"I SHOULD HAVE QUIT WHEN I WAS AHEAD!"
Dunbar is a professional gambler with a strong mathematical background and a Ph. D. in biophysics. In 2005 he created his acclaimed software Dunbar's Risk Analyzer for Video Poker 1.0, which enables video poker players to assess risks and bankroll requirements for short- and long-term trips. Now Dunbar's Risk Analyzer for Video Poker 2.0 is available for about $20 from either of these fine establishments: http://www.shoplva.com/collections/video-poker/software, and http://gamblersbookclub.com/DUNBAR-S-RISK-ANALYZER-FOR-VIDEO-POKER-689.html#.VlW_0HarTBQ.
How many times have you heard someone in a casino lament, "I should have quit when I was ahead"? How many times have you said it yourself?! In this article, I want to look at what happens if you DO stop when you're ahead, specifically when you're ahead at video poker, and how the outcomes when you stop compare to what happens when you just keep on playing.
There are several factors that could affect the choice of stopping when you're ahead. If you're playing for a very short time, it doesn't matter much if you stop when you're ahead, because you don't have much time to lose back what you've won. If you're playing a relatively less volatile game like Jacks or Better, there's less impact of stopping when you're ahead compared to playing a more volatile game like Double Double Bonus.
After the fact, we can always say precisely when we should have stopped. But picking a stopping point beforehand isn't so easy. The greater your target stopping goal, the smaller the chance you'll ever reach it; but also, the smaller the chance you'd lose a significant portion of it by continuing to play instead of stopping.
With so many factors, we'll have to settle on just a few examples to get a feel for what happens when we "quit when we're ahead".
A WEEKEND TRIP
Let's look at a weekend trip in which we've brought $500, and we plan to play about 16 hours of video poker. We're playing 25c single-line games, and our host casino has 8/6 Jacks or Better ("JOB") and 9/6 Double Double Bonus ("DDB").* Assume we can leisurely play 500 hands an hour making very few mistakes.
Example 1: I'm determined to come home a winner!
If we highly value coming home a winner, we can almost guarantee it by setting a very small goal and by stopping when we reach it. In the most extreme case, we could quit when we're one bet ahead. For 25c JOB video poker, that would be $1.25 ahead. If we stop as soon as we're $1.25 ahead, we'll be able to say "I won!" to the spouse or partner, 94% of the time that we return from a trip. Somewhat surprisingly, we'll lose our entire $500 bankroll 3% of the time just trying to get one bet ahead. Still, for every time we come back a loser there will be 15-16 trips that we come back a "winner." On average, you'll get to play about one hour, but almost 25% of the time, our "trip" will consist of just one hand of video poker. Another 11% of the time the trip will end on the 2nd hand!
Maybe one hand or even one hour of video poker isn't your idea of a fun weekend trip to a casino. What happens if we try to play the intended 16 hours, regardless of what we win? If we keep playing, then our chance of going home a winner drops from 94% to 21%. Our chance of losing our entire $500 bankroll rises from 3% to 28%. So, it's more likely we'll lose $500 than we'll win anything. Offsetting that bad news somewhat is the fact that our chance of doubling our $500 bankroll has risen from 1% to 14%. Here's a summary of the two strategies:
STOP WHEN WINNING $1.25 VS CONTINUING TO PLAY**
Example 2: I want to double my bankroll!
What if our idea of coming home a winner is more ambitious than winning $1.25? Say we want to win at least $500.
Game I: JOB
STOP WHEN WINNING $500 VS CONTINUING TO PLAY
As the table above shows, with a bigger goal, the difference between stopping and continuing to play is substantially lessened. By continuing to play, you give up a few of the times you would have had a $500 win, but most of those times you'll still have a substantial win of $300 or more.
JOB is a game with less flux than most video poker. So, what about a game like Double Double Bonus, which is a lot more volatile?
Game II: DDB
STOP WHEN WINNING $500 VS CONTINUING TO PLAY
With DDB, if you keep playing, you will achieve your goal much less often than if you'd quit. (17% vs 30%) Your overall chance of winning goes down, too, but on average you do get to play somewhat longer. (12 hours vs 9 hours).
In any event, most players would find a 50% RoR unacceptable. The RoR could be lowered by either (1) bringing more money, (2) planning to play fewer hours, or (3) foregoing DDB in favor of a less volatile game like JOB. For example...
Example 3: JOB with $1000 bankroll and $800 goal
On the surface, this table makes stopping look like an attractive option. When you stop, you finish at least $800 ahead 12% of the time. If you keep playing, you finish at least $800 ahead just 5% of the time. The average length of play looks okay, too, when you stop. And either way, the RoR is very low. Not shown in the table, however, is the 8% chance that you will be done before half (8 hours) of your planned hours of play.
It's usually a good idea to have some kind of plan when you go to a casino. Setting a maximum amount you are willing to lose is always a good idea. In some cases, you might want to include a win goal-and plan to stop if you reach that goal.
The main advantage of stopping when you reach a win goal is avoiding the lament, "I should've quit when I was ahead!" If you play on to the end of your stay, more often than not you will finish below the point where you had considered stopping.****
A big disadvantage of stopping when you reach a goal is that you may have only played a small fraction of the time that you allotted to play. The choice of whether to stop at a goal is a personal preference and is dependent upon how much you value the guaranteed win versus how much you enjoy the actual time spent playing the machines.
There are other plans which may allow you to get closer to the best of both worlds. You could, for example, say that you will play at least 8 hours, and only after those 8 hours you will stop at some predetermined win goal. Or you could break up your 16 hours into several 2-4 hour sessions, and have smaller goals set for the individual sessions. These scenarios are beyond the scope of this article, however.
This article is longer than any other I've written for Blackjack Insider. I think I'll quit while I'm ahead.*****
*"8/6" means this version of JOB pays 8 times your bet for a full house and 6 times your bet for a flush. Likewise for 9/6 DDB.
**All calculations for this article were done with Dunbar's Risk Analyzer for Video Poker 2.0.
***RoR is the risk of ruin. It's the chance you lose your entire $500 bankroll.
****I'm assuming you are playing a game with less than 100% payback.
*****Good luck with whatever comes next, Henry!
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