proability of wining in HOA

It's hard to say how many votes will be needed to win, the simple answer is that the three with the most votes will be considered the winners.

Most likely, far fewer than 200 will vote, you should find out from your governing documents how many you need to constitute a quorum. If you don't have enough owners to make a quorum, the results are open to challenge.

I'll add that you should also determine if your docs allow for cumulative voting. Assuming there are three positions open, typically each owner would get three votes. If cumulative voting is allowed, then owners could place all three of their votes for a single candidate. If it is not allowed, they can only place one vote for each candidate.

So the answer to your question "what no.of votes we need to be elected" depends primarily on how many people vote, and whether cumulative voting is allowed.

Typically BOD Elections are held at the HOA Annual Meeting.

Typically in order to conduct business at the Annual Meeting (including elections) you need to establish a Quorum.

Typically your Bylaws will tell you how many owners must attend or submit a Proxy to make Quorum. I have seen as few as 10% (in your case 20) and as many as 50% (in your case 100).

In your case, the top 3 vote getters of the 6) will be elected to the BOD. The BOD then meets and elects its own Officers.

The above assumes there are no (super voters) holders as there are when a Declarant is still in control. Typically a Declarant may have multi votes such as 100 to one votes thus being able to control the vote.

Hope this helps you understand the process better.