Bet spreads and true counts

I was wondering how experienced players correlate their bet spreads to the true count. I have read a lot of different opinions on this with most people putting their max bet out at a true count between 4-6. I have also read about Kelly criteria but see conflicting views on this.

For example many people say you should bet a fixed portion of your advantage based on the true count, around .75 for shoe games. So if the house started with a .5% advantage and the true count was 6 you would bet 1.88% (2.5*.75) of your total bankroll.

In Professional Blackjack it says take half the true count and subtract the initial house edge to find the percent of your total bankroll to bet, which at a true count of 6 would be 2.5% (3-.5). This is quite a difference, especially if you have a large bankroll.

I mainly wanted to know how people matched their bet spread to the true count, assuming a spread of 1-4 for single deck, 1-6 for DD, and 1-12 for anything more.

Any clarification would be appreciated.
Thanks

For any game and penetration and spread there is an optimal ramp. The Brett Harris and Karel papers in the Green Chip archives and on bjmath describes the fundamentals but the math is rather intimidating.

In brief, the bet size for all counts except the highest and the top count obey the .75 expectation rule because all are Ev/Var with the variance of blackjack being about 1.33. The size of the unit bet is calculated by taking the overall Ev divided by the overall variance which includes the variance caused by bet variation and is much greater than 1.33. The highest bet is made where the unit bet multiplied by the spread just exceeds the expectation.

A better game has a larger unit bet so the max bet will be at a higher level, a higher expectation. A worse game with a smaller unit bet and the same spread will max out at a lower expectation. A lower spread, of course will max out sooner also. The upshot is many multideck games max out at a +4 and that is a decent rule of thumb.

The optimal ramp can be calculated in a number of ways but there is no longer a reason to do that because Blackjack Risk Manager, Statistical Blackjack Analyser, and the new CV programs can make the calculations for about any game. Any and all of these software are highly recommended.

Your post seems to assume that Kelly is the way to go for everyone. Few pros would agree with this, or so it seems from posts I've read on these boards.

ETF

Could you elaborate a little more on systems besides Kelly?

Thanks

The optimal ramp is the same whether one wishes to play a full Kelly betting scheme with its risk of ruin or some smaller fraction with a smaller ROR.

IMHO it is most easily calculated at full Kelly and then adjusted in size but the size relationship of the bets one to another at different counts must remain the same to optimize results. The Harris proof includes the ROR adjustment for fractional Kelly.

The optimal ramp is the same whether one wishes to play a full Kelly betting scheme with its risk of ruin or some smaller fraction with a smaller ROR.

We must have different definitions of the word "ramp." To me, it means either 1) The multiplier you use to go from advantage to bet, or 2) The complete betting schedule that maps TC to bet. What's your definition?

I agree you can calculate bets with Kelly, then adjust proportionally for another ROR. It's just easier that way because of the way software is set up currently.

ETF

The ratio of the specific unit bet to all other bets at higher advantages. The optimal ramp will be the one calculated by the Harris method because that produces the smallest Nsub0. Whether betting full or partial Kelly, the same proportions will be used. If two unit bets are dictated at +1 and full Kelly, two unit bets need to be bet at +1 if the unit bet is 1/10 Kelly.

I agree the existing software makes substitution simpler but the optimal ramp will always remain the optimal ramp.

I know you've spent some time studying this, so I went back and reread many old posts on this subject. I don't believe there's a real consensus on what the word "ramp" means, but I do believe my definition is closer to the common usage. None of the classic posts on optimal betting (including yours) uses the word "ramp" even once!

The ratio of the specific unit bet to all other bets at higher advantages.

I'm still not sure if your "ramp" is a set of ratios (you can't really have one ratio to "all other" bets), or the quantity "A" introduced by Harris when going from unit bets to actual monetary bets in the real world, or the quantity (win per hand)/(SD per hand) you use in your analysis, or perhaps even the reciprocal of that.

I'm afraid even your definition of "unit" is not universal. I know it corresponds to the BJRM usage, but I think most red/green/black chippers, when asked "what is your unit" would answer 5/25/100 dollars. In fact, people often report wins and losses in terms of "units," which conflicts with your usage.

To be honest, I wish BJRM made no reference to these esoteric units. It's unnecessary, and I think it confuses some people. It could all be done in terms of units of one, or else let the user specify his own unit for convenience.

My definition of ramp corresponds roughly to the usage in KO Blackjack. It's something some people actually use at the tables. For any given optimal betting scheme, in the range between minimum and maximum bet, you can generally calculate the amount to bet as: (TC-k)xR, or TCxR - K, where k is a constant function of house edge off the top, the floating advantage, etc; K = kxR; and R = what I call the "ramp." It won't result in perfectly optimal bets, but it's quite close enough, considering rounding issues. It allows me to go from good games (with late surrender) to poor games and keep roughly the same ROR without memorizing a whole new bet schedule.

So my "ramp" changes according to the quality of the game. In fact, I'd bet if we let the issue drop, then take a poll three months from now, asking GC members "For a given bankroll and ROR, should your betting ramp change if the game(s) available markedly improve or deteriorate?" the overwhelming majority would say "yes."

Sincerely,
ETF

Any complex game has what I once called a Yamashita number which generalized the concept of the summation of Ev's times frequency divided by the summation of variances times frequencies. This number defines the percentage of bankroll for the unit bet (and all other bets because they are already defined in terms of the unit bet). That value provides the fastest growth for the predefined game. That is if I have decided I will bet 2 at +1, 4 at +2, and 8 at +3 and above, the Yamashita number is calculable and is better to use than any other unit bet *for that defined betting strategy*.

But that only starts the inquiry. My 1,2,4,8 pattern may be suboptimal as to an eight spread. A better pattern for the characteristics of the game being played might be 1,2,4,6,8 peaking at +4. That pattern might give a higher (Ev^2)/(Var^2) and that is the pattern which should be sought. Two things, the unit bet and the ratio of bets at different counts to the unit bet are maximized. That pattern is also calculable, notably on BJRM but in other ways. Some time ago I distributed and published a program which came up with the same results using a precise method rather than the brute force BJRM uses.

These ratios are independent of whether one is betting full Kelly (the Yamashita number) as a unit bet or 1/3 Kelly as a unit bet. The cards do not know what percentage of bankroll is being bet, only the bankroll knows that. I might be sitting beside DD' betting a dime unit bet and he might be betting a hundred but we would be using the same ramp and we might both be playing to the same ruin.

Certainly, one has to round in a casino unlike the calculation of SCORE which is a purely ranking tool but it has been found departing from the optimum theoretical ramp which might dictate a 3.7 unit bet at +2 does not have a great effect on win rate. The theoretical ramp still remains the best starting point and this ramp is totally independent of what relation the unit bet has to the Yamashita number (assuming, of course, table limits are not a factor).

My only point was that our words should follow common usage, or if they don't they need to be carefully redefined for each new discussion. It's a little confusing to say "The optimal ramp can be calculated ..." if your definition differs from the usual one.

If I understand you correctly, the "ramp" you speak of is a set of ratios of a theoretical unit to units bet at various counts. I don't think the average reader would ever guess that. Actually, wouldn't it be simpler to just say "the set of numbers of units bet at the various counts"? We're taking ratios to 1, correct?

I did find one post of MathProf's where he speaks of "ramping up" a betting schedule in proportion to bankroll. :-)

ETF

At least DD' and I have been using the term "optimal ramp" but your way of putting it is very possibly clearer. I think DD' coined it but perhaps it was me or someone else. There is an optimal "number of (unit) bets" for each count in any blackjack game using a specific spread and that figure is calculable but if you are a sissy you can use BJRM or similar programs to calculate it for you.

The point is the ratios of bets at specific counts are invariant, whatever fraction of Kelly (the Yamashita number or the number Brett has defined as the EKB (equivalent Kelly Bet)) is being bet. DD' uses about 1/3. If I ever go back to playing using my own funds only I will probably use 2/3 which translates to about 5% ROR. But if DD' and I were sitting side by side and both had done our homework correctly and were using the same spread and same system, we would both be betting the same multiples of our unit bets at each count.

The best I remember, the language of a "bet ramp" which is a nice description was first used in KO Blackjack and IMHO it can be successfully morphed into the term "optimal ramp" to describe that concept.

Could you elaborate a little more on systems besides Kelly?

The reason Kelly is of theoretical importance (or one reason among many) is that IF you use "proportional betting" (ie. revise your betting schedule in proportion to your bankroll whenever it changes significantly), then Kelly will beat all other proportional betting systems. Eg. You will PROBABLY have more money, in a sense that can be made precise, and you will reach any fixed target in a shorter average time. Your ROR will be ZERO, as it is with all proportional betting system.

However, MOST blackjack players DO NOT revamp their betting schedule at frequent intervals. It's simply too much hassle. If you don't resize at all, Kelly gives a 13.5+% ROR, which is higher than most people can tolerate. Even if you revamp frequently, Kelly results in enormous swings in bankroll. It assumes you have NO INTEREST in your bankroll, other than to leverage it for future growth. Most people aren't built that way. Most people get a little attached to their winnings.

However, if you just make up your mind to resize your bets if you should you lose HALF your bankroll, your ROR comes down to about 7% (somebody can remind me of the exact figure), which isn't too terrible. There are many other ways to proceed. It all depends on how much of a risk you are willing to take with how much money. It's a personal decision -- but you need the proper tools to evaluate your decision before you start. You should know your bankroll, your EV, and your ROR before you sit down to play your first hand.

ETF

If one says they spread 1:10 with a ramp:1,3,6,10, it means that they use 1 as the base bet with the max of 10 @+3. Another 1:10 ramp might be: 1,5,10. The optimal ramp is the method of getting from min to max that maximizes DI or minimizes N0. This is independent of bankroll and not entirely the same as Kelly optimal, which may call for the max earlier if bound by table limit constraints. In any case, the ramp is the progression of intermediate bets between the min and max. Unless otherwise specified, the first bet is generally the negative ev bet and the second step in the ramp is the one made at +1TC, or first positive ev count.