Last week we discussed (and simulated) a small Martingale, and we discovered that a Martingale is not a good strategy to use, and also that deuces were not particularly good either. I also hinted that the “go for broke” strategy might not produce great results either.
Now, with 100,000 players each starting with a $100 bankroll, and each player playing only a $1-five spot, and playing until either he went broke or hit a solid five, we ended up with these results:
Solid fives hit: 7,121; Odds against a solid five: 1 in 14.04; Games played per player: 1,107; Dollars wagered: $11,070,270; Dollars won: $5,775,131.
Note that by NOT playing the Martingale on the deuce, we’ve improved our performance considerably; instead of one chance in 23 we’re down to one chance in 14 of hitting a solid five! Also, instead of the total players win of $3,498,654 we win $5.7 million or so. It is apparent that by omitting the deuce we are improving our performance. That’s the good news.
The bad news is that our win is only 57 percent of our initial bankroll, on a game which has a theoretical win for the player of about 72 percent. What’s wrong? It must be our strategy of “going for broke.” The “go for broke” strategy calls upon us to keep playing until one of two provisos is met: Either we go broke, or we win the solid five, nothing in between. But if all players merely played their $100 bank roll completely and then quit, we are guaranteed over the long run that our win will be about 72 percent of our initial bankroll, with nearly the same chance of hitting a solid five. Of course, many players will end up with a few dollars, some with none, and some with the solid five, but it is the “in-between” players, who quit with some money left who make the disparity in the player’s win percentage (and its additive inverse, the house percentage.)
This implies to me that the best gambling strategy is NOT to play Martingales or “go for broke.” The best strategy is to set your bankroll, play it, and then quit once you have run through your bankroll one time. This is the way to best preserve at least some of your bankroll, maximize your keep vs. the house percentage, give yourself a chance to hit big, and minimize your chances of going broke.
The principle is self-discipline, setting your playing limit per session. Although we have applied it to keno, its application to other games and situations is self evident.
On a scale of one to five spikes, with five being the highest, Keno Lil rates setting a session playing limit:
Well, that’s it for now. Good luck! I’ll see you in line!