topology decision, there is no standard formula on decision of Farm Topology.
We have already covered the topics relevant to Farm topology,
- Multi server farm implementation for SharePoint 2013 and SharePoint 2010
- Capacity Planning and Sizing of SharePoint 2013
- Load Balancing Service Applications on multiple application Server for SharePoint 2010 and 2013
There are few factors to be considered while deciding on Farm topology,
SINGLE SERVER FARM
Typically It would be used, user base is less than 100(Users<100).
This farm consists like WFE + APP server + DB all runs in single server
Two Server Farm
Typically It would be used, user base is 100 to 10,000(Users are 100 to 10000).
This farm consists of 1 web server that performs all application services.For high availability clustered or mirror database recommended.
Two-Tier Small Farm
Typically it would be used, user base is 10,000 to 20,000.
Two webservers, 1 webserver performing tasks of the of the application server and the databases server(Clustered or mirrored)
Three-Tier Small Farm
Three-tier small farm is much more similar to the two-tier small farm.
A dedicated app server would be added for the services.
To improve search service, search database would be moved to a dedicated database server.
The general rule is planning is to have 10,000 users for a WFE server.
First Tier we can utilize two or more Web Servers.
Second Tier there are two servers dedicated to crawling contents and serving search queries and one or more servers for all other application services.
Third Tier there are dedicated servers for Search Databases and one or more servers can be used for all other SharePoint Databases.
A Large Farm is similar to the Medium Farm. Additionally a Large Farm could consist of dedicated servers for Sandboxed code.
Hope this article helps.