vpFREE2 Forums

why CE is better than EV

#1

EV is an ok beginner's way to rank plays but it doesn't take into account variance and bankroll. CE takes into account EV, plus variance and bankroll:

CE = EV - variance/2xBankroll

Example:

FPDW hand: 22299

holding all five returns 15 bets

holding just 222 returns:

deuces: 46/1081 x 200 = 8.511
wrf: 40/1081 x 25 = 0.925
5k: 67/1081 x 15 = 0.930
sf: 108/1081 x 9 = 0.899
4k: 820/1081 x 5 = 3.793
total EV = 15.058

deuces: 46/1081 x (200-15.058)^2 = 1455.470
wrf: 40/1081 x (25-15.058)^2 = 3.657
5k: 67/1081 x (15-15.058)^2 = 0
sf: 108/1081 x (9-15.058)^2 = 3.667
4k: 820/1081 x (5-15.058)^2 = 76.738
total variance = 1540

solve for when CE>15:

15.058 - 1540/2xBankroll > 15
Bankroll > 13,276 bets > 16.6 royals

So, even though just holding 222 is the maxEV play, it's not a Kelly overlay unless your current bankroll exceeds 13,276 bets or 16.6 royals. Gamblers might typically play FPDW with a 5 royal bankroll, so 16.6 royals represents a much larger bankroll (more than 3x) than typical. For a quarter player, 13,276 bets is $16,595.

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#2

Nice post! I've never seen CE (Certainty Equivalent} laid out so clearly before.

--Dunbar

---In vpFREE@yahoogroups.com, <nightoftheiguana2000@...> wrote :

EV is an ok beginner's way to rank plays but it doesn't take into account variance and bankroll. CE takes into account EV, plus variance and bankroll:

CE = EV - variance/2xBankroll

Example:

FPDW hand: 22299

holding all five returns 15 bets

holding just 222 returns:

deuces: 46/1081 x 200 = 8.511
wrf: 40/1081 x 25 = 0.925
5k: 67/1081 x 15 = 0.930
sf: 108/1081 x 9 = 0.899
4k: 820/1081 x 5 = 3.793
total EV = 15.058

deuces: 46/1081 x (200-15.058)^2 = 1455.470
wrf: 40/1081 x (25-15.058)^2 = 3.657
5k: 67/1081 x (15-15.058)^2 = 0
sf: 108/1081 x (9-15.058)^2 = 3.667
4k: 820/1081 x (5-15.058)^2 = 76.738
total variance = 1540

solve for when CE>15:

15.058 - 1540/2xBankroll > 15
Bankroll > 13,276 bets > 16.6 royals

So, even though just holding 222 is the maxEV play, it's not a Kelly overlay unless your current bankroll exceeds 13,276 bets or 16.6 royals. Gamblers might typically play FPDW with a 5 royal bankroll, so 16.6 royals represents a much larger bankroll (more than 3x) than typical. For a quarter player, 13,276 bets is $16,595.

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#3

And this is probably beating a dead horse but just to complete the circle you can see where that approximation I like to throw around comes from. Not only is a positive EV preferred, but also a positive CE is preferred, because it predicts future bankroll growth instead of bankroll shrinkage. So, take the CE formula, set CE>0, and solve for the bankroll:

CE=EV-Variance/2xBankroll>0

Variance/2xBankroll

2xBankroll>Variance/EV

Variance/2xEV

That's the bleeding edge, it's normal to take at least a 2x safety factor to cover unknown unknowns, and you get:

Variance/EV bets

At that bankroll, CE=50% of EV, at double that bankroll, CE=75% of EV, at 5x that bankroll, CE=90% of EV, for infinite bankroll, CE=EV.

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#4

Hello. I'm not new to VP, but I am new to some of the terms such as EV and EC. If it is not too much bother, could you please explain briefly what these terms mean?
I play mainly DDB.
Thanks so much.
GM

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#5

Some terms like EC are not listed in the glossary. Most of the regular posters on this site have advanced degrees in statistics,so don't expect (DE) much help in the form replies which the common man can understand. I suggest a 4 year BS in math from MIT might level the playing field. Excuse the feeble attempt at humor.

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#6

gilrus47 wrote: "I suggest a 4 year BS in math from MIT might level the playing field."

Probability and Statistics is a high school level course. Entrants to technical colleges are expected to have this already under their belts.

But you don't need to master P&S to gamble, obviously. Just keep your CE (Certainty Equivalence) positive, and you do that by only gambling if your current bankroll exceeds variance/2xEV bets. You can get computer perfect numbers for variance and EV from the interwebs, just beware that you probably won't approach those numbers in the real world of a casino without a lot of practice. And because of the tax situation, if you're going to gamble, you need to gamble a lot, you need to be able to put down at least variance/EV/EV hands in the current tax year, otherwise you're just kidding yourself. Does this sound hard? Well, in many ways, it is. But you do have a choice, you can do something else instead of gambling.

Example: quarter Full Pay Deuces Wild:

computer perfect EV = +0.00762
computer perfect variance = 25.84

bankroll > variance/2xEV = 25.84/2x0.00762 = 1,696 bets

1,696 bets at quarter 5 coin FPDW = 1,696 x $1.25 = $2,120

This is an estimate, for more precision some games have their Kelly numbers available on the interwebs, FPDW is one of them, its Kelly number is 2925, so bankroll > $1.25 x 2925/2 = $1,828.13 .

variance/EV/EV hands = 445,023 hands. You have to be able to play at least this number of hands in the current tax year or you'll be paying a substantial tax penalty.

some Kelly numbers: jazbo.com/videopoker/kelly.html

some variance/EV/EV numbers: west-point.org/users/usma1955/20228/V/Bank_NO1.htm

Patton giving a speach to prospective gamblers: youtube.com/watch?v=9b5g1avyCSA

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#7

Tangential but related I think: PBS NOVA The Great Math Mystery, is math the ultimate reality or just a human invention? Why is it that so many things are predicted by math but also so many other things are poorly predicted by math? In the show, which can be viewed online, they teach a Lemur to play low ball poker, and they are as good as or even better than college students.

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#8

ret.gunslinger5380 wrote:

Hello. I'm not new to VP, but I am new to some of the terms such as
EV and EC. If it is not too much bother, could you please explain briefly
what these terms mean?

vpFREE Acronyms:

http://www.west-point.org/users/usma1955/20228/V/Gloss.htm

From the vpFREE FAQ:

9. What does Expected Value (EV) and Expected Return (ER)
mean? - EV is the weighted sum of all possible outcomes
(after each outcome has been multiplied by its probability
of occurring). Relating this to VP, the EV of a video poker
hand is the average value of all the wins attainable, after
holding the optimum cards and redrawing. EV is expressed in
units of coin-in or dollars.

ER is a percentage return figure that is a function of EV,
and it equals [EV] divided by [Coin-in].

As an example, FPDW has a RF cycle of 45,281.93 hands, and
the EV of playing those hands by a 25c player ($1.25 per
hand) is $57,033.72. Total coin-in equals $56,602.41, so the
ER is 100.7620%.

9a. What does Certainty Equivalent (CE) mean? - CE is a
guaranteed return that someone would accept, rather than
taking a chance on a higher, but uncertain, return.

CE = EV - variance/2xBankroll.

#9

I did some work on Kelly-adjusted strategy a while back, but came to
the conclusion that it was like penalty cards... a theoretical
amusement that is insignificant compared to real-world factors. For
your FPDW example, with a five-royal bankroll, I get a certainty
equivalent of 100.4652% playing max-CE strategy and a certainty
equivalent of 100.4641% playing max-EV strategy. 0.0011% is a penny
an hour playing quarters.

If there are VP examples where a CE-aware strategy makes a big
difference, I'd be interested to hear about them. I haven't found
any.

(As for penalty cards, they're barely worth paying attention to in
JW2, where they're worth about 0.02%. In most games they add
complexity but are worth only 0.001-0.002%. Additional complexity
means more to think about, which means slower play and more errors and
more mental fatigue, which costs a lot more than 0.002%. I still play
a couple of penalty rules for my most-played games like JoB and NSUD,
but if I could wipe them from my brain, I would.)

- five

···

On Mon, Apr 13, 2015 at 2:33 PM, nightoftheiguana2000@yahoo.com [vpFREE] <vpFREE@yahoogroups.com> wrote:

EV is an ok beginner's way to rank plays but it doesn't take into account variance and bankroll. CE takes into account EV, plus variance and bankroll:

CE = EV - variance/2xBankroll

Example:

FPDW hand: 22299

holding all five returns 15 bets

holding just 222 returns:

deuces: 46/1081 x 200 = 8.511
wrf: 40/1081 x 25 = 0.925
5k: 67/1081 x 15 = 0.930
sf: 108/1081 x 9 = 0.899
4k: 820/1081 x 5 = 3.793
total EV = 15.058

deuces: 46/1081 x (200-15.058)^2 = 1455.470
wrf: 40/1081 x (25-15.058)^2 = 3.657
5k: 67/1081 x (15-15.058)^2 = 0
sf: 108/1081 x (9-15.058)^2 = 3.667
4k: 820/1081 x (5-15.058)^2 = 76.738
total variance = 1540

solve for when CE>15:

15.058 - 1540/2xBankroll > 15
Bankroll > 13,276 bets > 16.6 royals

So, even though just holding 222 is the maxEV play, it's not a Kelly overlay unless your current bankroll exceeds 13,276 bets or 16.6 royals. Gamblers might typically play FPDW with a 5 royal bankroll, so 16.6 royals represents a much larger bankroll (more than 3x) than typical. For a quarter player, 13,276 bets is $16,595.

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------------------------------------
Posted by: nightoftheiguana2000@yahoo.com
------------------------------------

vpFREE Links: http://www.west-point.org/users/usma1955/20228/V/Links.htm

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Yahoo Groups Links

#10

NOTI wrote "Just keep your CE (Certainty Equivalence)
positive, and you do that by only gambling if your current
bankroll exceeds variance/2xEV bets."

Nope. This is wrong.

#11

I like fivecard's perspective on the subject of CE (and penalty cards).

It's apparent that sometimes technical discussion along the lines that noti (and perhaps myself) introduce here proves to be more of a distraction than it is informative when it comes to members simply looking for the best means by which to strengthen their play.

Concepts such as CE and penalty cards have their place, and I don't think the value of either should be easily dismissed. Relative to most other aspects of play, their value is fractional. But in isolated situations, that value is significant.

A small number of rules for handling frequently occurring penalty card situations (in games such as DW, JB, or DB) when adopted into play, can capture the lion's share of the return shortfall between penalty-free strategy and optimal strategy. You needn't sweat every single conceivable penalty situation for meaningful gain.

And the concept of CE is very illustrative when considering the full implications of breaking 3-2's from 5K in FPDW, or 3-A's from a FH in FPDB. A gambler can't consider themselves fully informed if they merely follow rote strategy in such cases without a decent grasp of the bankroll considerations involved in breaking a sure thing in looking for a stronger draw that's only fractionally better.

That said, I look at the utility of CE and penalty card considerations as being roughly analogous to that of body shaving in competitive swimming. In either case, unless your game is finely honed to near-perfection, you're probably misspending your time by focusing on them.

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#12

Extra credit for people who believe in CE: Suppose I have a game where I bet
$100. One in 40,000 times the payback is $100,000. The rest of the time I
get my $100 back. How big a bankroll do I need to play this game?
Cogno

#13

If "The rest of the time I get my $100 back" is correct, you can play
forever on $100. Show me where I can play that game!

Tom C

···

On Fri, Apr 17, 2015 at 10:15 AM, Cogno Scienti cognoscienti@hotmail.com [vpFREE] <vpFREE@yahoogroups.com> wrote:

Extra credit for people who believe in CE: Suppose I have a game where I
bet
$100. One in 40,000 times the payback is $100,000. The rest of the time I
get my $100 back. How big a bankroll do I need to play this game?
Cogno

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#14

NOTI wrote "Just keep your CE (Certainty Equivalence)
positive, and you do that by only gambling if your current
bankroll exceeds variance/2xEV bets."
bp wrote: "Nope. This is wrong."

You prefer this form: variance/(2xEV) bets?

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#15

Probability and Statistics is a high school level course. Entrants to technical colleges are expected to have this already under their belts.>>>

Some of us were English majors and got lost. We don't know how we got here.

C

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#16

fivespot wrote: "If there are VP examples where a CE-aware strategy makes a big
difference, I'd be interested to hear about them. I haven't found
any."

It's something to keep an eye out for. For video poker my thought would be to start with minROR strategy. For small edges, there's not much difference between minROR and maxEV strategy. I think your FPDW example would look better with minROR and with smaller bankrolls. Another thing to watch would be a promotion that's juicy enough for you to consider moving up in denomination, even though you'd be gambling with a smaller bankroll in relation to the new betsize. So, in summary, if you have a big bankroll and are playing tight edges, maxCE strategy will be close to maxEV strategy, for smaller bankrolls and larger edges the difference will grow. At half the Kelly bankroll, maxCE strategy and minROR strategy are the same. At infinite bankroll, maxCE strategy and maxEV strategy are the same.

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#17

Count me among that “lost” group. I figure what bankroll we need for play more in terms of “gobs of money.”

I don’t do math good but I read good, and what any math person says you need I just double – or triple - the amount. I have always had a healthy dose of fear of “going broke.”

···

------------------------------------------
Jean $¢ott, Frugal Gambler
http://queenofcomps.com/
http://jscott.lvablog.com/
UPDATED TAX BOOK
(Download 2015 eBook now)

From: mailto:vpF…@…com
Sent: Friday, April 17, 2015 1:06 PM
To: vpFREE@yahoogroups.com
Subject: [vpFREE] Re: why CE is better than EV

Probability and Statistics is a high school level course. Entrants to technical colleges are expected to have this already under their belts.>>>

Some of us were English majors and got lost. We don't know how we got here.

C

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[Non-text portions of this message have been removed]

#18

And yet the CE formula says you need over $1200 to play this game.

Cogno

···

-----Original Message-----
From: vpFREE@yahoogroups.com [mailto:vpF…@…com]
Sent: Friday, April 17, 2015 11:43 AM
To: vpFREE@yahoogroups.com
Subject: Re: [vpFREE] why CE is better than EV

If "The rest of the time I get my $100 back" is correct, you can play forever on $100. Show me where I can play that game!

Tom C

On Fri, Apr 17, 2015 at 10:15 AM, Cogno Scienti cognoscienti@hotmail.com [vpFREE] <vpFREE@yahoogroups.com> wrote:

Extra credit for people who believe in CE: Suppose I have a game where
I bet $100. One in 40,000 times the payback is $100,000. The rest of
the time I get my $100 back. How big a bankroll do I need to play this
game?
Cogno

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------------------------------------
Posted by: Thomas Calaci <quickquads@gmail.com>
------------------------------------

vpFREE Links: http://www.west-point.org/users/usma1955/20228/V/Links.htm

------------------------------------

Yahoo Groups Links

#19

Cogno wrote: "And yet the CE formula says you need over $1200 to play this game."

I think the solution to this quandary is that CE only applies to money at risk. In your example you have $0 at risk. Another thing to watch for is that the formula presented (EV-Variance/Bankroll/2) is valid for a normal distribution, which is a reasonable approximation for most if not all video poker, but it is an approximation. CE can be solved for without assuming a normal distribution, but it involves more math.

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#20

fivespot wrote: "If there are VP examples where a CE-aware strategy makes a big
difference, I'd be interested to hear about them. I haven't found
any."

The biggest non-progressive base game that I can remember is Bally's full pay All American (800-200-50-8-8-8-3-1-1). I would expect a big difference between its maxEV and minROR strategies but haven't looked at it in a while, and it's been while since I've found the game in a casino. It's not an easy game to play so my first pass would be the easiest strategy between maxEV and minROR, so that's another way to use these alternate strategies: to simplify complex strategies. Basically any strategy between maxEV and minROR is reasonable, nothing is any kind of a real world play mistake. If your bankroll can take it you'll win more in the long term with maxEV but minROR is the easiest on your bankroll. MaxCE is somewhere in the middle and comes into play when your bankroll is not big enough for full maxEV.

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