Isn’t it always the way it happens? The people who come to Las Vegas with lots of dough are always the ones who win the most. The people at the $5 slots just seem to have all the luck, while the penny players get wiped out.
We have all seen examples of this type of scenario, which we attribute to the perverse nature of Lady Luck. But, the fact is that in many cases there is a simple mathematical basis for what we observe. The $5 slots are generally looser so players get more jackpot winners and hit winners more frequently.
The size of a player’s bankroll can have a direct bearing on how well we examine the situation calmly.
Most seasoned players have heard of this phenomenon, but because the subject is generally shrouded in complex math, not much practical information gets circulated among average players.
In its simplest terms, we can state that a player who starts out playing with too small a bankroll will get distinctly worse results than one who is properly bankrolled. To illustrate this principle, we have set up an easy to understand example.
Consider a group of 100 players each playing a (non-typical) game, which returns, on average, 100 percent of all the bets. In this game, the player gets a number from 100 drawn at random after one-unit is wagered. If the number is one, the player is paid 50 units. If the number is two, the payout is 25; if it is three, the payout is 10; if it is four through 18, the payout is only one unit. All other numbers lose. Since the numbers are randomly selected and each is equally likely, the long-term payback is exactly 100 percent.
If 100 players play this game with a starting bankroll of only 10 units, this is what we can expect to happen to them:
64 players go bust within 10-20 games.
10 players go bust within 21-40 games.
6 players go bust within 41-80 games.
5 players go bust within 81-160 games.
5 players go bust within 161-500 games.
10 players go bust after 500 games.
If one player were to start 100 series of games, each beginning with a 10-unit bankroll, the same results, would occur to that one player, i.e. in less that 20 games, the player would bust out 64 times.
If these players start out with 20 units in their bankroll, then the typical results would be:
48 players go bust within 20-40 games.
13 players go bust within 41-80 games.
13 players go bust within 81-160 games.
17 players go bust within 161-1,000 games.
9 players are still playing after 1,000 games.
Give them 40 units in their starting bankrolls and these results will be typical:
34 players go bust within 40-80 games.
16 players go bust within 81-160 games.
15 players go bust within 161-320 games.
9 players go bust after 321-640 games.
12 players go bust after 641-2,000 games.
14 players are still playing after 2,000 games.
Remember, these players are in a game returning 100 percent and you can see that with bankrolls of 40 or less, at least 34, 48 and 64 were virtually instant losers.
Gambler’s ruin – too small a bankroll for the averages to work out! Sure, the game is still paying 100 percent if we look at the bottom line, but those instant losers didn’t enjoy their play time, nor did those who were wiped out nearly as fast.
But just give these players bankrolls of 500 and none will ever go bust and everyone will swear the game is great to play. The onlookers will shrug and say, "Money always goes to money."