The benefits of a team are:
1. You can combine bankrolls, so each person can bet as if the entire bankroll is his.
2. You get into the long run faster.
3. Teammates help you train more effectively, improve morale, enable task specialization.
How do blackjack teams work when it comes to splitting the result?
Incentives matter. A lot. Any agreed-upon way to set things up can work for a while, but after a little while problems will crop up. Blackjack banks are an ideal laboratory for devising and testing compensation schemes.
Here are common problems encountered:
1. Many times, players are rewarded only when the bank wins money. This is analogous to the usual payment scheme for hedge fund managers, who get 20% of the win, and none of the loss. There are two problems with this:
Desertion effect: If the bank is losing badly, players have little financial incentive to play, since every dollar they make at that point goes to investors. Essentially, players have an option whose value has diminished since it’s so far out of the money. Hedge fund managers can swing for the fences with a high-variance strategy, but this is not an option for card counters.
Bandwagon effect: If the bank is winning a lot, players will flock to the tables trying to grab a piece of the overly generous pie. This increases the likelihood of burning themselves and the game out, in a replay of the tragedy of the commons. Player’s option is not only deep in the money, under some schemes it’s greater than the value of their play.
You could try to get players to invest, so that their interests would not be completely dominated by their view as a player. But new players, or ones without money, would have a problem. This can be done somewhat by paying players shares, so that when the bank is down, they have an investment.
If you pay players a fraction of their return as salary, you can ameliorate the desertion effect (but the bandwagon effect remains). In the scheme that MIT used from 1994 onwards, we paid players 25% of the CE of the game as salary.
It was a tiered payment scale. First, player pay at 25% of CE. Then investor return at the same amount. Then investment return of 18% (arbitrary). Any remainder was split 50-50 between investors and players. It worked fine when the returns were strong, but when the play diminished and the 18% became onerous, the bank sputtered. Also, the bandwagon effect was strong.
We tried the “infinite bank”: Break the bank after each trip, paying players on a free-roll basis. This requires good reporting and record-keeping, since the percentage paid to players will be quite sensitive to the statistics of the play.
Although it seemed mathematically elegant, it had a significant flaw: It hurt team morale, because each trip made no difference to the players who weren’t on it. The desertion and bandwagon effects are still there, just limited to a single trip. In particular, desertion manifests itself in why should a player go to the trouble to negotiate a loss rebate? Also, in the middle of a losing trip he may bail, instead of trying to dig out.
You can avoid these problems by scheduling mass attacks every trip, so that everyone is involved, and it’s unclear to the individual players how they stand. Play until either you win or get thrown out. This is what the Greeks did, and it worked fine until they burned out the games.
2. If you pay each player at the same rate, there is little incentive for a less skilled player to improve his skills. The difficulty is in measuring the contribution. How do you decide how much a BP gets vs a spotter? A GBP?
For players in the same category, you adjust pay for each player based on the errors made during checkouts, and metrics based on effectiveness. Spotters, for example, could be paid according to: # of shoes spotted + 5*(# of shoes played). We never tried this. It may be that objective measurements cannot capture the full behavior and that players would game the system in perverse ways (including sabotaging their teammates, or being uncooperative, or keeping performance secrets to themselves). If so, perhaps a (mandatory?) bonus rewarded at the subjective discretion of the managers might do the trick.
In Blackjack Forum, Don Schlesinger wrote an article on the incremental value of each additional spotter. It makes various assumptions, but in any case, it’s a good starting point. The BP-spotter split can be computed using this as a basis, adjusting for specific conditions.
3. If you cover expenses (like airfare, hotel, car rental, legal costs), a player has no incentive to keep costs down.
Solution? Charge each party his proportional share of the expense. So if players get 40% of the win, charge them 40% of the expense. Do not aggregate this in the win figure; the statistics on the games are not necessarily accurate (due to fallible memory, unnoticed player mistakes, and modeling error), but expenses are.
4. If you don’t pay for management, you won’t get any. The result is minimal recruitment and training, no development of new games, poor record-keeping, long delays in pay, haphazard trip planning. In the long run, the demise of the team is likely. Accounting and training take by far the greatest number of hours, but they are relatively low value-added per unit time activities that can be automated to a great extent. Game development is a high value-added activity that is crucial in the long run. This is for at least 2 reasons. One, a single approach gets burned out after a while. Two, you can’t use the money once your bankroll exceeds a million or so. Blackjack, however, is not the only way to make money.
Solution? Come up with measurements for each of the things that are valued and pay for them. For example, accounting, trip planning, record-keeping, and general management are important, but their value is limited by the amount of play gotten. Perhaps 5-10% of the value of the play should be devoted to that. Recruitment? Each recruit’s shares in his first 3 months of play are matched by the investors to his recruiters. Training? 5% - each training session attended gets some credit. Game development? 5%, subject to games developed making money greater than the amount paid for them.
These percentages are ballpark estimates.
5. Spinoffs. Golden handcuffs via vesting or benefits can be used. Otherwise, personality conflicts and self-interest as investors will tend to break up the group.
6. Compensation for game development: pay developers dry shares on the game in question. If it makes money, so do they. Practically speaking, this can be difficult if accounting cannot distinguish between result due to counting or result due to technique #4, but an estimate can be made on the basis of random spot checks or simulations.
Intangibles like the camaraderie between teammates (which can lead to fruitful collaborations) are hard to measure, but they have real value. There are also longer-term results from play, such as comps, or return from movie or book deals, lawsuits. And results from research will take some time to work themselves into play return. Measuring the value of such assets is not easy, but a share-based scheme puts people into the long run and makes this measurement less important.
Creating objective measurements of performance is not easy, but can make things run more or less automatically. To head off a huge problem or conflict, everyone must agree in principle that there must be a measurement, and that this measurement can be reviewed and amended. If the measurement has inherent uncertainty, you can use utility analysis to set a CE for it.
The percentage split between investors and players is rather arbitrary, depending mostly upon the alternatives available to each, or perhaps philosophical arguments. MIT generally split it 50-50.
If recruitment and training, game development are not an issue because all the players are experienced and knowledgeable, there are simpler methods. If everyone is adequately bankrolled, you can simply split the result 1/n for each of the player-investors. This generally requires a strong underlying game, and limits that are generally far below what the group could bet without constraints. Hole-carders do this on a routine basis.
If a player is not so well-bankrolled, the player can take a free roll. You decide what long-run percentage of the result a player will receive. Then you gather statistics to compute the distribution of results. Assuming a normal distribution with an estimated mu and sigma, you can compute the percentage of win that corresponds to that long-run percentage. For most games this percentage settles to a particular value fairly quickly. But if varying conditions cause your edge and variance to also vary, gathering the statistics can become daunting.
A counting game is weak, about 1-2% edge to the players. This is close enough to zero that errors can cause some players to play a losing game. The more likely problem is that errors (everyone makes them) diminish the quality of the game significantly enough such that a much larger than expected bankroll to withstand swings is required — 800 unit downswings are not unheard of. Most players are under-bankrolled, and will tap out as a result. Proper money management is required to allow your edge to work for you.
Money management? What’s that? Basically it’s how much you bet when you have an edge. If you bet too much you’ll likely go broke. If you bet too little you are leaving money on the table. What’s the right amount? The short answer is to bet proportional to your edge, inversely proportional to your variance. If you bet an amount bankroll * edge / variance (full kelly), this is very aggressive, leaving little room for error. Due to inevitable errors, you’re better off betting a fraction of this. MIT chose to bet at 30% of full kelly. And this is for a mathematically solvable game. For investors in the markets, a much tougher game with many more unknowns, betting half as much as that is probably pretty reasonable.
Here’s my current thinking on this: Pay players 40% of the CE as shares, valued at the pre-trip bank level. Do not allow players to cash out more than half their shares after any bank. This puts some of their skin in the game for the long term. Pay out management shares on the same basis, under the following categories: 5% R&D, 5% accounting / record-keeping / trip planning / general management, 5% training, 5% recruitment. The remaining 40% goes to investors.
A share-based scheme makes it simple in theory to raise or reduce capital investment as needs require. Assuming that capital can be raised and disbursed quickly, play for a short period can easily be accommodated.
Issue dividends if and when capital on hand exceeds what can be used.
Actually, this scheme does not require that the bank ever be broken. This alone is a benefit, since we lost a fair amount of play as a result of reforming each bank and even stopping play in the middle of a trip. Also, a limit on the maximum shares a player can cash amounts to a vesting scheme. Perhaps no more than half of a player’s compensation could be cashed out every half year, unless the amount remaining was under some value not worth worrying about anymore, say $100 or so.
This method is quite sensitive to the estimation of the value of the game. If you play a game whose value is very sensitive to conditions or mis-reporting, it would be a bad method. If you play a mix of games, some of which are more sensitive than others to these problems, it would be easy to pay some players far more than their play was worth. This could easily destroy a team.
Perhaps a better way would be to use Bayesian techniques to estimate the expectation and variance of a game. Some games have zero variance, other games have huge variance, some games are hard to estimate the value of. Under the Bayesian framework, you can account for all this. You state your prior, then as results come in you modify that prior, using that value as the basis of pay. It’s important to include all relevant parameters that may change the value in the Bayesian analysis. This may prove impractical under all conditions, the Achilles heel of the approach.
How can things go wrong?
The biggest problem is poor quality play. This includes choosing to play under poor conditions, modeling error, and carelessness with handling money. The next biggest problem is poor record-keeping and accounting. If a player’s game is materially different from what he reports, someone (most likely everyone else) is getting screwed. If you forget to record a transfer of 10K (could easily happen in the heat of battle, if a player transfers money surreptitiously in the middle of a session), the player who is 10K short can feel rather disturbed.