Smash Vegas

A betting system is a method of bet sizing depending on predetermined factors.  The most common betting systems use a progression where you bet more or less depending on whether you have just won or lost.  There are also betting systems where you look for an event which is statistically “due” (e.g. you’re playing roulette and the last 4 numbers have been red so you bet black).  Obviously the latter are examples of the gambler’s fallacy.

The problem with all betting systems is that bet sizing does not affect the house edge.  It can increase your chance of winning in the short term, but that will always be balanced out by a large loss later (as in the martingale system).  The longer you play, the closer your loss will be to the house edge.

The reason that bet sizing cannot affect the house edge is simple - expected value is linear.  This means that:

expected value (A+B) = expected value (A) + expected value (B)

In other words it doesn’t matter what the individual amounts you wager are, overall your loss will equal the total you wager multiplied by the house edge.  There cannot be a clever way of sizing bets which would change this - otherwise expectation would not be linear.

Thus we find (although we already knew) that the equation for your loss at a gambling table is:

loss = (total amount wagered) * (house edge)

No betting system can alter that.