When I used to stake I had a theory I used to use.
The following stakes;
1. I'd stake about 1M first, just to get started.
2-4. Continue with small stakes.
5. If the previous stakes were Losses, I'd bet 5-10M.
6. I'd usually go 5-10M again if I Won/Lost.
7. If the past 2-3 stakes were Won. I'd stake 500k-1M stakes hoping that I'd lose.
8. Once I lost 2-3 stakes, I'd stake 5-10M again. Repeating this process.
Since it's 50/50, if you lost the previous stake you'll most likely win the next stake. However their are a number of factors to consider.
-Your odds/Opponent odds. If you're opponent has lost a few stakes in a row, they'll most likely win. This is the hard part, because unless you've had a session with them you don't really know. If you watch certain names, you'll see their chats increase from 'Whip-2M' to 'Whip 4M' so you can assume they most likely just won. I'd stake these people.
-The odds theory.
First stake is (1/2). To win two stakes in a row it's (1/2)*(1/2) which is (1/4).
To win;
3 Stakes in a row (1/8)
4 stakes in a row (1/16)
5 stakes in a row (1/32)
6 stakes in a row (1/64)
7 stakes in a row (1/128)
8 stakes in a row (1/256)
9 stakes in a row (1/512)
So obviously if you get lucky and win 3 stakes in a row, the next stake you have a (1/16) chance of winning. I've won 8 stakes in a row, and have also lost 8 stakes in a row. From my experience I'd stay away from the arena, unless it's a one off thing. I used this theory and went from 21M to 180M, and 3M to 250M over 8 hours, and 6 hours. I ended up losing the first 180M, losing 8 stakes in a row, and sold 100M of the 250M and lost the remaining 150M. To make money of the arena you need to know when to cash out and leave. For me personally it was way too addicting and destroyed my Runescape experience.