## Wednesday, April 27, 2011

### Bankroll Considerations

Recently, I answered a question from a reader about what to do when you win ‘big’ early in your session.  Of course, both ‘big’ and ‘early’ are rather subjective terms.  Ironically, the definition of big probably has less to do with the denomination you are playing and more to do with the size of your bankroll.  If you showed up with \$20 and you hit a \$100 hand, you’re more likely to stop than if you came to the casino with \$1000 and hit a \$100 hand.  In the first case, the Player was probably bankrolled too small and in the latter case, it was overkill.  But it is just a normal human reaction to place the size of the winnings next to the amount of money we show up with to determine what ‘big’ is.

So, what does this bankroll really do for us?  Well, it sets a maximum that we can lose over some defined period of time.  Maybe it is a single session over a single day/night.  Or, maybe it is the amount we are willing to lose over a week-long vacation.  Why is it important?  Well, besides setting some limits for ourselves, it is also tells us that at the point we’ve lost that much, we are done.  There is no coming back from that loss with a hot streak.  So, if we were to sit at a \$5 blackjack table with \$5, we have to realize that if we lose that very first hand, we’re done.  If we sit down with \$20, then we have to lose 4 more hand than we win (ignoring doubling and splits) to be ‘broke’.  If we sit down with \$1000 then we’d have to lose 200 more hands than we won.  With a \$5 bankroll, you have a greater than 50% chance of going bust just on the first hand.  With a \$1000 bankroll, you might be able to play weeks or months before going bust.

While we assign a payback to every game, and we can calculate the anticipated loss over a period of time for that game, this is just a theoretical average over time.  Most casino games are fairly volatile which is simple terms means STREAKY.  So, if you play an hour of \$5 blackjack, you can realistically expect to lose about \$8.  If you start with \$100, you’re almost guaranteed to get thru that hour.  If, however you start with \$10, your chances of playing the entire hour go down considerably, which ironically means that you would lose MORE than the ‘average’.  By not allowing yourself a reasonable opportunity to come back from a cold streak, you in essence do yourself a grave disservice.  This is why showing up with the right size bankroll is so important.

One could thus argue that the right size bankroll is one that makes sure that you have ZERO chance of going bust before you are done playing the amount of time you want to play.  There is a certain amount of truth to this notion, but it removes the human element.  It is too easy for us ‘greedy’ human to decide to play longer or up our wager if we have too much cash on hand.  Also, sometimes it is not so practical to do this.  To play an hour at \$5 blackjack, we would merely need to show up with \$150-\$175.  If, however, we wish to play 3 hours of video poker – max-coin quarters – we would need almost \$2000 (assuming 500 hands per hour).  This is probably overkill if you’re playing a full-pay jacks or better machine.

I created a program that simulated video poker.  It started with different bankroll amounts.  If at any point in the 1500-hand session the Player lost more than his bankroll, he was considered to have ‘busted’ and the session ended.  For the moment, I just focused on the percentage of busts and did not bother keeping track of how far into the session the Player was or how he would’ve done had he decided to go beyond his bankroll (i.e. how often does he recover his initial bankroll by using yet more money).

If the Player starts with 200 wagers (\$250 for a max-coin quarter machine), he went bust only 1.39% of the sessions.  If we cut our bankroll down to 120 wagers (\$150), our Player went bust just a smidge under 20% of the time.  If the bankroll is reduced to 80 wagers (\$100), we find that the bust rate goes up to over 43%.  If the Player tries to get away with a mere \$50 bankroll, he’ll find that he’ll lose it all about 73% of the time.  Try and get away with only \$25 and you’ll lose the entire bankroll more than 87% of the time.

So, what’s the right amount of bankroll?  There is no absolute right answer for that.  You have to decide how much you’re willing to risk that your session ends prematurely.  But, if you’re looking for some advice, based on the numbers presented here, I’d go with 120 wagers (\$150).   You’ll go bust only 20% of the time, and if you’re night is going that bad, you might just be best off calling it a night.