But the question is whether arbitrage is possible within the same bookmaker (which I doubt)? As I understand it, the odds are adjusted in such a way that the bookie is always earning something, no matter who actually wins. This, more or less, leaves no room for and essentially rules out internal arbitrage, or fork as you call it (read, they are not fools)
Of course this is possible even within the same bookmaker
Pre-match it's a bit harder to achieve, because the markets move slow, but in-play you can do it all the time.
Look at these odds:
Source: https://www.betonline.ag/sportsbook/politics/electoral-collegeIn
this post, you can read that "The Field" had 2.04 in the past:
It's also ~4% surebet with betonline.ag (2.16 Trump at Betfair, 2.04 "The Field" at betonline), if anyone is interested.
Now you put 53% of your stake on the 2.04 and 47% of your stake on the 2.30 and you have 8.11% surebet (trading/arbitrage profit). You can also get unlucky of course and the odds don't move in your favour - thats the risky part about trading/arbitrage
Bookmakers don't like it of course, but they kick out winning players anyway, no matter if you do arbitrage or not. Doing arbitrage at traditional bookmakers is a bit meh though, since you pay the house edge for every bet. Exchanges like Betfair are better suited, because you just pay a commission on your net profit.
Another example would be a football match; inplay. You bet on team A to win for odds of 2.00. The next second they score the lead. You can now play X2 for 3.00 et voila, you have a sure profit, no matter what is FT result. Bookmakers even urge you to take sure profit with offering a "cashout option" more and more (it's value/valuable for them, if you use it, thats why they offer it).