Suppose the casino offers only one game: you bet £1, then with probability 49% you win £2 (otherwise you lose your wager). Your expected net is -£0.02. Now if you know that half your total losses will be refunded, here's how it breaks down.
One bet: Win £1 with 49% probability, lose £0.50 with 51% probability, expected gains £0.23½.
Two bets: Win £2 with $.49^2$ probability, wash with $2\cdot.49\cdot.51$ probability, lose £1 with $.51^2$ probability. Expected gains £0.2201.
Three bets: Expected gains £0.33015.
...
47 bets: Expected gains £0.6824276...
It seems that for this simple game 47 is the best you can do. The specifics will vary, but probably the rough result will remain the same: you can expect to win back a fraction of a single bet.