Positive effects on downswing variance of waiting to double at a high bets

[Three]

I have been not helpful trying to get a point across so I will use data from a matchup to illustrate the point. I chose this matchup because it illustrates the point I am trying to make as the index is the highest frequency TC and the first downswing averse index is also a RA index and the second downswing averse index appears to have a steep price tag. But a closer look shows it really is a cheap way to stack your largest contributors to variance in favor of upswing variance while reducing downswing variance. The EV maximizing index is TC 0 but the best playing count from the info gathered is a combined count so so bets are not at all correlated to the count and I could have anywhere from a minimum bet out to a maximum bet when the playing TC is at the index of 0:


At the index the EV for hitting is .1536 and the EV for doubling is .1537. So the EV gain at the index is $0.01 per $100 bet if you double (note, since this bin is just for RC 0 the previous data is for RC 0 only. the following info is global info for the total matchup).
The percentage of the time you would double the matchup using that index is 60.36%.
If you use the index of TC 0 the total EV for the matchup is .1843,
For the 60.36% of the time you double the total EV is .2229,
The remaining 39.64% of the time you hit the total EV is .1254.

The first "downswing averse" index is to double for positive RC only:
At the index the EV for hitting is .1600 and the EV for doubling is .1680. So the EV gain at the index is $0.80 per $100 bet if you double.
The percentage of the time you would double the matchup using that index is 56.91%.
If you use the index of Positive RC the total EV for the matchup is unchanged at .1843,
For the 56.91% of the time you double the total EV is .2271,
The remaining 43.09% of the time you hit the total EV is .1277.

The second "downswing averse" doubling index is TC +1:
At the index the EV for hitting is .1701 and the EV for doubling is .1903. So the EV gain at the index is $2.02 per $100 bet if you double.
The percentage of the time you would double the matchup using that index is 40.84%.
If you use the index of TC +1 the total EV for the matchup is .1830,
For the 40.84% of the time you double the total EV is .2504,
The remaining 59.16% you hit the total EV is .1365.

So for the first downswing averse index there is no change in overall EV for all the times you get the matchup by getting an extra penny at RC 0. But the increased EV and frequency of hitting and the increased EV and decreased frequency of doubling clearly makes a positive RC a better index for any bet size than the EV maximizing index of TC 0 and in fact indicates that RC 0 barely has any EV gain and is played 3.45% of the time you get the matchup.

The second downswing averse index of TC +1 is even more interesting. It gains you $2.02 per $100 bet when the TC is +1. That sounds like a lot to give up but if you flat bet all the TCs it costs the total matchup $0.13 per $100 bet in EV while doubling almost exactly 1/3rd less often. The EV all your doubles went up by over 10% due to a higher success rate of doubles. The frequency of hitting goes up 37.3% and the EV for hitting increases by 6.9%. In other words you have less frequent double loses and more frequent double wins which stacks variance to be more positive if done only for your biggest bets. Your small bets the swings for doubling aren't significant enough to worry about using a downswing averse index. Plus the matchup happens 3.52% of the time so the cost to overall EV is less than a half a cent per $100 bet.

So we have established the cost to overall EV and the EV for the total index play for this downswing averse play is minimal despite costing $2.02 per $100 bet at the DSA index to change the index from TC 0 to TC +1. Let's look at the impact on BR growth. Your exposure to the large swings associated with doubling at your largest bets is 47.8% higher if you use the EV maximizing index of TC 0. So exposure swings associated with the play are increased by almost half. In that 50% increase in large swing exposure from big bets the gain in EV is small for the overall matchup at $0.13 per $100 bet and you lose a much higher percentage of those doubles as indicated by the increase in double EV of 10%. This is because you have moved 5% of the total doubles that were losers into the winners for a net increase of 10% in double EV but with a lower double frequency. This is great for certainty of BR growth. A higher percentage of big upswings and lower percentage of big downswings associated with the biggest bets for the matchup. Variance will get a little less but the causes of variance are skewed toward more positive variance and less negative variance.

Then we look at the impact of hitting for the matchup. Hitting frequency goes up by 49.2% and the EV for the total matchup for hitting increases by 8.9%. You have a much higher success rate hitting than doubling generally speaking nut you wouldn't take another card for this matchup so the success rate at the index is unchanged, but the EV for hitting when hitting the matchup increases by 8.9%.

I might still double this one even at big bets but the argument to for increased certainty of BR growth should be obvious for big bets. Using an example where the EV maximizing index is TC 0 has the largest impact on frequency of altering the index so the certainty gain and EV cost are both amplified for your overall approach. But I hope you all get the idea of using downswing averse indices to help shape variance to be your friend that is more heavily upswing variance for the biggest contributors to variance, your big bet doubles and splits.

For big bets the same principle applies for the even biggest variance reducer, surrender. EV maximizing decisions are not the best decisions for increasing certainty of BR growth. Some highly volatile surrenders like split surrenders really scream for aggressive downswing averse moves to the EV maximizing surrender index, but many other surrender plays have little EV gain for the first TC or so that you would not surrender using EV maximizing decisions.

If you have a lot of EV I feel it is worth spending some to help make variance your friend rather than your enemy by stacking the largest contributors to variance and the strongest reducers of variance for your biggest bets to be more user friendly. I often here practitioners of the simple approach say things like a 5% gain in EV is not worth the extra effort even though the gain in EV is more like 10% to 20%. I ask: Is that extra percent or two of EV worth the added downswing variance it produces to get it when you can give it up and really stack the largest swings more toward upswing variance and less toward downswing variance?

[Norm]

Not again

[21forme]

Does the sun rise in the morning?

[ZeeBabar]

T3, don't understand but are you suggesting a higher level count, or are you saying something else? What is the bottom line, that you suggest a different way of spreading?

[Three]

T3, don't understand but are you suggesting a higher level count, or are you saying something else? What is the bottom line, that you suggest a different way of spreading?

Simply pointing out that if you already have a high EV It costs very little to spend a little EV to affect the likelihood of BR growth in a positive way. Personally I gather more information and use it in a different way so I am simply giving back some EV gain to reduce your frequency of your largest downswings. This only applies to your biggest bets. You don't have to worry about downswings from small to medium sized bets. It is a simple concept. The higher EV at the next TC for doubling is higher because you win a higher percentage of your doubles.

When you don't double you win a higher frequency if you might take another card. You are simply increasing the big bet win to loss ratio for both hits (if you might take another card) and doubles. These are your biggest contributors to large downswings. Cost depends on the random EV when the index is exceeded. Correlation to playing count tags affect the gain after the index is exceeded. By carefully looking at the gain at each index where you would risk more money you can very cheaply cherry pick the least costly ones. Non-negative indices have the biggest impact on doubling frequency with an index of 0 being the biggest doubling frequency reduction. Of course doubling much less frequently will reduce downswings. If you can do it at a minimal cost where it has its biggest impact on doubling frequency you get the best results. It isn't a change you should make without doing the research. Variance doesn't change much but as you can see from the increase in double EV for the matchup of over 10% in this case by not doubling where EV gain is smallest and doubles are most frequent, at the index, the contribution to downswing variance has a strong impact for the play this is a good idea for.

Basically by shaping the contributors to variance to favor upswing variance over downswing variance the same stats that are calculated using total variance have better results when it comes to BR growth. So the same CE would actually have a higher likelihood of BR growth if the biggest variance contributors are made to be more from positive variance than negative variance. You can't argue with the "logical math" of it. Variance is sign blind. If you do what makes sense to reduce the biggest contributors to downswing variance at little cost in EV results will be affected favorably even if the stats are not due to variance not differentiating from the causes of variance.

[Dbs6582]

Simply pointing out that if you already have a high EV It costs very little to spend a little EV to affect the likelihood of BR growth in a positive way. Personally I gather more information and use it in a different way so I am simply giving back some EV gain to reduce your frequency of your largest downswings. This only applies to your biggest bets. You don't have to worry about downswings from small to medium sized bets. It is a simple concept. The higher EV at the next TC for doubling is higher because you win a higher percentage of your doubles.

When you don't double you win a higher frequency if you might take another card. You are simply increasing the big bet win to loss ratio for both hits (if you might take another card) and doubles. These are your biggest contributors to large downswings. Cost depends on the random EV when the index is exceeded. Correlation to playing count tags affect the gain after the index is exceeded. By carefully looking at the gain at each index where you would risk more money you can very cheaply cherry pick the least costly ones. Non-negative indices have the biggest impact on doubling frequency with an index of 0 being the biggest doubling frequency reduction. Of course doubling much less frequently will reduce downswings. If you can do it at a minimal cost where it has its biggest impact on doubling frequency you get the best results. It isn't a change you should make without doing the research. Variance doesn't change much but as you can see from the increase in double EV for the matchup of over 10% in this case by not doubling where EV gain is smallest and doubles are most frequent, at the index, the contribution to downswing variance has a strong impact for the play this is a good idea for.

Basically by shaping the contributors to variance to favor upswing variance over downswing variance the same stats that are calculated using total variance have better results when it comes to BR growth. So the same CE would actually have a higher likelihood of BR growth if the biggest variance contributors are made to be more from positive variance than negative variance. You can't argue with the "logical math" of it. Variance is sign blind. If you do what makes sense to reduce the biggest contributors to downswing variance at little cost in EV results will be affected favorably even if the stats are not due to variance not differentiating from the causes of variance.

Three, in reading through all your posts on reducing variance and downswings, it sounds awful similar to risk adverse indexes, basically waiting for a higher index than max EV calls for before doubling with your max bet out there.

This is a discussion we’ve had in the past and you’ve helped my game. Thanks! Now I wait till a slightly higher index number before I double 10 vs 10, 9 vs 7, 8 vs 5 and 6, etc. I like this approach better than what I was doing.

Is what you’re saying here more complicated than that?

[Three]

Three, in reading through all your posts on reducing variance and downswings, it sounds awful similar to risk adverse indexes, basically waiting for a higher index than max EV calls for before doubling with your max bet out there.

Yes. It is more aggressive RA indices for your largest bets.

Is what you’re saying here more complicated than that?

Not the basics of it. RA indices have a formula for the cut off point. This is just more liberal at giving up some EV than RA indices. I have found that last little bit of extra required to maximize any stat is very expensive. If you maximize SCORE that last little bit to get to maximization costs a lot of EV. If you maximize EV you really hurt both SCORE and CE getting that last little bit of EV to maximize EV. That last little bit of EV to maximize EV comes at a high cost in variance. I found it best to maximize the stat cluster as a whole than any individual stat. But I realized everything but SCORE is based on variance, a stat that is blind to weather the big percentage contributors to variance are positive or negative swings. The same value for SCORE or CE could be wildly different if the composition of the contributors variance are more biased toward positive swings than downswings. So rather than improving your stats, as almost all put their stock in, you improve the quality of your results by making the likelihood of BR growth increase by changing the composition of the biggest contributors to variance. Variance will reduce a little if you don't use the change to gain EV by increasing bets but more importantly the TC bin you don't double or split in has the highest contribution to downswings and the least EV gain.

The example I used had the most frequent TC bin, TC 0, changed from double to hit. The cost to EV was pretty high. But despite the high frequency and high cost the overall cost for your total overall EV was about 4/10ths of a cent per $100 bet. This one is probably the most expensive double or split move 1 TC, which is one of the reasons why I chose it. Most doubles and splits have a much smaller frequency at the index and a much smaller EV gain at the index. Meaning the cost to total overall EV is less than 1/10th of a cent per $100 bet. It is the maximizing of a single statistic that costs a lot. And the lack of realization that not all variance is created equal that leaves big opportunities to improve the way wins and losses stack up to cut downswings and increase the frequency of winning sessions while decreasing the frequency and severity of losing sessions.

How this affects stats. You can bet more on every advantage round with the same RoR so you generate extra EV on every round. Or you can take some of that EV gain as reduced RoR if you play at a high RoR. Variance goes down a little but the composition of the biggest contributors to variance, where you wait to for more EV to add more money to the table, has a reduction in downswing variance where the EV generated from adding more money to the table is least and downswing variance is highest. This way you give up the worst of the last little bit to maximizing EV that is so costly to other stats to allow likelihood of BR growth to go up. You should see yourself more likely to be on the good side of expectation and less likely to be on the bad side of expectation and particularly severely on the bad side of expectation as play accumulates. I have learned what is statistically called "optimal play" is not really optimal play if your goal is to make money with a higher degree of certainty. Variance should be a 3 part stat; total variance, downswing variance, and upswing variance. When you do this you understand that minimizing total variance out of the three isn't as important as minimizing downswing variance. If you can minimize downswing variance while maximizing upswing variance, total variance doesn't really matter much. The stats in the OP tell the story. You can reduce downswing variance or double 50% more often for a small gain in EV and a lot more downswing variance.

But you need to do research to find the cost of the change and pick the ones that make the most sense concerning how much EV gain there is at the index, the correlation of count tags to the playing EoRs for the hand, and how big the bets are. If bets are not large you don't need to worry about structuring downswing variance. The contribution to total variance won't be much to begin with so you don't need to worry about it. For many plays my playing count has little correlation to my betting count but for other plays there is a very high correlation. It depends on which multiple of one count added to the other gets me the strongest index play for the matchup. Ace reckoned counts usually have a 100% correlation since the betting count is usually the playing count. The opportunities to use this approach are very limited in that instance. Ace neutral counts have much less of a correlation. Assuming ace adjustments are used for playing decisions, when aces act as high cards the correlation is high, but for matchups where aces count as low cards the correlation is lower.

More exotic approaches using balanced side counts can have little to no correlation for many matchups. The amount of the time this approach is useful depends on how many playing TCs you might have big bets out for. The lower the correlation between the betting count and the playing count the more playing TCs you will get to consider this approach since you need big bets out to consider it. So I guess this is another good opportunity to increase the likelihood of BR growth that is largely lost to simplicity if you use a simple approach. I would say if you use Hilo you are looking at doubling and splitting indices that are TC +3 or +4 or higher depending on your bet size at those counts. I am guessing that is a very short list of index plays to consider, so the impact on results won't be that significant. I guess this really doesn't have much of an application for how most people count.

[Norm]

RA indices already take into account bet size, as well as other indices, bankroll (assuming you are using optimal betting), risk, rules, penetration, variance by count, overall variance, strategy, etc. They are the optimal indices for the growth of limited bankrolls.

[Three]

RA indices already take into account bet size, as well as other indices, bankroll (assuming you are using optimal betting), risk, rules, penetration, variance by count, overall variance, strategy, etc. They are the optimal indices for the growth of limited bankrolls.

I totally agree. What I was talking about went a little further with big bets out. Not optimal if EV is how you judge optimal. But after trying to relate it to the way other people tend to count, the high correlation between the betting count and the playing count makes this idea have little usage making it not worth pursuing. You need to have the playing index non-negative and the bet to be large. In my example I forgot to include the frequency of large bets, which would have greatly reduced that 4/10th of a penny cost per $100 bet. But for most people there would be no instance where they would have a big bet out with a playing TC of 0. Just when the TC changes a lot after the bet and before the playing decision.

My doubling playing counts may not be at all correlated to the betting TC so no move in the TC is required to be in that situation when the playing count and betting count have little correlation. Sometimes I forget how many opportunities are forfeited when you commit to a simple count or even a traditional count. Sorry everyone. I see what Bosox has been complaining about. Many of the avenues I pursue just don't exist for most players' approaches. The less complicated the approach the more the avenues to improve are closed off for you. Nothing wrong with the simple approach. It gets the money in the long run. But if you gather more info and/or use information differently opportunities are there to improve things concerning EV, CE, and more specifically changing the variance makeup concerning swings. But that small subset where any count have a big bet out and are at the doubling or splitting index this concept applies. For most that convergence of conditions is too rare to have much of an impact on results.

[Three]

Suddenly the light bulb goes off and Three you notice there are other perspectives. Is my projection or I should say imagination for your appearance resemble this following late actor?

I just never thought about how many opportunities are closed to you when you decide to use a very simple approach. The concept is valid but the number of times you can apply it using a simple approach with no extra info and a traditional way of using info seems quite limited. You need to be at the double/split index with a big bet out. The frequency of the time you are putting more money out when this is the case is very small. I usually compare my approach to Hiopt2/ASC since that is my main count. Hiopt2/ASC would have more opportunities but still not have that many. Any use of this concept helps but you need a certain percentage to really feel the effect in your results. Those that gather and use extra info would be more likely to see a higher frequency of usage of the concept. With few unseen cards left just card removal might get a big bet out at the doubling index. But some people mostly play shoe games and rarely play DD or SD. Not much of their play will have cards removed after they bet and before they make their paying decision get the count where it needs to be for more common doubles. Some soft doubles and doubling 7 and 8 are in play for all counts without the latter effect. Most other plays need some help from card removal if you use a simple traditional approach.

[ZeeBabar]

[QUOTE=Three;261999I
. Those that gather and use extra info would be more likely to see a higher frequency of usage of the concept.[/QUOTE]

It's whether the process of gathering the extra info and the time spent learning to use that info versus the alternatives. I have a friend who went on to do a Ph'd while I quit after my Masters degree. We made about the same $$$. He enjoyed the research and study and I preferred to do other things with my time.

[BoSox]

Sometimes I forget how many opportunities are forfeited when you commit to a simple count or even a traditional count. Sorry everyone. I see what Bosox has been complaining about. Many of the avenues I pursue just don't exist for most players' approaches. The less complicated the approach the more the avenues to improve are closed off for you.

What Norm allows to be posted by you I consider bragging on a large scale, that is of no help to anyone. Meanwhile, my innocent joke trying to compare you to a certain late actor's resemblance put as a question that you can agree with hurt no one gets deleted right after posting it. I think Norm should suspend himself for a week.

[21forme]

What Norm allows to be posted by you I consider bragging on a large scale, that is of no help to anyone.

If you believe any of it.

If you can't dazzle them with brilliance, baffle them with bullshit.

I think Norm should suspend himself for a week.

THAT'S funny!