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The Fibonacci system uses the Fibonacci Sequence - the next number in the row is the sum of the two previous numbers that is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. You start from a one unit bet. If you win the first hand, you will start again with one unit. If you lose the first hand, then you make a one unit bet again. If you lose again, you must bet two units. If you lose your fourth hand your bet will be 3 units and after that as follows:

1 lose 1 lose 2 lose 3 lose 5 lose 8 win 3 win 1

After a win, cross out the last two numbers in the sequence. Once you revert to a one unit bet the sequence ends.

For example, you are playing at a table with $500 table limit. You bet $10. If you lose nine hands in a sequence you will reach the table limit:

Bet Size
1st $10
2nd $10
3rd $20
4th $30
5th $50
6th $80
7th $130
8th $210
9th $340
10th $550