MJ: ? Don: Bankroll Management

[MJ]

Suppose a counter sets up his betting schedule such that he is playing with a 5% RoR and 50 SC0RE employing a 1 to 20 bet spread with his minimum bet = table minimum. Let us also assume his style is play-all. After his first weekend to the casino, his BR incurs a 20% hit. Ideally, the counter would like to preserve his 5% RoR by resizing his unit downward but the problem is that if he does then his minimum bet would be below the table minimum. So what is the counter to do assuming he wants to continue with his play-all style?

I suppose he could decrease his bet spread sufficiently such that RoR is restored to 5%. But the problem with that is WR will be reduced accordingly and N0 increased. From that point on, either one of two things will happen:

1) He continues to lose in which case it was a good thing he reduced the spread. But how much can one decrease the spread before WR becomes too small and N0 too large? At what minimum point should the spread be frozen and whatever happens, happens?

2) He goes on a winning streak and does not restore the 1 to 20 spread until he wins back what he lost.

On the other hand, after that first disastrous trip he also has the option of leaving his spread intact and hoping that he wins back what he lost in the future. But, if he continues to lose then he will regret not having reduced his spread and RoR will continue to rise exponentially. Yikes!

Do you think the best way to handle this type of situation where your minimum bet = table minimum is to simply increase and decrease the bet spread after each session so that 5% RoR is preserved? Isn't this sort of like kelly wagering in that we are changing the betting ramp after each trip as the BR increases and shrinks with the only difference being that the minimum bet is fixed? I do realize that kelly wagering does not involve changing bet spread, but it is sort of similar in that by altering spread a certain RoR can be maintained.

MJ

[Don Schlesinger]

I've addressed questions like this one in the past, and while there's no "correct" answer, I'll be happy to share my thoughts with you.

> Suppose a counter sets up his betting schedule such
> that he is playing with a 5% RoR and 50 SC0RE

You'll permit an initial scolding. If you're quoting a bona fide SCORE, then the ROR is 13.5%. Otherwise, you're quoting a win rate or a C-SCORE. End of scolding. :-)

> employing a 1 to 20 bet spread with his minimum bet =
> table minimum.

OK.

> Let us also assume his style is
> play-all. After his first weekend to the casino, his
> BR incurs a 20% hit. Ideally, the counter would like
> to preserve his 5% RoR

Then it wasn't a 5% ROR to begin with! If you "chicken out," and reduce the bet, because you've lost a portion of your bank, then if that strategy had been enunciated at the start, you wouldn't have called it 5% ROR, would you have? If you keep resizing, then your theoretical ROR is zero, isn't it?

> by resizing his unit downward
> but the problem is that if he does then his minimum
> bet would be below the table minimum.

Right.

> So what is the
> counter to do assuming he wants to continue with his
> play-all style?

Get more bank, play with a greater ROR, or find a better game (back-counting comes to mind).

> I suppose he could decrease his bet spread
> sufficiently such that RoR is restored to 5%.

Don't be so sure. ROR is purely a function of e.v. and variance. When you decrease your bet spread, you surely decrease your variance, but you kill your e.v. at the same time. So, if the ratio of var/e.v.. isn't decreased, then neither is your ROR.

> But the
> problem with that is WR will be reduced accordingly
> and N0 increased. From that point on, either one of
> two things will happen:

> 1) He continues to lose in which case it was a good
> thing he reduced the spread. But how much can one
> decrease the spread before WR becomes too small and N0
> too large? At what minimum point should the spread be
> frozen and whatever happens, happens?

Not -20%. Personally, I played for many years never touching the bets until, say, 50% of the bank was lost. Too frequent resizing is not a good idea.

> 2) He goes on a winning streak and does not restore
> the 1 to 20 spread until he wins back what he lost.

You have to ask yourself why you would necessarily wait until you won it ALL back. Suppose you were to lose only 10% of your bank. Would you scale down? No. So, if you lose 20%, scale down, and then win back 10%, is that any different from having lost only 10% to start with? In both cases, you have 90% of the original bank, but in the first case, you don't cut back, while in the second you did, simply because, ..., well, WHY? :-)

> On the other hand, after that first disastrous trip he
> also has the option of leaving his spread intact and
> hoping that he wins back what he lost in the future.

That's what I would do. If you truly were OK with original ROR of 5%, then you have to accept the down swings.

> But, if he continues to lose then he will regret not
> having reduced his spread and RoR will continue to
> rise exponentially. Yikes!

Hindsight is 20-20. The game doesn't come with a crystal ball.

> Do you think the best way to handle this type of
> situation where your minimum bet = table minimum is to
> simply increase and decrease the bet spread after each
> session so that 5% RoR is preserved?

No. Definitely not.

> Isn't this sort
> of like kelly wagering in that we are changing the
> betting ramp after each trip as the BR increases and
> shrinks with the only difference being that the
> minimum bet is fixed?

Yes, and it's not a particularly good idea. I don't know anyone who plays that way.

> I do realize that Kelly wagering
> does not involve changing bet spread, but it is sort
> of similar in that by altering spread a certain RoR
> can be maintained.

My advice: have sufficient original bank to make the fixed-betting ROR a number that you are comfortable with. Then, man up (!) and accept the fact that you might actually lose that bank. As a parachute, if you want to resize when you lose, say, 50% of the bank, be my guest. If you start winning some back, consider restoring full stakes before you hit 100%, in keeping with the principle I enunciated, above.

Don

[MJ]

> I've addressed questions like this one in the past,
> and while there's no "correct" answer, I'll
> be happy to share my thoughts with you.

Thanks.

> If you
> "chicken out," and reduce the bet, because
> you've lost a portion of your bank, then if that
> strategy had been enunciated at the start, you
> wouldn't have called it 5% ROR, would you have?

I suppose. Maybe playing to 0.6 kelly would be a better way to put it.

> Get more bank, play with a greater ROR, or find a
> better game (back-counting comes to mind).

Getting more bank isn't really a viable option. The investors will only put up so much money which is stipulated at the onset of the bank. Aside from margin-calls which have been agreed to should the bank go south, the investors will not continue to supply unlimited money just so the RoR can be preserved throughout BR fluctuations.

Some people might feel okay with RoR climbing exponentially as BR diminishes, but I do not think that is me.

> Don't be so sure. ROR is purely a function of e.v. and
> variance. When you decrease your bet spread, you
> surely decrease your variance, but you kill your e.v.
> at the same time. So, if the ratio of var/e.v.. isn't
> decreased, then neither is your ROR.

Hmmm...when I decrease spread on CVCX from 1 to 20 to say 1 to 15, RoR diminishes. This pretty much holds true for all realistic scenarios. Now if you go from a 1 to 6 spread to a 1 to 2 spread, the RoR for the 1 to 2 spread will be higher than that for the 1 to 6 spread.

> Not -20%. Personally, I played for many years never
> touching the bets until, say, 50% of the bank was
> lost.

Waiting to adjust bets until 50% of BR is depleted seems a bit risky. Assuming your minimum bet was = table minimum, how would you adjust the bet schedule? Would you decrease the bet spread such that RoR was restored to its initial value at the start of the bank?

> Too frequent resizing is not a good idea.

What is the downside of too frequent resizing? I never heard this before.

Do you mean resizing of unit while leaving spread intact or resizing of spread while leaving unit intact?

Mathematically is there anything flawed with the idea of adjusting spread to remotely mimic kelly wagering?

> You have to ask yourself why you would necessarily
> wait until you won it ALL back. Suppose you were to
> lose only 10% of your bank. Would you scale down? No.
> So, if you lose 20%, scale down, and then win back
> 10%, is that any different from having lost only 10%
> to start with? In both cases, you have 90% of the
> original bank, but in the first case, you don't cut
> back, while in the second you did, simply because,
> ..., well, WHY? :-)

Good point.

> That's what I would do. If you truly were OK with
> original ROR of 5%, then you have to accept the down
> swings.

I'm okay with an original RoR of 5%, but the keyword is 'original'. Now if that RoR shoots up to 25% if the BR is down, then adjustments must be made at some point.

> Yes, and it's not a particularly good idea. I don't
> know anyone who plays that way.

Well it is the closest thing to kelly wagering that I can think of for those that have a minimum bet = table minimum.

MJ

[Don Schlesinger]

> Getting more bank isn't really a viable option. The
> investors will only put up so much money which is
> stipulated at the onset of the bank. Aside from
> margin-calls which have been agreed to should the bank
> go south, the investors will not continue to supply
> unlimited money just so the RoR can be preserved
> throughout BR fluctuations.

If that's your arrangement, so be it.

> Some people might feel okay with RoR climbing
> exponentially as BR diminishes, but I do not think
> that is me.

As I said, to each his own.

> Hmmm...when I decrease spread on CVCX from 1 to 20 to
> say 1 to 15, RoR diminishes.

That's possible. I said it wasn't automatic. There are times when decreasing spread will increase ROR.

> This pretty much holds
> true for all realistic scenarios. Now if you go from a
> 1 to 6 spread to a 1 to 2 spread, the RoR for the 1 to
> 2 spread will be higher than that for the 1 to 6
> spread.

And if you go from many other scenarios, as well.

> Waiting to adjust bets until 50% of BR is depleted
> seems a bit risky.

I never said otherwise. I said it was the way I played.

> Assuming your minimum bet was =
> table minimum, how would you adjust the bet schedule?

If you can't find a lower-minimum table, and you can't get more bank, then you're somewhat out of the various options I gave you. You're left with decrease the spread and/or back-count instead of play-all.

> Would you decrease the bet spread such that RoR was
> restored to its initial value at the start of the
> bank?

Already asked and answered: no. It's not clear to me if you asked the question so that I'd agree with you, or if you wanted to know what I, personally, would do. I told you that there are no "right" answers to questions like these, only different approaches. However, one thing that I surely would have done would have been to have had this policy in place, whatever it might be, BEFORE the loss occurred.

> What is the downside of too frequent resizing? I never
> heard this before.

Not winning at the same rate as when you accept more risk. Read seminal papers such as Wong's "What Kelly Wagering Does to Your Win Rate," among others.

> Do you mean resizing of unit while leaving spread
> intact or resizing of spread while leaving unit
> intact?

The former.

> Mathematically is there anything flawed with the idea
> of adjusting spread to remotely mimic kelly wagering?

Most people, who don't wind up winning all the money in the world, will win at a lower rate than those who take more risk.

> I'm okay with an original RoR of 5%,

No, actually, you're not, and you don't understand that.

> but the keyword
> is 'original'. Now if that RoR shoots up to 25% if the
> BR is down, then adjustments must be made at some
> point.

Then, I repeat: you weren't OK with 5% in the first place, because 5% means that you leave the bets alone, and once every 20 banks, you tap out and lose all your money. If your plan is to resize the bank as you lose, then you've calculated the 5% incorrectly in the first place. The 5% is predicated on never making any adjustments.

Again, I don't care if you adjust, but understand that stating 5% ROR simply isn't accurate. What you really mean is, "I'll leave the bets alone, provided we don't start losing, in which case I'm going to panic and cut back the bet size." In which case, I'm telling you that you haven't accepted 5% ROR in the first place. You need to be clear about that.

> Well it is the closest thing to kelly wagering that I
> can think of for those that have a minimum bet = table
> minimum.

Not sure what you're looking for here -- my "blessing" for cutting back spread? You have investors. You should have had a pre-enunciated plan of what the strategy would be if losses of x% occurred. Making it up on the fly, after the fact, is a singularly bad idea.

Don