## Fibonacci Gambling

I call going  to Nevada “visiting my money.”  Years ago every time I went there I played blackjack.  One year I rode my bicycle down Nevada’s US 97 staying in small towns and gambling at the local casinos.   I was a net loser though I had the occasional lucky streak.  I think I really gambled for social reasons.  I just liked sitting at the table and talking to the players and the dealer and watching the cards.  Thus my main objective was to lose my money slowly.  Since I wasn’t wealthy,  my secondary objectives were to win big and do so using the casino’s money.  To these ends I devised a Fibonacci betting sequence.

The idea was to increase my bets every time I won according to the Fibonacci sequence, $1,1,2,3,5,8,13,21,34,55,89,144,233,...$.  Say I got my bet up to $13$ units.  If the dealer won that hand, the money I lost was the $5$ and $8$ units I had won on the previous two hands.  So my next bet would be $3$ units – dropping back two steps in the sequence.  I would still be playing with the casino’s money, the money I had won on the two hands previous to winning $3$.  The odds of getting very far into the sequence are low but once or twice I was actually wagering more than one hundred dollars.

Last year I decided to simulate this scheme with a Markov process.  My Markov states were the amount of money I had (my stake)  along with  the location in the betting sequence.  I built the matrix in EXCEL since I wanted to label the columns and then I used EXCEL’s limited matrix tools.  The absorbing states were defined to be losing  the initial stake (zero money) or the possible winnings I could make using  a  stopping rule of  any amount 16 or over.  I let the probability of a winning  hand be .49.  Of course this Markov process doesn’t come close to simulating the play in blackjack since you can only do well  if you double down and split pairs at the right times. After eliminating some  unreachable states, I generated the fundamental matrix.  Here are the results.

Fibonacci Gambling - Simulation Results

On the average the results are as dismal as expected given a house edge of two percent.  For my purposes consider the fourth row.  If I start with a stake of 4 units and define “winning big” as winning 16 units or more,  I will “win big” 18 percent of the time and stay at the table for 17 hands.  That is actually not too bad – a one in five chance of walking away a “big” winner.  In reality I would  keep on playing trying for a bigger score.  That’s why going to Nevada is “visiting my money.”