It is usually not that way and yes, it does depend.
On one side you have small cheaters. Like... WorldBet for example. They copy odds from other bookies, take your money and if you win, they don't pay. Their threshold... hard to define.
Then you have big movers. Companies that balance the book, not the clients. For example big asians, pinnacle etc. There are automatic limits and for some dodgy leagues they can be quite small or they don't even offer them.
Next in line are big crappy bookies. Also known as "joke" bookies. I won't mention names, but some of the most known european bookies are on that list. You can win 40 euros and they kick you out. I know a person, who got 4 accounts closed there in a month and he won maybe 200 euros in total. They are generally despised amongst bookies and punters.
Last to mention are normal bookies that don't belong to any of those categories.
- The bigger the bookie is, the higher the threshold is. The reason is, that the best of them do try to balance the book as much as possible and because of high turnover winners are able to sneak in without causing problems for the bookie.
- The other factor is, do they compile odds themselves. Some of these bookies mostly copy odds from others and they don't have opinions. If bookie doesn't have opinion, they will be more cautious when it comes to accepting bets. Usually you can easily see if bookie has their own compilers by checking the odds: time of publishing odds and positioning on the market tell you the whole story.
- The third factor is the way their risk management works. Do they have RM at all? If they have only automatic limits, winners will have hard time. If they have combined risk management with certain amount being automatically accepted and the rest going to the risk manager, winners will be able to bet more. Good punters usually always try to place a bet with such a bookie; most of the times his bet will be limited, but if compiler happens to have different opinion, his whole bet (10k+) is probable to come through - even if he is consistent winner.
- I will say that when it comes to good bookies, winners are not customers that have most problems. More limited than winners are cheaters and arbers (unless compiler decides to take arbitration money). Whatever you do, don't cheat. I know of a case where a real highstakes pro bet on a match 5 minutes after it started and he send an email immediately, saying that it was his mistake because he didn't check the starting time. Normal customers wait till the game ends and then decide whether to send an email or not. Once you get that cheater note, you are not in best shape with any bookie. Except Worldbet, they will cheat you back.
BTW, if your usual stake is 100 euros or less, you don't have to worry with most of these bookies - you will always be able to bet whatever you want, unless price has moved a lot.
- One other breed of punters that raise a lot of suspicion (and faster limits) are those that bet dodgy competitions, small leagues, strange sports - and not losing. If you want to bet Champions League and NBA, I don't think that any of the bookies from last group is ever going to limit you. The market is just too strong and they trust that you will be losing longterm.
- Just remembered another one... it depends also HOW do you bet. How selective are you, do you bet only singles, what is the structure of your doubles, triples etc. How is the price that you bet on positioned on the market...
So bottom line... yeah it depends.