MJ: Methods to Reduce Variance (long)

[MJ]

I was pondering some of the ways a counter can reduce variance. Here is what I have thus far:

1) Cap the bet spread/reduce kelly/play a smaller unit. For shoe games, use around a 1 to 10 spread for play all game with Hi-Lo. Although a 1-12 spread is recommended, a 1-10 spread will reduce variance. Try to find games with good rules like late surrender and play as few deck as possible. Does resplitting of aces reduce or increase variance?

2) Wong in and out of shoes. If no midshoe entry is allowed, then at the very least you can wong out when the TC <= -1. But what if the TC = -.75 or -.50? Would these TCs justify wonging out of the shoe or is there still hope for the count to shoot up? If it makes a difference, I round the TC to the nearest integer.

3) A. Form a team!! More players mean more bets/hour...and if one player has a bad day that can be offset by the earnings of other players. It just helps to smooth out negative fluctuations and gets to the long term faster! Do not underestimate the laws of large numbers!!

B. Also, teammates playing independently from the same bankroll is superior to the BP/Spotter approach. Using this idea, teammates from different parts of the country can attack casinos without the hassle of playing at the same time in the same casino. Also with this method you don't have to worry about the BP getting signaled into tables at the same time when the count is good at different tables. So train people that you trust and set them loose on the casino.

4) You can play multiple hands in positive counts and actually REDUCE variance while keeping EV constant(I think). Let me provide an example:

You are spreading from $30 to $300 in a shoe game. When you place your max bet at $300, play 3 hands of $100 each. This way if the dealer pulls a good hand like a 20 at least one of your 3 hands might push or reach a total of 21 whereas if you just bet 1 hand of $300 you would probably have lost. I realize this approach does not optimize EV, and will ultimately yield fewer rounds in positive counts. Again, the point is to reduce variance and not maximize EV.

For someone looking to maximize EV while keeping variance the same with another player at the table then play 2 hands of $210 each.

5) Ironically, look for games with lousy penetration. The TC frequency for high TCs will be lower and as a result you will place fewer max bets/hr which will help to reduce variance. I believe Fred Renzey mentions this in his book.

6) Do not play at all! :-)

For those of you with other ideas, please post your comments.

MJ

[Don Schlesinger]

NIce post. Ironically, most of your ideas tend to boil down to your #6!! That's not meant to be sarcastic, but it is a fair assessment of your plan. Comments follow.

> I was pondering some of the ways a counter can reduce
> variance. Here is what I have thus far:

> 1) Cap the bet spread/reduce kelly/play a smaller
> unit.

All reduce e.v., too. Play less, bet less, reduce variance. But, at what cost?

> For shoe games, use around a 1 to 10 spread for
> play all game with Hi-Lo. Although a 1-12 spread is
> recommended, a 1-10 spread will reduce variance.

And profits, commensurately.

> Try
> to find games with good rules like late surrender and
> play as few decks as possible.

Surrender reduces variances. If bet optimally, playing fewer decks doesn't.

> Does resplitting of aces
> reduce or increase variance?

Anything that adds more hands and, therefore, increases the total wager, increases variance, by the very definition.

> 2) Wong in and out of shoes. If no midshoe entry is
> allowed, then at the very least you can wong out when
> the TC

See above. If bet optimally, back-counting increases variance, but it also increases profits a lot.

3) A. Form a team!! More players mean more
> bets/hour...

And, therefore, much more variance!

> and if one player has a bad day that can
> be offset by the earnings of other players. It just
> helps to smooth out negative fluctuations and gets to
> the long term faster! Do not underestimate the laws of
> large numbers!!

Absolutely correct. But, please understand the difference between lowering the percentage that variance is with regard to expectation, as opposed to lowering the absolute magnitude of the variance. If you play more hours, your variance increases. Period. Now, I understand what you mean, but make sure to state it properly.

> B. Also, teammates playing independently from the same
> bankroll is superior to the BP/Spotter approach. Using
> this idea, teammates from different parts of the
> country can attack casinos without the hassle of
> playing at the same time in the same casino. Also with
> this method you don't have to worry about the BP
> getting signaled into tables at the same time when the
> count is good at different tables. So train people
> that you trust and set them loose on the casino.

Sounds like a plan!

> 4) You can play multiple hands in positive counts and
> actually REDUCE variance while keeping EV constant(I
> think). Let me provide an example:

> You are spreading from $30 to $300 in a shoe game.
> When you place your max bet at $300, play 3 hands of
> $100 each. This way if the dealer pulls a good hand
> like a 20 at least one of your 3 hands might push or
> reach a total of 21 whereas if you just bet 1 hand of
> $300 you would probably have lost. I realize this
> approach does not optimize EV, and will ultimately
> yield fewer rounds in positive counts. Again, the
> point is to reduce variance and not maximize EV.

Yes, that's all correct.

> For someone looking to maximize EV while keeping
> variance the same with another player at the table
> then play 2 hands of $210 each.

No, not quite. The e.v. increases, but the variance also increases (by the same percentage). It's the ROR that stays the same.

> 5) Ironically, look for games with lousy penetration.
> The TC frequency for high TCs will be lower and as a
> result you will place fewer max bets/hr which will
> help to reduce variance.

And help to keep you in the poor house. Bad idea!

> I believe Fred Renzey
> mentions this in his book.

> 6) Do not play at all! :-)

That's what all of the above boils down to, I'm afraid.

> For those of you with other ideas, please post your
> comments.

You've covered most of them, ... for better or for worse.

Don

[Don Schlesinger]

... while we're at it, one more: Play games with the lousiest rules, such as split pairs only once, no soft doubling, or doubling on 10 and 11 only. Sure to reduce variance, while reducing your winnings apace.

Don

[AutomaticMonkey]

That is, if you want to keep your profits.

First of all, Wonging out of bad counts is an absolutely essential skill for a shoe player. Once a shoe goes to hell you can be playing at negative EV for a long time, time that could be spent playing another, potentially profitable shoe. Wonging tends to increase variance (in terms of dollars) because you are playing more hands at good counts and thus laying more money on the table. But because your average win rate per hand is increased, you are playing a more profitable game and thus you can decrease your betting unit or max bet and make the same amount of money. This sounds like what you're looking for. Increasing profitability without betting more money is the same thing as reducing risk.

Spreading to two hands is almost always a good idea.

One little extra that you didn't mention is playing negative split and double indices on SD and DD games, where you aren't Wonging out of bad counts. These represent times when you don't use a basic strategy split or double play because the count is sufficiently low. These indices don't have any significant cash value in terms of win rate but they do allow you to play at the same win rate while laying less money on the table. DD 9 vs. 3 and DD 10 vs. 9 are examples of negative indices that I use. All of the surrender indices have the same effect.

> I was pondering some of the ways a counter can reduce
> variance. Here is what I have thus far:...

[ToJeDobro]

How about:
1. Switch to risk averse indices (accepting the loss in EV)
2. Increase the number of certain indices used
3. Learn a stronger system
4. Play with coupons
5. Add shuffle tracking, hole-carding, etc to your tool box
6. Practice, practice, practice to eliminate playing & betting errors
7. Arrive at the casino rested, sober & focused; Then leave before it changes
8. Work on mental & emotional comportment, again to avoid being shaken and making errors
9. Be alert to unanticipated exploitable opportunities

[Coug Fan]

You need to clarify what you are trying to accomplish. It is not really a rational goal to decrease variance in isolation. That is easy, just don't play.

More to the point, if we say that the goal is just to reduce variance (while also playing), then we reach illogical results like using a 1:1 spread at the lowest table min in the casino, and also seeking out games that pay even money on blackjack.

It sounds like your real goal might be to decrease variance faster than you decrease EV. In this case, you should look for surrender, hole card opportunities, promotions like match play coupons or loss rebates, new dealers that make alot of errors, etc.

[Don Schlesinger]

> How about:
> 1. Switch to risk averse indices (accepting the loss
> in EV)

Yes, but little impact. And, there is no loss in e.v.

> 2. Increase the number of certain indices used

Avoiding some doubling and splitting; yes.

> 3. Learn a stronger system

Not necessarily a variance reduction. Sometimes leads to both an increase in e.v. and variance.

> 5. Add shuffle tracking, hole-carding, etc to your
> tool box

My guess is that ST would greatly increase variance.

Don

[MJ]

> All reduce e.v., too. Play less, bet less, reduce
> variance. But, at what cost?

Thanks for the information Don. Well I guess the idea is to try and reduce variance at a faster rate then EV. That is ideal goal.

> Surrender reduces variances. If bet optimally, playing
> fewer decks doesn't.

As far as playing fewer decks is concerned, I would not mind sacrificing some EV in order to reduce variance. The EV on SD games is quite high to begin with just by employing a marginal spread. Remember, everybody has a different tolerance for variance. I get the impression you think that reducing variance is a waste if it also reduces EV at the same rate. If that is your attitude, then why bother playing anything less then full kelly? Don't you lose EV and reduce variance when you play less then full kelly?

> Anything that adds more hands and, therefore,
> increases the total wager, increases variance, by the
> very definition.

Well said.

> See above. If bet optimally, back-counting increases
> variance, but it also increases profits a lot.

Hmmmm...well what if you don't bet optimally? :-) Sacrifice some EV!! With wonging, even if you don't bet optimally, can't you still reduce variance more so then with a play-all game and still have a higher SCORE? That would be the ideal scenerio. Also, when you state "bet optimally" that carries with it a hefty 13.5% ROR. I don't know about you, but that scares the daylights out of me. Most professional teams play at between .3 and .4 kelly. Hence they bet a smaller unit and reduce ROR and variance while accepting a loss in EV. There is a trade-off between EV and variance I guess. Each individual must determine that balance for themselves.

> 3) A. Form a team!! More players mean more

> And, therefore, much more variance!

> Absolutely correct. But, please understand the
> difference between lowering the percentage that
> variance is with regard to expectation, as opposed to
> lowering the absolute magnitude of the variance. If
> you play more hours, your variance increases. Period.
> Now, I understand what you mean, but make sure to
> state it properly.

I think I understand your point. What I described does not really reduce variance at all, but just lowers the absolute magnitude of the variance. In other words, playing a great deal of hands with team play would increase variance, but ultimately the increase would be minimal compared to the accumulated EV of thousands and thousands of hands.

> No, not quite. The e.v. increases, but the variance
> also increases (by the same percentage). It's the ROR
> that stays the same.

How can variance increase and the ROR remain the same? If you bet more money on any given round I would think the ROR would increase with variance.

> You've covered most of them, ... for better or for
> worse.

Well there was one other point I forgot to mention:

#7 Seek out tables that are crowded so you play fewer hands per hour and therefore reduce variance. Unfortunately, the EV diminishes right along with the variance. :-)

Alright Don, how do you propose to decrease variance at a faster rate then EV? That is the dilemma all counters face.

MJ

[Sonny]

> Thanks for the information Don. Well I guess the idea
> is to try and reduce variance at a faster rate then
> EV. That is ideal goal.

Exactly. Reduce risk and increase reward. That's the goal.

> I get the impression you think that reducing variance is
> a waste if it also reduces EV at the same rate.

The problem is that they are rarely reduced, or increased, at exactly the same rate. As you said, the goal is to increase your EV more than your SD.

I think you are too concerned with short term variance and should look more at your long term variance. Increasing your EV will usually increase your variance along with it, but if you can increase your EV more than your variance then you are lowering your ROR. You may experience larger fluctuations but you have reduced your overall exposure to risk.

Don's approach is to maximize the ratio of reward to risk, aka SCORE. By defenition, having the highest EV with the lowest SD will produce the lowest ROR. Once you find the best strategy you can chose your unit size to match it. That is how you play optimally and still preserve a manageable ROR. Giving yourself the lowest ROR will allow you to use the biggest unit size possible, which will increase your win rate even more.

By playing in crowded games with lousy penetration you are reducing your short term variance but you are reducing your EV even more. That gives you a smaller win rate and a higher ROR. You are winning less money and taking a higher risk to get it. Beacuse of the higher ROR you are also using a smaller unit size which further reduces your win rate.

> How can variance increase and the ROR remain the same?
> If you bet more money on any given round I would think
> the ROR would increase with variance.

No, because the win rate is higher so there is less chance, in the long run, that you will go broke. The variance on that particular hand has gone up, but the size of your bet has preserved your original ROR.

> Alright Don, how do you propose to decrease variance
> at a faster rate then EV? That is the dilemma all
> counters face.

That's a very long and involved question. Luckily, Don has written an entire book devoted mostly to that topic. =)

-Sonny-

[MJ]

> Anything that adds more hands and, therefore,
> increases the total wager, increases variance, by the
> very definition.

> 3) A. Form a team!! More players mean more

> And, therefore, much more variance!

> Absolutely correct. But, please understand the
> difference between lowering the percentage that
> variance is with regard to expectation, as opposed to
> lowering the absolute magnitude of the variance. If
> you play more hours, your variance increases. Period.
> Now, I understand what you mean, but make sure to
> state it properly.

Don,

1) I am still a bit confused on this one. What do you mean when you say "lowering the percentage that variance is with regard to expectation"? What equation are you using... Variance/EV? I take what you stated above to mean that playing more hands per hour increases variance because you are putting more money into action but at the same time somehow reduces it. This is the part I don't understand. Can you please clarify what you meant? If you could provide a simple example that would be great.

2) Suppose a BS player after playing only 1 hour falls within a 1 St Dev range of -8.84 units to 8.20 units and has a negative expectation of -.32 units. Would an example of lowering the absolute magnitude of the variance mean simply mean shortening the interval, IE -6 units to 5 units after only 1 hour of play? I suppose lowering the absolute magnitude of variance is not possible given a fixed time constraint.

MJ

[Don Schlesinger]

> Don,

> 1) I am still a bit confused on this one. What do you
> mean when you say "lowering the percentage that
> variance is with regard to expectation"? What
> equation are you using... Variance/EV?

Yes. But, if I stated it as variance, rather than as s.d., then I was mistaken. Anywhere you see "variance" I should have written "standard deviation." Sorry for any confusion.

> I take what you
> stated above to mean that playing more hands per hour
> increases variance because you are putting more money
> into action but at the same time somehow reduces it.

It reduces the importance of s.d. with respect to e.v., expressed as a ratio of s.d./e.v. Because e.v. is a linear function and s.d. is a square-root function.

> This is the part I don't understand. Can you please
> clarify what you meant? If you could provide a simple
> example that would be great.

If you play 100 hands/hr., hourly e.v. might be one unit while s.d. might be 15 units. The ratio of s.d./e.v. is 15 to 1. If you play 400 hands per hour (impossible, but humor me; the math is simpler) your e.v. is now four units while your s.d. is 30 units. The s.d. is larger in magnitude than it was before, but, expressed as a ratio of s.d./e.v., we now have 30/4, or 7.5 to 1, instead of 15 to 1.

Play long enough, and e.v. eventually catches up to s.d. The number of hours (or hands) required to do this is what Brett Harris referred to as N0 (N-zero).

> 2) Suppose a BS player after playing only 1 hour falls
> within a 1 St Dev range of -8.84 units to 8.20 units
> and has a negative expectation of -.32 units. Would an
> example of lowering the absolute magnitude of the
> variance

Let's stick with s.d.

> mean simply mean shortening the interval, IE
> -6 units to 5 units after only 1 hour of play?

Yes.

> I suppose lowering the absolute magnitude of variance is
> not possible given a fixed time constraint.

Play more slowly! :-) Or, use risk-averse indices for your strategy departures. Or, always seek out LS games.

Don

[MJ]

> If you play 100 hands/hr., hourly e.v. might be one
> unit while s.d. might be 15 units. The ratio of
> s.d./e.v. is 15 to 1. If you play 400 hands per hour
> (impossible, but humor me; the math is simpler) your
> e.v. is now four units while your s.d. is 30 units.
> The s.d. is larger in magnitude than it was before,
> but, expressed as a ratio of s.d./e.v., we now have
> 30/4, or 7.5 to 1, instead of 15 to 1.

Thanks Don. Excellent example! Simple and clear. :-)

> Play long enough, and e.v. eventually catches up to
> s.d. The number of hours (or hands) required to do
> this is what Brett Harris referred to as N0 (N-zero).

Ok, so if I were to graph EV and SD the point where the two curves intersect is N0 (when EV = SD). Initially, SD exceeds EV but after a looooong time EV exceeds SD. This is after the two curves intersect. I suppose you could set up a system of equations to find the intersection point. Intuitively, I can tell that the slope of the SD function approaches 0 as the number of hands played approaches infinity. Play enough hands, and the accumulated EV leaves the SD in the dust....good thing EV is linear.

MJ

[Magician]

> Ok, so if I were to graph EV and SD the point where
> the two curves intersect is N0 (when EV = SD).
> Initially, SD exceeds EV but after a looooong time EV
> exceeds SD. This is after the two curves intersect. I
> suppose you could set up a system of equations to find
> the intersection point.

N₀ = Var/EV² = (SD/EV)²