There has been a lack of helpful posts lately, and I was curious as to what the rest of the CC community uses, so I decided to combine the two into a post that hopefully people will enjoy and possibly learn from. I tried to make this short(er) to make this as simple as possible for those not already familiar with SCORE/CE, but if you don't feel like reading this, you can just respond to the poll.
I first want to state my credentials, as they are not as appreciable as many other posters on this site. I have been playing BJ for about 2 years, 1.5 of which as a (attempted) card counter. I use the zen count with a full deck divisor (original zen) using approximately 60 indeces. I have an Every Man For Himself team with my cousin, although there is a bit of expansion occurring at the moment. We have a 14k bankroll and when we play, we play with a 1.83% RoR, although not necessarily half kelly. While I am not completely studied in the mathematics of probability and risk analysis, I believe that I know enough to help others choose between games that are available to them.
There are advantages to both SCORE and CE, as well as disadvantages. Depending on what you want to evaluate, you may want to choose one over the other, as explained later.
SCORE (Standard Comparison of Risk and Expectation)
-------------------------
For those of you who read Don Schlesinger's Blackjack Attack (an excellent book), D.S. introduced the idea of SCORE to find a way to make an objective comparison between games and count systems. The basic definition of SCORE is what kind of win rate you can expect with a $10,000 bankroll, playing at full kelly (13.53% RoR) at 100 hands/hr. Most players wouldn't not want to play with such a high risk of ruin, however, since this is just a tool to compare games, it works just fine. SCORE is a perfect tool to use when comparing games with different rules/pen/count systems/spread, as comparing SCOREs can immediately tell you which situation can give you the best win rate for the same risk when disregarding restricting qualities like heat or table limits. Its also excellent for sharing the conditions of games with other players that do not have the same bankroll or risk utility. While it is great for comparing games, problems arise when some real world situations occur. However, most of the problems are fixed with c-SCORE (custom-SCORE), as they are able to reflect custom betting patterns.
CE (Certainly Equivalent)
-------------------------
The basic definition of CE is the minimum amount of money that you would be willing to accept in return for not playing an advantageous game. It takes into consideration your current bankroll, kelly factor, bet size, win rate, and the variance of the game. Although not suggested, one can use CE to decide whether to work for a salary or play an AP opportunity. If CE > salary, you would rather play. Note: if you are going to do this, I would assume that you would have a very low risk tolerance and therefore should be reflected with your kelly factor. CE is a great tool for deciding between games that you, personally, are going to play, since it reflects all the conditions that are relevant to you. It also tells you if you are over-betting (CE/WR < .5) or under-betting (CE/WR > .5). However, CE does not reflect your growth potential to your bankroll with the defined spread (although a kelly player will be playing with a CE/WR ratio of .5).
Most card counters already bet according to a kelly utility function, therefore most of the time, CE and SCORE will agree with each other when choosing between games (If not I highly suggest doing so). The most notable difference between CE and SCORE can be seen an a game where a player with a very large bankroll is playing at a table with low limits (Ex: 50k BR on a 10-100 table). (S)He will probably have an extremely aggressive spread (min bet at -EV hands, max bet at all +EV hands). This bet pattern will generate a low SCORE, but a high CE.
SCORE Advantages
While I could think of only the one disadvantage for CE, this is a very important one to notice. A high CE may have a strong win rate, but it may also take a very long time to get there. In the end, it is a personal decision in what you want to accomplish. Hopefully this will help you make your decision. If there are any additions that others would like to add, feel free to comment.
I first want to state my credentials, as they are not as appreciable as many other posters on this site. I have been playing BJ for about 2 years, 1.5 of which as a (attempted) card counter. I use the zen count with a full deck divisor (original zen) using approximately 60 indeces. I have an Every Man For Himself team with my cousin, although there is a bit of expansion occurring at the moment. We have a 14k bankroll and when we play, we play with a 1.83% RoR, although not necessarily half kelly. While I am not completely studied in the mathematics of probability and risk analysis, I believe that I know enough to help others choose between games that are available to them.
There are advantages to both SCORE and CE, as well as disadvantages. Depending on what you want to evaluate, you may want to choose one over the other, as explained later.
SCORE (Standard Comparison of Risk and Expectation)
-------------------------
For those of you who read Don Schlesinger's Blackjack Attack (an excellent book), D.S. introduced the idea of SCORE to find a way to make an objective comparison between games and count systems. The basic definition of SCORE is what kind of win rate you can expect with a $10,000 bankroll, playing at full kelly (13.53% RoR) at 100 hands/hr. Most players wouldn't not want to play with such a high risk of ruin, however, since this is just a tool to compare games, it works just fine. SCORE is a perfect tool to use when comparing games with different rules/pen/count systems/spread, as comparing SCOREs can immediately tell you which situation can give you the best win rate for the same risk when disregarding restricting qualities like heat or table limits. Its also excellent for sharing the conditions of games with other players that do not have the same bankroll or risk utility. While it is great for comparing games, problems arise when some real world situations occur. However, most of the problems are fixed with c-SCORE (custom-SCORE), as they are able to reflect custom betting patterns.
CE (Certainly Equivalent)
-------------------------
The basic definition of CE is the minimum amount of money that you would be willing to accept in return for not playing an advantageous game. It takes into consideration your current bankroll, kelly factor, bet size, win rate, and the variance of the game. Although not suggested, one can use CE to decide whether to work for a salary or play an AP opportunity. If CE > salary, you would rather play. Note: if you are going to do this, I would assume that you would have a very low risk tolerance and therefore should be reflected with your kelly factor. CE is a great tool for deciding between games that you, personally, are going to play, since it reflects all the conditions that are relevant to you. It also tells you if you are over-betting (CE/WR < .5) or under-betting (CE/WR > .5). However, CE does not reflect your growth potential to your bankroll with the defined spread (although a kelly player will be playing with a CE/WR ratio of .5).
Most card counters already bet according to a kelly utility function, therefore most of the time, CE and SCORE will agree with each other when choosing between games (If not I highly suggest doing so). The most notable difference between CE and SCORE can be seen an a game where a player with a very large bankroll is playing at a table with low limits (Ex: 50k BR on a 10-100 table). (S)He will probably have an extremely aggressive spread (min bet at -EV hands, max bet at all +EV hands). This bet pattern will generate a low SCORE, but a high CE.
SCORE Advantages
- Normalized bankroll/kelly factor/speed gives easier insight to the quality of the game
- SCORE does not change with different bankroll size or kelly factor
- Utilizes kelly proportional betting to obtain most objective comparison of game quality
- Normalized to your specific needs
- All game factors considered (rules/pen/count strategy/speed/bankroll/risk factor/table limits)
- Personally specified bet pattern
- No indication of over/under betting
- Does not consider certain table conditions
- Normalized to specific conditions (BR, game speed, kelly factor)
- Does not evaluate growth potential
While I could think of only the one disadvantage for CE, this is a very important one to notice. A high CE may have a strong win rate, but it may also take a very long time to get there. In the end, it is a personal decision in what you want to accomplish. Hopefully this will help you make your decision. If there are any additions that others would like to add, feel free to comment.
Last edited:
