How does a ArrayList's contains() method evaluate objects?

ArrayList implements the List Interface.

If you look at the Javadoc for List at the contains method you will see that it uses the equals() method to evaluate if two objects are the same.

I think that right implementations should be

public class Thing
{
    public int value;  

    public Thing (int x)
    {
        this.value = x;
    }

    @Override
    public boolean equals(Object object)
    {
        boolean sameSame = false;

        if (object != null && object instanceof Thing)
        {
            sameSame = this.value == ((Thing) object).value;
        }

        return sameSame;
    }
}

The ArrayList uses the equals method implemented in the class (your case Thing class) to do the equals comparison.