I've spent maybe a mill or two total (I know it's not a lot) in betting (I spend 150~250k each time) and I've only won back 200k. =/
My strategy is to see who and who is against each other. I look at which mercs each has, and their formation. The AIs don't really heal the main character when needed, nor do they move characters in front of them so they aren't in the open, so it doesn't really matter for me whether they have a shaman or not. AIs also like to use magic, so I look at if there are vikings on the team. If team A has a viking in the second row, and team B has viking, sword sword in front, then viking from A could freeze most of team B's attacker mercs. If a team has a lot of artillery men, then I'll bet for them also.
So far I get kinda close with my bets, but not quite good enough. The dividends for those who usually win (Beatrice and Alexandra) is really low, so you'll have to spend a good amount of money.
"Even a broken clock is right twice a day."