You want that gold star, huh? Well, don't ever let your opponent take Siam, 50/50 chance of that happening, depending on if they get the first move. If they do get the first move (turn 1 and turn 3), they will take Siam on turn 3. But they should be weak enough to be defeated.
Here's how to win in six (or seven turns, if AI gets first turn order):
The quickest route to Australia is to lunge directly into Middle East with all your armies, do not attempt to take Ukraine, as tempting as it may be. You will take Ukraine on your second turn with your reinforcements.
Put 3 armies in Scandinavia, to attack Ukraine. Put the other 2 with your forces in Middle East, and take India.
If you're lucky, you have first move order in the even turns. Click on the game button in the lower left corner, and see your history to confirm. You can only take Australia by turn six if you have first move on the odd turns. You can surrender and “Try Again” (Click on the game button in the lower left corner, there’s no shame), or just play it out, and try again later.
If you move first on odd turns:
To capture Australia by turned six, you need for him to attack you in Siam, on turn three, after you captured it, and again on turn four, as a counterattack into Indonesia. So, how do you accomplish this mean feat? Simple mathematics, but you have to figure it out backwards in time. In other words, you know for certain how many he will attack with on turn three, and then again on turn four, and you know the turn order.
He will attack neutral Siam with 9 on his first round of turn three, without considering that you have first move. If you 5 or less in Siam from the first sequence, he will capture Siam, and you’re in for a protracted struggle. So if you attack Siam with anywhere from 7-15, leaving 6-14 of your armies in Siam, you will repulse his attack. The question is, how many do you want to leave in Siam, for him to attack next turn (thereby successfully counterattacking Indonesia on turn four)? You want to have a small enough number to entice the enemy to attack Siam from Indonesia on turn four.
I have a much more detailed explanation, and video to go along with it, probably way more than you want to know.