Back in the days, there were secure trade option to make a safe transaction between the players.
However, this function was broken and unfortunately never fixed
The only way to 'trade' nowadays is indeed selling card through private sales.
I believe secure Trade Option was closed because according to Chaos in a post explaining about Secure Trades, there was an exploitable bug that allowed duplication of a card you owned as a result of using this.
Personally when it comes to Private Sales, my general rule is that I look at the player`s profile page for general information on them regarding the trustworthiness of the player and some of their public forum posts. I do take the time to check their collection ranking and cards they have put up in sales and make a quick decision to determine if they really have the cards.
If a player is a friend who has done a past successful trade with me, I go straight into it. I always double check and send PMs to verify details of what is to be exchanged to ensure there is a mutual understanding of what we is being traded.
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If you are trading cards and a player buys a card in your PS and does not do the same by letting you buy a card in your PS, you can remind them via PM to uphold the deal.
If it takes more than 24 hours, I can suggest contacting Customer Service and show them info on your Sales Thread, Purchases and Sales History as an indicator.