A small Martingale for a small-spot ticket

October 30, 2001 2:55 AM
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This week I tried out a little strategy, a small Martingale. I programmed my computer to play a one dollar five spot, with a house percentage of 28 percent, with pay outs of $1, $9, and $811 for catches of three, four and five of five, respectively. I set each player to an initial bankroll of $100, and each player played a $1 five spot each game, with the provision that the player would stop playing if either he hit a solid five, or if he went broke.

In addition, the player would Martingale a two spot, with the two spot played for a multiple of $1 that would regain the initial $100 bankroll if hit. For example, suppose the player was down $25, with a remaining bankroll of $75. He would then play his $1 five spot, plus a $3 deuce, thus giving him $75 -$4 +$36 if he hit the deuce. This would give him $107, thus restoring his original bankroll plus a few bucks. I set the program to play 100,000 players, thus the initial play would be $10,000,000 of keno. As we might suspect, the great majority of players went broke, but a higher proportion than you might think hit a solid five. 4,314 players out of the 100,000 players hit solid, which is about one in 23 players!

Now, one chance in 23 of hitting a solid five doesn’t sound too bad, so what’s wrong with this picture? Well, a couple of things, actually. I’ve set up this demonstration so the player either goes broke or wins $811. With 1 chance in 23 of doing this, his mathematical expectation is $811/23, or $35.26! Remember, the house percentage is about 28 percent, so our strategy has unfortunately DOUBLED the house keep! Also, if we merely asked the 100,000 players to play a straight five spot for 100 games, we’d expect to see some 6,447 solid fives on ten million dollars worth of action, instead of only 4,314! And this is ignoring the extra money we would have won on the pushes and the four out of fives.

Why is this happening? For one thing, our average wager is $2.88 per game, for 6,688,818 games, and we are spending 65 percent of our total wagers merely playing deuces. If we stick to straight five spots, ALL our wagers go towards hitting a solid five. For another thing, the Martingale, which is supposed to protect our bank roll and thus lengthen our staying power, has resulted in a REDUCTION of some 33 percent in the amount of games played, so we have that many fewer chances of hitting a five spot.

In addition, the basic strategy of playing to win or bust might be faulty. We’ll look into that next week.

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