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To: vpFREE@yahoogroups.com
From: Harry Porter
Date sent: Tue, 15 Nov 2005 16:06:56 -0000
Subject: [vpFREE] Re: Tournament Play
When you perform a standard "max EV" game analysis with any software, an ending win of 1000 credits after a given number of hands is treated as being worth exactly half of an ending win of 2000 credits. When playing a tournament, that's hardly true. If it turns out that you need a minimum of 1400 credits to finish in the money, than ending with 1000 credits is of no greater value than 500.
Speaking generally, it's not only important to maximize expected score but also to maximize the likelihood that you'll come out on top of the pack. The strongest tournament strategy will vary depending upon format but it will likely reflect a tradeoff between these two goals.
It sounds like you're looking for some advice on the "V P Shootout" tournament you describe, involving a 9/6 DB paytable. I'll comment that later, but to outline the approach I take in a tournament I want to use the Millionaire Maker as my example, where the game is DDB.
You recall a post I'd written on vpmail a couple of years ago. I'm a little wiser now and therefore will remark that Skip and Dancer, as well as others, are likely to have stronger insight. Nonetheless, here's what I have to offer up, likely improved by better available tools (notably, Frugal VP software):
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Variance is the tournament player's ally. It has the quality of increasing the odds that you'll finish higher than others ... but, mind you, also the odds that you'll finish lower. On the downside, if you're faring poorly in any case you're unlikely to worry about coming in rock bottom rather than 5th from the bottom. But on a strong finish, a modest nudge up can make the difference between being in the money and not ... and if you're finishing near the top, advancing just one place can mean several hundred dollars improvement in win ... or more.
At the same time, you don't want to go for the big wins to the exclusion of all else. When it comes down to it, if you and another player have performed equally well on quad hits (something that luck has more to do with in the course of 10 or 20 minutes than any strategy), the player who betters the other is the one who has successfully scored stronger on the basic hands that comprise 75%+ of the return in most games.
So, in forming a modified tournament strategy, you want to take more shots at hands such as quads, but at the same time not terribly impair your overall expected return.
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In striving for a decent tournament strategy for DDB, I used Frugal Video Poker to weed out those holds that impaired my chances for a big hit while at the same time didn't make a strong EV contribution. You can, of course, wing this without a tool such as Frugal but it's a beautiful software program for this application.
I loaded DDB and went into the feature to "Tweak Strategy Charts". For each strategy hold, the EV and % contribution to game EV are shown. From this, I selectively weeded out hands I indicated and resequenced holds that had similar EV's in order to favor those that yielded large pays.
Deletions:
-- I quickly opted to dump any SF hold other than a pat hand and a 4 card SF. In general, a 250 pay for a SF is very poor relative to the probability of a hit and the chart numbers confirmed this. I did opt to keep any 3-card open and 1 gap SF with no highs over a full redraw. There's enough value difference here. But, if any high cards were involved, I favor keeping just the high cards.
-- I got rid of any 4cd ins S (I kept JQKA). The relatively low S pay doesn't warrant going for this infrequent win, even if the alternative is to toss the hand.
-- The other deletion was unsuited JQK (I prefer to leave open chances for a quad or FH),
Resequences:
-- 3K (2-4) over FH (exc. w/ pair A)
-- 3RF A-hi over 4F
-- pair (2-4) over 4S open
-- Ace over unsuited QJ
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These changes are entirely subjective but I found them to be those that improved the chance of high paying hands without overly impairing ER. Because I understand only the winner often advances in a "qualifier", one might choose to go for more aggressive changes ... but I'd choose to stick with these. The same would go for a tournament in which only a very small handful of players finish in the money.
The ER consequence of these strategy changes is a reduction of 0.3%.
I also considered holding just the high pair of 2 pair (a novice mistake in standard play), however this alone had an ER cost of .4% and was a poor choice.
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The Harrah's vp Millionaire Maker tournament is, as I understand the format, fairly attractive to the skilled player. Some tournaments allow a very large number of hands to be played, if you're fast enough ... sometimes allowing as many as 20 or more hands a minute. The Harrah's tournament allows bets totally 1000 credits, or 200 hands, over the course of 15 minutes -- a max speed of 800 hands/hr. For the player who has a a hundred thousand hands or so under their belt, that may be a very comfortable speed at which to make careful strategy consideration when a strategy with which they're
adept is applied.
But, no doubt, taking a wing at modified strategy after only a couple hours of practice is going to risk more than any likely gained value. Stick w/ standard DDB strategy unless you get the modified strategy down COLD (and then, beware when you play for real money in the casino!)
On the other hand, when the tournament is a (forgive the expression) "balls to the wall" competition, it's time to risk glaring errors in favor of additional hands. Most likely errors will cost less than the EV of each additional hand played (unless you REALLY get sloppy).
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Ok ... concerning your questions on the "Shootout" tournament. Because flushes and straights pay more strongly in DB than DDB, this strategy is likely very ill-suited for a DB based tournament. I'd advise using the method I've outlined to arrive at a strong modified strategy.
I definitely would avoid using a 10/7 Strategy and, since you're suggesting you would instead learn the strategy changes for 9/6, you might as well go whole hog and strive for a strong tournament strategy and get it down pat.
When it comes to "Crunch Time", say 10 minutes into a 15 minute tournament, it's certainly time to glance around quickly and guage where you stand. No doubt, if you're well out of the money (say, in the bottom half), you may choose to begin taking pot shots and Royals and Aces. But if it's the case that a single set of quad Aces would put you in good stead for a qualifying finish, you may want to leave the Aces to luck and focus on strategy. When you hit the wire, often the differences between players in what happens on the intermediate hands can be the critical differentiator.
- Harry
(written with my usual flurry of fingers and limited time so I'll apologize in advance for evidence of poor (no) editing ;)
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To: vpFREE@yahoogroups.com
From: nightoftheiguana2000
Date sent: Fri, 18 Nov 2005 00:21:08 -0000
Subject: [vpFREE] another approach to optimum tournament strategy
Say, in a tournament of N hands, that you need a royal (4000 coins) or equivalent to get into the money. The chances of getting one royal in N hands of play is Pr x (1-Pr)^(N-1) x N. Let's assume double-double bonus and max-er strategy for starters. Well, two aces with
kicker is also 4000 coins, and the chances of getting that in N hands is Pak^2 x (1-Pak)^(N-2) x N!/(2!x(N-2)!). The ratio of those two probabilities gives you the ratio of their values.
For example, for DDB max-er strategy, Pr=.000025, Pak=.00006, chances of getting one royal in 500 hands is 1.2%, chances of getting two aces with kicker is 0.04%, ratio is 1.2/0.04=30; repeat for other paying hands; to get the strategy, take FVP or VPSM and set royal win to 4000, aces with kicker to 4000/30, etc.
If you hit a royal in play, you should switch to a strategy that optimizes the chances of getting any winning hand, if you hit one aces with kicker, you should switch to a strategy that values a royal or aces with kicker equally, etc. Very roughly speaking, a royal only strategy doubles your chances of getting a royal over max-er strategy. That doesn't mean you will win the tournament, but doubling your odds of winning over a max-er or similar player ain't bad.
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