paranoid android: risk reducing betting scheme

[paranoid android]

Consider a scheme where I use x as my base betting unit for a trip as long as I am up or even, and switch my base unit to x/2 if I'm down.

I believe that if a bankroll moved in infinitesimally small continuous units, this scheme would result in cutting my downside risk in half, while maintaining the same EV.

Of course in reality a bankroll moves in discreet units, so using this scheme has a cost. Every time my bankroll crosses from positive to negative, I lose something trying to get back to positive. The bet that I lost to get into negative territory is on average twice as big as the bets that get me back into positive territory, so EV is damaged.

My question is how much is this cost? If my bankroll crosses back and forth between positive and negative a small number of times (on average) during a trip, I'm guessing it may be worthwhile to bet this way. Can anyone tell me on average how many times this occurs in a trip of say, 16 hours (100 hands/hour)? Any other thoughts appreciated (but go easy on me if this is completely ridiculous :-) Thanks.

[Contrail]

If I understand your intention correctly, then I think this approach is flawed. You're not approaching a more 'proportional like' betting scheme since you're lowering your unit size by a fixed factor of two irrespective of the decrease in your bankroll and you're not increasing your unit size when your bankroll increases.

Instead, if your initial unit was full fixed Kelly then part of the time you would be betting full Kelly and part of the time you would be betting half Kelly. The net impact will be to mess up your long term growth.

Consider a more severe hypothetical example. You sit down at a $100 table and relatively quickly lose something consistent with a 1 s.d. fluctuation. You then head to a $10 table cutting your unit size by a factor 10. After what seems like a lifetime you're even again and now head back to $100 table hoping that you don't repeat the whole process again. You're not cutting your unit size as much and you're decreasing your unit whenever you're down, but I think the idea is the same. Any gain while betting x when you're winning will be offset by the time spent betting x/2 when you're losing.

If you're comfortable with your long term ROR for a given unit size, then arbitrarily decreasing that unit size in response to short term fluctuations is, imo, a waste of time.

[PunkEye]

[Contrail]

PA wrote:

"Consider a scheme where I use x as my base betting unit for a trip as long as I am up or even, and switch my base unit to x/2 if I'm down. "

I did not interpret this to mean flat betting nor was I referring to flat betting in my response. Sorry if something in my post inferred flat betting.

Beyound that clarification, I don't see the value in either decreasing the base unit when losing during a session, as I think PA was considering, or decreasing after a winning shoe, as you seem to be suggesting. I've said all I really wanted to say about it in my previous post. But I do find the thought of all three of us at the same table a little amusing.

With respect to your second thought concerning a dealer beating my "bloody brains" out, I usually do not have a problem in that regard. I'll just politely tell them that their dealing is no longer welcome at my table although they are free to go over to the craps table if they want to.

[paranoid android]

The idea was to use the method for a trip where one wouldn't typcially recalculate his betting unit (no, I'm not referring to flat betting as someone suggested below). You correctly identified the problem with this method as did I in my original post (my communication skills are obviously lacking).

After further consideration I'm sure it's impractical due to the problem we both mentioned. Note, however, that for some extreme cases, it is superior to having x as my base betting unit all the time for the trip. These cases are for trips where you never cross from negative to positive territory, as that's when your EV takes a hit. If on the trip you only win money (your trip bankroll never crossing to negative territory), you win the same as before. For trips where you lose immediately or, win first then drop to negative territory and never cross back into positive, you would lose about 1/2 has much as if you kept x as your betting unit all the time.

The 3am thought I had was that even if you did cross from negative to positive territory a very small number of times, the hit to your EV may be small enough to justify reducing your downside risk in half. Unfortunately, I believe that on a typical trip, your trip bankroll moving back and forth from negative to positive territory happens many times, making this impractical.

> If I understand your intention correctly,
> then I think this approach is flawed. You're
> not approaching a more 'proportional like'
> betting scheme since you're lowering your
> unit size by a fixed factor of two
> irrespective of the decrease in your
> bankroll and you're not increasing your unit
> size when your bankroll increases.

> Instead, if your initial unit was full fixed
> Kelly then part of the time you would be
> betting full Kelly and part of the time you
> would be betting half Kelly. The net impact
> will be to mess up your long term growth.

> Consider a more severe hypothetical example.
> You sit down at a $100 table and relatively
> quickly lose something consistent with a 1
> s.d. fluctuation. You then head to a $10
> table cutting your unit size by a factor 10.
> After what seems like a lifetime you're even
> again and now head back to $100 table hoping
> that you don't repeat the whole process
> again. You're not cutting your unit size as
> much and you're decreasing your unit
> whenever you're down, but I think the idea
> is the same. Any gain while betting x when
> you're winning will be offset by the time
> spent betting x/2 when you're losing.

> If you're comfortable with your long term
> ROR for a given unit size, then arbitrarily
> decreasing that unit size in response to
> short term fluctuations is, imo, a waste of
> time.

[PunkEye]

[Parker]

> I was trying to make the impression that
> shoes, from time time will favor one side or
> the other as far as results. I know it
> happens in dice fairly regularly.

You're coming dangerously close to voodoo here, if I understand you correctly. Sure, dealers have hot streaks, just like players, but it is impossible to predict when these will stop and start. They can only be recognized in hindsight.

Any attempt to exploit "table bias" "dealer bias" or whatever term the snake-oil system sellers are calling it these days, is doomed to failure.

There is no reason on earth to leave a table where conditions (rules, penetration, number of players) are good, simply because you seem to be losing a lot.