Don’t rely too heavily on stats

Oct 2, 2006 3:09 AM

Let’s compare two six spot tickets, one with a house percentage of 30%, which is a bit higher than usual, and one with a house percentage of 25%, which is a little lower than usual. (Typical house percentages in Nevada are in the range of 27-29%.)

The chart below delineates the differences between the two tickets after a million games have been played on both tickets, one thousand players each playing \$1,000. The average refers to the mathematical average won by each player, the median is the median (middle) amount won by the thousand players, the highest figure is the highest total amount won by any single player, the lowest is the lowest total amount won by any single player, the percent winners is the percentage of players who ended up winning more than \$1,000.

 25% Six-Spot 30% Six-Spot Average \$740.82 Average \$707.27 Median \$530.00 Median \$537.50 Highest \$5,659.20 Highest \$3,730.60 Lowest \$191.00 Lowest \$182.00 50% Range \$706.00 - \$413.00 50% Range \$719.00 - \$420.00 Percent winners 11.60% Percent winners 13.10% Top 100 winners \$255,214.20 Top 100 winners \$204,980.80 Bottom 900 winners \$485,602.20 Bottom 900 winners \$502,293.20

The average amount won is about right for each ticket. We would expect the average on the 25% ticket to be about \$750, and the average on the 30% ticket to be about \$700.

But does the typical keno player win this much? No, because if you remember winnings on keno tickets follow a skewed distribution.

A much more realistic figure to use is the median, which is almost identical for each ticket, regardless of the big difference in house percentage.

The typical keno player playing either one of these six spots will win about \$530 to \$540 per \$1,000 played. For the vast majority of players the house percentage has virtually no meaning. This being the case, if you are trying to decide which casino to play your tickets in, you had best use some other criteria.

The distribution of keno winnings is no more even than the distribution of incomes — this is a hard fact of life. The real impact of the house percentage is only seen by those lucky few who win big.

If all you take into account is the house percentage, you will assume that you will win, on the average, \$50 more per \$1,000 played on the 25% ticket than on the 30% ticket.

In truth, it is the top 10% of players in winnings who average \$400 more per \$1,000 played, while the 90% of players who don’t win big average virtually the same amount in winnings.

Many people who play keno get frustrated because they know that they are playing a 25% game, or a 27% game, yet when they have finished their playing sessions, they have won far less than they should have, according to the house percentage.

By understanding the median figure above, this will lessen their frustration. Keno is after all, a lottery! Lotteries have a few big winners, and many relatively small losers, that is how they are constructed.

It is interesting to note that out of a thousand players playing \$1,000 worth of six spots, only 11-13% of them end up as net winners. Six spots are by far the most popular tickets, and yet other tickets like 9s, 10s, 12s and even 15s might be better to play.

Well, that’s it for now. Good luck! I’ll see you in line! e-mail: [email protected]