The Blackjack Page

Team Money Management

A critical aspect of successful team play is the development of a proper betting schedule and the adjustment of that schedule as you win or lose; something I loosely call money management. I define it that way because I’m not going to talk about cash management – the movement of $$$ within the team before, during and after playing sessions – although it’s an important part of any team’s strategy.

How much to bet and when is, of course, a concern to any Blackjack player but to the card counter it’s why we do what we do. Any sound counting system will identify the advantage (or lack thereof) you have on the next hand and that in turn can tell you how much to bet. Exactly how much that bet will be depends upon several things, like how big your bankroll is, what the table’s minimum and maximum bet limits are and how many $$$ you can put out there without attracting too much attention from the “pit critters”. A minimum bet attracts little or no attention, whereas a table maximum bet probably will. While camouflage may be important in many playing situations, I’m going to present only the mathematics of team betting without regard as to whether or not your team will be able to actually place the bets, but it’s something you need to think about as we go through this.

The money management principles for a team fall into two main categories: those where each team member plays at a separate table (the “traditional” method) and those where team members sometimes play together at the same table (the “big player” method). I’ll cover the math for a traditional team this time and the math for a big player team next time.

As I mentioned in my first article on this topic, the most appealing concept of team play is the fact that each member of the team may bet as though the entire team bankroll was his or her own personal bankroll. In other words, if five players, who each have a $1000 bankroll, team up then each of the five may bet as though s/he had a $5000 bankroll and the “risk of ruin” (total loss of the bankroll) would remain the same.

Now understand, this doesn’t mean your team can go out there and start making max bets all over the place; there’s nothing about team play that guarantees you’ll win. You can still lose, but the ups and downs of your mutual bankroll will be smoothed out by the fact that you have five players in action at any given time. Those bankroll swings are what we call variance and it’s something you need to understand, be it as a “lone wolf” player or as a member of a team. The nice part is that it’s really simple.

A well-established means of determining how much to bet is to use the “Kelly Criterion”, which basically states that the growth of your bankroll will be most efficient if you bet a percentage of your bankroll that’s equivalent to your advantage on the hand. For example, if your bankroll is $5000 and your counting system indicates that you will have a one percent advantage on the next hand, a bet of $50, which is one percent of your bankroll would be appropriate. If you were to win the hand, your bankroll would likely now be $5050, so if your advantage is still one percent, you should bet $50.50 on the next hand. Should you lose the original $50 bet, your bankroll would now be $4950, so you should bet $49.50 on the next hand, assuming your advantage is still one percent.

Well, you can easily see the main problem presented by this proportional betting system. It will call for a different bet each time the bankroll changes and some of those bets will be impossible to place. Making a bet of $42.93 just isn’t practical at most Blackjack tables, not to mention such precise betting will undoubtedly tip off the pit critters that you’re up to something. Gamblers do not bet precise amounts – counters do – and we want to look like gamblers, right? But we can still use the Kelly method of betting by making a few adjustments so that we’ll at least appear to be more of a gambler than we really are.

The first adjustment we have to make involves the variance we have on each individual hand of Blackjack that we play. Variance is a measurement of all of the possible outcomes of a hand: lose one bet (most common), win one bet (less common), win one-and-a-half bets (a “natural”), win two bets (double or split), lose two bets (ditto) and so on. The variance of a hand is determined by what options the player has. In a game where doubling is restricted to 10 or 11, the variance will be lower than a game where you may double on any first two cards, for example. In other words, a “high” variance game will see you placing more bets on the table than a “low” variance game and we must account for that in adjusting the Kelly Criterion for our bankroll. While the precise variance of a hand can be calculated on a spread sheet like MS Excel, it can also be done through simulation. Better yet, I’ve done it for you and have converted that data to a more meaningful number.

For the vast majority of Blackjack games you’ll run into, a figure of 75% will serve as a proper adjustment to “Kelly”. What this means is that you should multiply your advantage by 0.75, then multiply that by your total bankroll in order to determine the proper bet. Going back to the first example, if your advantage on the next hand is one percent and your bankroll is $5000, “Kelly” says to bet $50 but Kelly was not created for Blackjack (He worked for Ma Bell and it was about transmission rates of data over a phone line.) Anyway, you should multiply that $50 by 0.75 and bet $37.50. Now you know how to determine the proper bet for any hand: Multiply your advantage by 75% and then multiply that result by your total bankroll. Now remember that you must subtract the casino’s basic edge from the edge your count is showing in order to arrive at your advantage. Generally, that’s about one-half of one percent, so if your counting method says you have a two percent edge at a True Count of 4 (like the Hi/Lo Count does), your actual edge at TC 4 is 1.5%. Multiply that by 0.75 and you get 1.125%. Multiply that by your bankroll of, say, $5000 and you get a bet of $56.25, a weird number that brings us to the second adjustment we need to make.

It’s not practical to bet in increments of less than $5 at most BJ tables and again I want to point out that precise bets are the hallmark of a card counter, which means we must round up or down so we look like the average gambler. Plus, it’s really not practical to constantly change the size of our bankroll after each and every hand, so we cannot be absolutely proportional in our betting. Proportional betting by the Kelly Criterion method implies that we will never go broke, but that might mean making a bet of $1.73 if our bankroll were to get very small. So we make a tradeoff by accepting a certain amount of “risk of ruin” in exchange for a more practical bet schedule. Under a typical use of the Kelly Criterion, our risk of ruin is 13.5% if we adjust the betting schedule whenever we have a 50% change in the total bankroll. So, if we make up a new schedule when we lose $2500 or win $2500 and we do reasonable rounding of the various bets, the probability of losing the entire bankroll is about 15%, which should be fine for most part-time teams. In contrast, many professional teams operate with a much lower risk of ruin percentage; I personally prefer two percent. Just remember that cutting the Kelly percentage slows the growth of your bankroll, but it also lowers the risk of ruin. On the other hand, going to more than two times Kelly will virtually assure you of losing it all.

Next time I’ll talk about the money management principles for teams using the “big player” approach, which is different in several ways.

See you then.

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