What is the algorithm, messy though it may be, you used to calculate the betting schemes in Chapter 10 of BJA3?
David
What is the algorithm, messy though it may be, you used to calculate the betting schemes in Chapter 10 of BJA3?
David
> What is the algorithm, messy though it may be, you
> used to calculate the betting schemes in Chapter 10 of
> BJA3?
I didn't. It's an iterative process, first described in the literature by Yamashita, and then further discussed by many others, including Thorp, Brett Harris, and Karel Janecek.
Norm programmed the algorithm and did all the optimal-bet ramps for me, as I mentioned in the prefatory remarks to the charts (which no one ever reads!! :-))
Don
> I didn't. It's an iterative process, first described
> in the literature by Yamashita, and then further
> discussed by many others, including Thorp, Brett
> Harris, and Karel Janecek.
As always, thanks for your prompt answer.
So you mean I can't just plug some variables into a formula and have it spit out the optimal bets for every set of rules, penetration, and playing strategy? I'm shocked! :-)
In lieu of this magical formula, is there a particular paper or report you'd recommend to gain a little insight into the iterative process?
> Norm programmed the algorithm and did all the
> optimal-bet ramps for me, as I mentioned in the
> prefatory remarks to the charts (which no one ever
> reads!! :-))
It looks like I might be adding CVCX to my suite of Casino V?rit? software...
Optimal bet at each count is Kelly equivalent bank (KEB)*EV/Var. The problem is that you must have the optimal bets to calculate the KEB. And you must have the KEB to calculate the optimal bets.
You start with a guess at the optimal bets. 1 unit at all negative EVs and max bet at all positive EVs.
Then you start the iterations:
Calc total win rate and variance given the current guesses. (requires sim data)
Calc KEB guess: KEB=variance/winrate
Calc new optimal bet guesses. For each TC, bet = KEB * TCEV/TCSD (TCEV and TCSD are the advantages and standard deviations at each True Count from sim data.)
Ensure that all bets are in the range 1 unit to spread units
Repeat the above until the guesses stop changing.
After all iterations, you have the KEB and optimal bets. This assumes a Kelly Factor of 1.
CVCX is a bit more complex since it also calculates 'rational bets.' Bets that don't look silly in a casino. You could just round to reasonable bet sizes - but they might all round in the same direction resulting in over or under betting. So CVCX uses a feedback mechanism to determine rational bets that approximate the desired risk while achieving the best SCORE.
Just one comment, for clarification. The "magical formula" that David is looking for is, indeed,
optimal bet = (bankroll x edge)/variance, at each true count that is between the lowest (non-advantage) bets (where you should be betting zero, but may be forced to bet) and the top bet (where you have decided to max out at a certain level (determined by your spread).
Finally, the above doesn't tell you what your unit size should be. :-)
Don
> optimal bet = (bankroll x edge)/variance,
Forgive me if this is a dumb question, but what variance should I use for this:
1) The per hand variance of playing with a particular ruleset and using flat betting,
2) The per hand variance of playing with a particular ruleset and using the optimal betting ramp (which means that using the formula would necessarily be iterative),
or 3) The per hand variance of playing with a particular ruleset at the specific count for which the bet is being determined?
I would think that it's "3," but I'm not sure.
David
> Just one comment, for clarification. The "magical
> formula" that David is looking for is, indeed,
> optimal bet = (bankroll x edge)/variance, at each true
Hmmmmm, why are you neglecting to mention Kelly-factor in your equation? Here is my equation:
Optimal bet = BR x Kelly-factor x (EV/Var)
> count that is between the lowest (non-advantage) bets
> (where you should be betting zero, but may be forced
> to bet) and the top bet (where you have decided to max
> out at a certain level (determined by your spread).
Ok, I never quite understood the logic of imposing a bet spread. It would seem that this is a constraint you impose unnecessarily. The only input that is required on the part of the counter is BR and Kelly-factor.
What does a bet spread have to do with optimal betting? If it is purely for camo purposes, that is fine. I recently asked AS about this topic on his board, and he said that there is no mathematical advantage from imposing a bet spread!! In other words, he is saying this will not help you to win more money!!
As I have pointed out in the past, the MIT Teams did not cap their max bet. They used a linear bet schedule and bet it up as high as the count went. Why not simply raise your bet as advantage rises, in accordance with the equation I wrote above?
You can say that what you are doing is "optimal", but you are adding a third variable (bet spread)to the equation that some others simply ignore. If you recall, I ran some simulations on this and posted over at BJI. You looked at the post and said that the comparisons were not apples to apples. If an apples to apples comparison can not be made to compare our different betting styles, how can you say that your "apple" is better than my "orange"?
MJ
> Hmmmmm, why are you neglecting to mention Kelly-factor
> in your equation? Here is my equation:
> Optimal bet = BR x Kelly-factor x (EV/Var)
> Ok, I never quite understood the logic of imposing a
> bet spread.
I'm sure Don and Norm will ably defend themselves, but I think the idea of an optimal betting ramp is that it provides you with optimum bets GIVEN a particular bet spread. Saying that using a spread at all is non-optimal is akin to saying that playing when the dealer hits soft 17 is non-optimal. Both are conditions which, detrimental though they may be, reflect the reality of casino play. The optimal betting ramps are created GIVEN a certain set of conditions, one of which may happen to be a bet spread.
> What does a bet spread have to do with optimal
> betting? If it is purely for camo purposes, that is
> fine. I recently asked AS about this topic on his
> board, and he said that there is no mathematical
> advantage from imposing a bet spread!! In other words,
> he is saying this will not help you to win more
> money!!
Of course a bet spread doesn't (directly) help you win more money...no restriction on the player's actions would. But a restricted bet spread is a reality of casino play. Being able to generate an optimal betting ramp for a realistic set of restrictions--both casino- self-imposed--is useful.
> As I have pointed out in the past, the MIT Teams did
> not cap their max bet. They used a linear bet schedule
> and bet it up as high as the count went. Why not
> simply raise your bet as advantage rises, in
> accordance with the equation I wrote above?
The MIT teams also tended to have much larger units (no sexual innuendo intended :-) ) than most players. Often, the limiting factor was the table maximum as opposed to a self-imposed max bet. Either way, however, there is a maximum bet.
> You can say that what you are doing is
> "optimal", but you are adding a third
> variable (bet spread)to the equation that some others
> simply ignore. If you recall, I ran some simulations
> on this and posted over at BJI. You looked at the post
> and said that the comparisons were not apples to
> apples. If an apples to apples comparison can not be
> made to compare our different betting styles, how can
> you say that your "apple" is better than my
> "orange"?
I don't think that anyone is saying that this "apple" is better than your "orange." However, these apples are actually available in the real world. Your orange, however delicious, may be very hard to find.
David
Fair enough, David. Let me ask you this.
Do you think it is possible to render an apples to apples comparison of two bet schedules given the following constraints?
Schedule A: Kelly-factor, BR
Schedule B: Kelly-factor, BR, bet spread
Schedule A is using Kelly wagering with a non definite spread, and B is using "optimal betting" with a fixed spread.
Assuming K-f and BR are the same in each schedule, is it possible to determine which schedule is superior? This is what I tried to do on CVCX a while back but finally gave up.
If this cannot be done, then in all fairness we cannot conclude A is better then B, either. But logic will dictate that B cannot be superior to A, due to reasons mentioned in your post. At worst they are equal, at best A is superior.
There must be a way. Perhaps if the avg bet of each schedule were equal...?
MJ
> Fair enough, David. Let me ask you this.
Pardon me for jumping in.
> Assuming K-f and BR are the same in each schedule, is
> it possible to determine which schedule is superior?
> This is what I tried to do on CVCX a while back but
> finally gave up.
> If this cannot be done, then in all fairness we cannot
> conclude A is better then B, either. But logic will
> dictate that B cannot be superior to A, due to reasons
> mentioned in your post. At worst they are equal, at
> best A is superior.
No, you are ignoring risk. Unless you are constantly resizing, schedule A will be much riskier than schedule B. The bet spread is not merely a constraint. It allows us to fix the risk so we can maximise return with respect to it.
Think of optimal betting as bringing Kelly to the real world, where we can't recalculate our bet every hand, can't bet on the dealer to win, can't infinitely divide our bankroll and can't bet more than the table maximum.
> There must be a way. Perhaps if the avg bet of each
> schedule were equal...?
There isn't a way because a fair comparison takes risk into consideration, whereas an unlimited bet spread ignores it. To put it another way, optimal betting is a real-world scenario and an unlimited spread isn't. Apples/oranges.
> Hmmmmm, why are you neglecting to mention Kelly-factor
> in your equation? Here is my equation:
> Optimal bet = BR x Kelly-factor x (EV/Var)
> Ok, I never quite understood the logic of imposing a
> bet spread. It would seem that this is a constraint you impose unnecessarily.
Applying a Kelly-Factor and applying a bet spread are both non-optimal constraints
> Forgive me if this is a dumb question, but what
> variance should I use for this:
> 1) The per hand variance of playing with a particular
> ruleset and using flat betting,
> 2) The per hand variance of playing with a particular
> ruleset and using the optimal betting ramp (which
> means that using the formula would necessarily be
> iterative),
> or 3) The per hand variance of playing with a
> particular ruleset at the specific count for which the
> bet is being determined?
> I would think that it's "3," but I'm not
> sure.
Yes, 3.
Don
David and Norm have answered you as ably as I could, so no response on my part is necessary.
I'll summarize: Some people (read: 99% of all card counters!) self-impose a bet spread because they are playing in the real world and not on a computer, and they'd like to be able to play for more than a week or two. :-)
You don't get to pick the constraints that you like and those that you don't, when you engage in this discussion. You don't like bet spreads? I don't like playing for 1/3 Kelly! :-)
Don
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