When your trade is matched you'll see updated positions information on the Positions tab of your My Trading panel:
Let's look at some scenarios for when a trade is matched.
You have no position and you enter an order to buy 10 shares of the Patriots to win proposition. When that order is matched by a corresponding sell order you'll have a new trading position of +10 shares (exactly as shown in the image above).
Now let's say you enter an order to buy another 15 shares of the same proposition. Once that order is matched you'll have a net position of +25 shares. The My Trading panel update to show this new position size immediately upon order matching.
Now let's say you enter an order to buy 50 shares and only 30 are available at the specified price. In this case, 30 will be matched and you'll have an open order for the remaining 20. This open order for 20 shares is managed on the Open Orders tab of the My Trading panel.