vpFREE2 Forums

Progressive strategy change and variance

#1

I’ve been trying to analyze some situations with FVP and VPW but can’t really get the results I want. I have been playing 9/6 JoB and 8/5 BP both with the optimal JoB strategy. I know that increasing the royal value by 200 coins roughly corresponds to a 0.1% increase in return.

I want to know what are the simplest strategy changes to make when the progressive gets higher to increase my result and also the effect of those changes on variance. For example, with FVP I was able to look at 9/6 JoB with a 8000 coin royal. With optimal strategy this gives a return of 101.86% but obviously has some big strategy differences because the variance is 81.75. If I choose to play normal 9/6 strategy on it then the return drops to 101.56% but the variance is obviously a lot better.

What I would like to know, though, is what the simplest changes to affect my return are, and how to analyze the variance if I make those changes. For example, one of the easiest to identify while playing might be to take 3 to a royal over a high pair. I can figure out how to tweak the strategy chart on FVP to make this change, but beyond this I cannot figure out how to analyze the overall return of that chart once tweaked, and what the variance is.

Any tips? Is this something that is trivially done with WinPoker?

#2

Just an update, I did figure out how to do all the stats/variance analysis with FVP. I was surprised to find that the standard 9/6 optimal strategy on a 9/6 machine with a 5500 coin royal went up from 19.5 to 34.1. I guess this just goes to show you that high variance is not necessarily a bad thing.

Now onto a simpler question. What are the common strategy differences you make when playing these progressives that have a high value? The two things that stand out to me are taking 3 to a royal over a high pair as well as including ATs towards the bottom of the list.

#3

I have mentioned this a couple of times over the years. (Bob Dancer did a couple of articles on this in Casino Player many years ago.) I have used this method for over 20 years back in the “Stanford Wong” VP days.

Almost all normal VP software will show you the ER for all possible plays. To find out when the RF play is better take the difference between ERs for the perfect 4000 coin play and the RF play and multiply that by the number of possible draws to the RF play (47 for a 4RF, 1081 for a 3RF, 16215 for a 2RF and 177,365 for a stiff high card.) Add the result to 4,000 (the
non-progressive RF amount.)

Ex: Playing 9-6 Jacks

  Dealt Kc, Qc, Jc, Jd, 2s. KQJ suited has an ER of 7.4422. JJ has an ER of 7.6827.

  Difference = 0.2405, Combos = 1081

  0.2405 * 1081 = 260.

  4000 + 260 = 4260 so you play for the royal at 4260 or higher.

Discussion of Max EV versus min risk or other strategies is beyond the scope of this.

Howard W. Stern

···

On Saturday, July 12, 2014 6:46 PM, “pede1…@…com [vpFREE]” <vpF…@…com> wrote:

Just an update, I did figure out how to do all the stats/variance analysis with FVP. I was surprised to find that the standard 9/6 optimal strategy on a 9/6 machine with a 5500 coin royal went up from 19.5 to 34.1. I guess this just goes to show you that high variance is not necessarily a bad thing.

Now onto a simpler question. What are the common strategy differences you make when playing these progressives that have a high value? The two things that stand out to me are taking 3 to a royal over a high pair as well as including ATs towards the bottom of the list.

#4

I’d go with min-cost royal strategy (below). The average cost of a royal is 976 bets. You could go 5 cycles without a royal (about 2/3% chance) so having a minimum bankroll at all times of at least 5x976= 4880 bets would be conservative. Find a safer gamble if your bankroll ever drops below 4880 bets. Note that the meter movement or progressive amount cannot save you from a 5 cycle royal drought, however it can help your bankroll once (if) you start hitting royals.

9/6 jacks min-cost royal strategy (avg. royal cost = 976 bets):

5SF>4RF>2P+>4SF>3RF>JJ,QQ,KK>KHTs>AA>AHTs>4FL>KQJT>1P>4ST>3SF0>QJs>AKQJ>2RF2H>4STi3H>3SF1>KQJ>JTs>2H>QTs>KTs>AQ>ATs>1H>3SF2

3SF0=no gaps, or 1 gap and 1 high, or 2 gaps and 2 high
3SF1=1 gap, or 2 gaps and 1 high
3SF2=2 gaps

#5

Any rakeback can significantly change the strategy, for example, at 2.1% total rakeback it’s a freeroll (on average) for the royal and the strategy becomes the min-royal strategy:

2P+>4SF>HP>4FL>KQJT>LP>4ST>3FL3H>3SF0>AKQJ>3FL2H>QJs>KHs>4STi3H>3SFdi1H>AHs>3SFi>KQJ>2-1H>3SFdi

For any rakeback inbetween, the strategy will be inbetween.

#6

This thread has been really eye opening and min-cost-royal stuff is new to me, so let me ask a few questions about it and about Dan’s software (or other software packages that will calculate it).

I’ve read up here: vpFREE FAQ Strategies

vpFREE FAQ Strategies
1
1038.6796 Royal Flush 2 48.8386 Straight Flush 3 24.7133 4/Kind 4 23.7749 4/royal 5 8.9654 Full House 6 5.9856 Flush 7 4.2856 trips 8 3.9942 Straight

View on www.west-point.org

Preview by Yahoo

So
one thing written there is that the min-cost-royal strategy is very close to min-risk, which lowers the risk of ruin. This is counter-intuitive to me, though. With the MCR strategy you are doing things like throwing away high pairs to take 3 to a royal – this by itself seems to me that it would add more variance. Additionally more of the % return is left to the royal that occurs more frequently. Those
in conjunction with the slightly lower EV seems to me like it would be more risky and it would lead to you busting faster. What’s the problem in my logic or my understanding of what the MCR strategy is?

Let me also see if I’m right about when MCR strategy should be used. Assuming a sufficient bankroll, we’d usually desire to just play standard max-EV strategy, but MCR (or best-shot-royal) would be a better
choice in the situation where we are playing a progressive for a finite
amount of time.

Now let me address the last couple of posts by you nightoftheiguana2000. Your first post with the 9/6 MCR strategy is slightly different from the FAQ, though you both have the 976 number. Is yours more accurate or just a simpler version to remember (e.g. you put ATs above all 1H, but the FAQ strategy has ATs only above A)? In your second post you talk about rakeback. I’m familiar with this term from poker playing days, but I assume in the VP context you mean slot club benefits. I don’t really understand what the 2.1% has to do with changing the strategy. Can you explain this in more detail?

Lastly,
regarding software, Dan said his would calculate MCR strategies for any
paytable. Can it, or any other software do the following:

Calculate MCR and best-shot-royal strategies
Calculate these strategies given the “rakeback” that iguana was talking about above.
Work for other games like BP/JW/DW44/etc. (nothing crazy like Ultimate X)
Provide variance and bankroll analysis for these strategies

Thanks in advance!

#7

pede1976 writes: “Let
me also see if I’m right about when MCR strategy should be used.
Assuming a sufficient bankroll, we’d usually desire to just play
standard max-EV strategy, but MCR (or best-shot-royal) would be a better
choice in the situation where we are playing a progressive for a finite
amount of time.”

MaxEV strategy should only be used if you have a monster bankroll for the gamble (many Kelly bankrolls) and a lot of time for the gamble (can play many N0 cycles). Min-cost-royal strategy should be used whenever you’re concerned about the cost of hitting the next royal. This of course applies to progressive royals which reset when hit, but also to video poker in general because royal droughts are the biggest problem with video poker, it’s the royal droughts that bankrupt people. Minimizing the cost of the royal drought just makes plain common sense.

pede1976 writes: "Your first post with the 9/6 MCR strategy is
slightly different from the FAQ, though you both have the 976 number.
Is yours more accurate or just a simpler version to remember (e.g. you
put ATs above all 1H, but the FAQ strategy has ATs only above A)? "

I used the wizard’s strategy generator with the royal set at 976:

http://wizardofodds.com/games/video-poker/strategy/calculator/

pede1976 writes: “I don’t really understand what the 2.1% has to do with
changing the strategy. Can you explain this in more detail?”

Rakeback reduces the cost of hitting the royal, i.e. it is no longer 976, in the case of 2.1% rakeback the cost is 0, if you use the right strategy. You get min-cost-royal strategy by putting the cost of the royal in the strategy generator instead of what it actually pays. Rakeback is any return you get for playing, could be cashback, freeplay, drawings, mailers, show tickets you monetize, rooms you airbnb, whatever.

#8

noti wrote:

MaxEV strategy should only be used if you have a monster bankroll for the gamble (many Kelly bankrolls) and a lot of time for the gamble (can play many N0 cycles). Min-cost-royal strategy should be used whenever you’re concerned about the cost of hitting the next royal

···

I agree in principal with value of mcr strategy when it comes to any higher risk play. However, for mosr of my cut and dry play, (ror =< 1%; or equiv b/r > 2 kelly), I find mcr yields inadequate risk reduction to be worth bother with.

#9

I simultaneously feel like I’m understanding and not understanding, and I keep coming up with more questions.

Bankroll-wise, I’m probably a bit conservative. I just estimated based on the ROR page on the Wizard’s site and went from there. I know the benefits and pitfalls of using Kelly (especially from my time as a poker player) but long story short my VP bankroll is around 15k and my usual game is 25c BP/JoB/NSUD. Sometimes on a multi-play I’ll play more (like 10-play 5c for a total bet of $2.50) or with a really good promotion I’ll go up to 50c NSUD. Right now my % advantage due to non-play winnings (freeplay, cashback, drawings) is 1.6%. I got lucky in some drawings but also I just started playing a few months ago so decent mailers are just now starting to show up. Feel free to tell me if I’m being too nitty with my bankroll. That said, I find myself in a situation where I sometimes play progressives so I feel that MCR is relevant.

A quick question about Kelly bankrolls. From the Wizard’s page he says it’s advantage/variance, so say you are playing 9/6 JoB and have a 1.5% advantage on top of that due to points. Then with max-EV it is 0.0104/19.5364 which is bet .05323% of your bankroll. Going back to my earlier example, let’s take 9/6 JoB with an 8000 royal, then use the max-EV 9/6 JoB strategy. This gives a game with (according to FVP) a return of 101.56% and a variance of 68.07. Including the 1.5% advantage due to points we have .0306/68.07 which is bet .04495% of your bankroll. This is counter-intuitive to me. We use the same strategy on the same game except that when the royal is doubled Kelly says we should bet less of our bankroll. Why?

Back to the main topic. I understand where the 976 number comes from and how you can generate strategies based on it. I’m still not clear on why rakeback should change the strategy. For example, when I drop the royal to 0 I get the min-royal strategy you came up with and it has 97.9% return. If you re-add in the value when you do (rarely) hit the royal (which we will say is a standard 800) then you wind up around 99%. While still a positive game with the 2.1% you add back on, you could do a lot better. Is the only benefit here a lower variance/risk of ruin/being able to play higher?

Another question, on the FAQ page it says the MCR strategy is static. Am I correct when I interpret this to mean that this MCR strategy is the MCR strategy for arbitrary values of the royal? As an example, if the royal was only 1 or if it was 10000, the MCR strategy is the same. Obviously at some point the royal would get so large that, assuming an infinite bankroll, you would just go with a max-royal strategy.

#10

pede1976 wrote: “Including the 1.5% advantage due to points we have .0306/68.07 which is bet .04495% of your bankroll. This is counter-intuitive to me. We use the same strategy on the same game except that when the royal is doubled
Kelly says we should bet less of our bankroll. Why?”

The variance increased. Variance is a big problem with progressives. The Kelly system measures the world by EV/Variance (approximately), so EV gain at the expense of an even greater Variance gain is not a net gain. Under the Kelly system, you get better bankroll growth with a reduced betsize, because the variance increased.

pede1976 wrote: “If you re-add in the value when you do (rarely) hit the royal (which we will say is a standard 800) then you wind up around 99%. While still a positive game with the 2.1% you add back on, you could do a lot better.”

Actually, from the measure of “cost of hitting a royal”, you can’t do better. You could get a higher theoretical EV, by using maxEV strategy, but it would take more time and money to grind out a reasonable portion of that theoretical EV.

pede1976 wrote: “Am I correct when I interpret this to mean that this MCR strategy is the MCR strategy for arbitrary values of the royal?”

That’s correct, it’s the strategy that produces the minimum cost to hit the royal. What you actually get for the royal (the payoff) has no effect on the strategy.

#11

vp_wiz wrote: “I agree in principal with value of mcr strategy when it comes to any higher risk play. However, for mosr of my cut and dry play, (ror =< 1%; or equiv b/r > 2 kelly), I find mcr yields inadequate risk reduction to be worth bother with.”

I’m not sure that double Kelly (or half Kelly, depending on if you’re looking at bankroll or betsize) is sufficient to just assume maxEV strategy. Maybe it is, maybe you need more like 5x Kelly. But there is also the time factor. MCR strategy is centered on that next royal, which is probably attainable this year. The Kelly approach is longer term, you need at least an N0 cycle, which is likely (hopefully) many royals, and you probably need to do that this year since you can’t (legally) carry forward gambling losses.

But I can’t find any fault with your basic argument, namely if you have a big enough bankroll and can play enough hands per tax year, then maxEV is optimal. Essentially, it’s a longer term view, you don’t really care what the cost of your next royal is, what you care about is your yearly result. This assumes you have lots of opportunities to hit these royals, which would be a questionable assumption on a progressive, and might be a questionable assumption on a promotion that may only last a month or so. Additionally, there might be hidden value in extending the time to hit a royal, such as gaining more meter movement on a progressive or perhaps getting one more mailer before cutoff.

Another angle would be the emotional angle. If you went into a 5 royal drought, would that cause you great emotional anguish? Now, MCR can’t protect you from 5 royal droughts, but would you sleep better at night knowing that if you play with MCR you would be minimizing the cost of that 5 royal drought? If so, you might be a candidate for MCR.

#12

Thanks for all your comments on this! It has really given me a lot to think about as well as developing new strategies for play.

One other semi-related question on the subject of progressives. Does meter speed factor into EV, or is it simply “what value is the progressive at right now as I start to play”? Say there is some game that costs $5 per hand, has exactly a 99% return at the start of the progressive, and the meter rises by 1% (so +$0.05 per hand). What could we say about the EV of this machine over the long term due to the meter speed?

#13

aonsf@reallymymail.com wrote:

Thanks for all your comments on this! It has really given me a lot to think about as well as developing new strategies for play.

One other semi-related question on the subject of progressives. Does meter speed factor into EV, or is it simply "what value is the progressive at right now as I start to play"? Say there is some game that costs $5 per hand, has exactly a 99% return at the start of the progressive, and the meter rises by 1% (so +$0.05 per hand). What could we say about the EV of this machine over the long term due to the meter speed?

On average, the progressive will hit in 1 cycle, so, in your example,
payback would average 100%. But that's normally irrelevant. Your
main concern, normally, should be what value your next hand will have,
independently of meter movement.

#14

Sorry for the delay in reply, noti … been pressing an “advantage” pretty hard these last few days :wink:

I’m relieved by your last comments … they position a viable middle ground on which I think we can both comfortably stand.

I’ll stress that it’s not my intent to dismiss MCR (or any other alternate goal strategies). They definitely have their place – were I to tackle an attractive royal with a base game ER of <= 96%, I’d consider MCR to be a valuable tool.

And, as you suggest, I can definitely see the value of MCR strategy for a player who plays significantly less frequently then I do. I grasp the implicit value when it comes to mitigating risk of a losing year, from a tax perspective.

I’m a little more dubious on the last count you cite – the “emotional angle” associated with a 5-royal drought. Assuming we’re talking play of a moderate drought cost game (such as, say, 8/5 BP) as opposed to the prior progressive discussion, while MCR will soften the expected damage of such a drought, it’s my impression that we’re talking about a loss reduction of no more than 5% (and likely considerably less).

I haven’t run the numbers since this was first discussed by you (something like 3 years back), but I came away from the math with the idea that the loss reduction wasn’t material enough in my book to reduce any resultant limp as I walked from the play.

—In vpF…@…com, <nightoftheiguana2000@…> wrote :

vp_wiz wrote: “I agree in principal with value of mcr strategy when it comes to any
higher risk play. However, for mosr of my cut and dry play, (ror =<
1%; or equiv b/r > 2 kelly), I find mcr yields inadequate risk
reduction to be worth bother with.”

I’m not sure that double Kelly (or half Kelly, depending on if you’re looking at bankroll or betsize) is sufficient to just assume maxEV strategy. Maybe it is, maybe you need more like 5x Kelly. But there is also the time factor. MCR strategy is centered on that next royal, which is probably attainable this year. The Kelly approach is longer term, you need at least an N0 cycle, which is likely (hopefully) many royals, and you probably need to do that this year since you can’t (legally) carry forward gambling losses.

But I can’t find any fault with your basic argument, namely if you have a big enough bankroll and can play enough hands per tax year, then maxEV is optimal. Essentially, it’s a longer term view, you don’t really care what the cost of your next royal is, what you care about is your yearly result. This assumes you have lots of opportunities to hit these royals, which would be a questionable assumption on a progressive, and might be a questionable assumption on a promotion that may only last a month or so. Additionally, there might be hidden value in extending the time to hit a royal, such as gaining more meter movement on a progressive or perhaps getting one more mailer before cutoff.

Another angle would be the emotional angle. If you went into a 5 royal drought, would that cause you great emotional anguish? Now, MCR can’t protect you from 5 royal droughts, but would you sleep better at night knowing that if you play with MCR you would be minimizing the cost of that 5 royal drought? If so, you might be a candidate for MCR.

#15

vp_wiz wrote: “I’m a little more dubious on the last count you cite – the “emotional angle” associated with a 5-royal drought.”

It depends on the game you look at. Let’s stick with the example cited, 9/6 Jacks +2.1%. If you stick with MCR, the average cost of a 5 royal drought, in fact any length drought, is zero. If you play MaxEV you’re losing .34% on average while not hitting royals. A 5 royal drought on dollars would cost you 5 x 40,391 x $5 x .34% = $3,433 on average.

Depending on the size of your bankroll, that number of $3,433 might or might not be significant. But in any case it is certainly significantly different on a ratio comparison with zero.

#16

Apologies, but just to jump in (maybe where I am not wanted), but a drought is a drought is a drought. Maybe you can look at it like a baseball player in a hitting slump. A manager usually sticks with a “good” player and the player usually is an asset to the team. If you play “good” games and make few mistakes, you break out of the drought. How many times have you gotten 3-4 RF’s in the course of a week or two?

… bl

#17

To write “a drought is a drought” betrays a lack of perspective.

A player who aggressively takes advantage of play opportunities, within a reasonable margin of risk, still confronts the possibility of encountering a play drought that is at the extreme of expectation. Should such a drought occur, there’s the distinct possibility that the associated bankroll drain will make continued play at present denominations unwise. In that event, “breaking out of the drought” and restoring your play position (at reduced stakes) becomes a daunting challenge.

That’s the focus of altered goal strategy – to reduce risk without significant EV sacrifice.

  • H.

—In vpF…@…com, <bornloser1537@…> wrote :

Apologies, but just to jump in (maybe where I am not wanted), but a drought is a drought is a drought. Maybe you can look at it like a baseball player in a hitting slump. A manager usually sticks with a “good” player and the player usually is an asset to the team. If you play “good” games and make few mistakes, you break out of the drought. How many times have you gotten 3-4 RF’s in the course of a week or two?

… bl

#18

I will not argue except to say that my field of view (persoanaly) is more far reaching. Maybe that point of view is irresponsible and/or lacking perspective. But, I do not play for the day. Yes, I wholeheartedly agree that there are specific opportunities of which one may take advantage but they do not encompass all my play.

I’ve learned a lot from this group and others similar to it. I value the information presented. Thanks to all for giving me the opportunity, from time to time, to express a personal opinion.

#19

Never! Ditto for months and years !!

···

On Wed, Jul 23, 2014 at 5:00 PM, bornloser1…@…com [vpFREE] <vpF…@…com> wrote:

Apologies, but just to jump in (maybe where I am not wanted), but a drought is a drought is a drought. Maybe you can look at it like a baseball player in a hitting slump. A manager usually sticks with a “good” player and the player usually is an asset to the team. If you play “good” games and make few mistakes, you break out of the drought. How many times have you gotten 3-4 RF’s in the course of a week or two?

… bl

–
"The commitments we make to each other - through Medicare and Medicaid and Social Security - these things do not sap our initiative; they strengthen us. They do not make us a nation of takers; they free us to take the risks that make this country great." President Barack Obama 1/20/13

#20

bl – We’ve both been around the bend here sufficiently (and on SHG, if I recall correctly) that there’s no need to thank anyone for the opportunity to vent your ideas. And I very much respect and value your contributions (to the extent that I didn’t feel the need to pull a punch re the “perspective” expressed via your comment).

FWIW, the idea behind alternate goal strategies has everything to do with playing for the long-term (and the increasing risk of encountering a blistering stretch over time) … not “playing for the day” (as you seem to suggest).

Mind you, while I acknowledge the value of alternate strategies, if you’ve followed noti’s and my dialog, I see a more limited application than he suggests. Still, I’ll simply suggest that if you want to consider yourself at the “top of your game”, it’s a critical concept to grasp, weigh, and be able to intelligently apply.

—In vpF…@…com, <bornloser1537@…> wrote :

I will not argue except to say that my field of view (persoanaly) is more far reaching. Maybe that point of view is irresponsible and/or lacking perspective. But, I do not play for the day. Yes, I wholeheartedly agree that there are specific opportunities of which one may take advantage but they do not encompass all my play.

I’ve learned a lot from this group and others similar to it. I value the information presented. Thanks to all for giving me the opportunity, from time to time, to express a personal opinion.