Playing hi-lo hit frequency

December 04, 2001 3:13 AM
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Is there any difference between tickets with a high frequency of winners and tickets with a lower frequency of winners, given that they have the same house percentage? It turns out that there IS a difference, even though with the same house percentage the house will win the same amount on each ticket, given a large enough trial.

Consider two eight spots:

We take these two eight spots and run a simulation: 5,000 players each playing 1,000 tickets on each eight spot. We discover at the end of our simulation that the house has won approximately the same amount of money, with the players having an approximate aggregate of $3,600,000 remaining to them. Well, no surprise. So the average player has about $720 left after playing 1,000 games ”” it doesn’t matter which ticket.

Wait a minute! We remember that Keno is like life, all the rewards are not commonly bestowed equally ”” the distribution is skewed. The average (arithmetic mean) includes the large numbers won by those lucky few who hit solid eights! To simplify, this is like saying that three people whose incomes are $100, $200, and $10,000 per month have an “average” income of $3,433 per month. In a skewed distribution the average does not describe reality very well. A better measure in this case is the median, which is the value halfway between the highest and lowest. In this case the high frequency player has a median value of $492, while the low frequency player has a median value of only $462, a $30 difference. It is worth pointing out also, that the player with the worst luck won only $90 playing the low frequency ticket, while the player with the worst luck playing the high frequency ticket won $140, a difference of $50!

The typical player of the high frequency ticket will have 30 more “bullets” to fire at the jackpot! The tradeoff? The jackpot will be a bit smaller. And remember, we are talking about tickets with the SAME house percentage, and importantly the SAME PRICE.

If you have a Keno question that you would like answered, please write to me care of this paper, or at kenolil@math.net. Well, that’s it for now. Good luck! I’ll see you in line!

Catch:  

High Freq.Pay:  

Low Freq. Pay:

4/8  

$1  

””

5/8  

$8  

$9

6/8  

$90  

$100

7/8  

$1,250  

$1,480

8/8  

$18,000  

$18,600

Win Freq.  

1/10  

1/48

House Pct.  

28.03%  

28.03%