Money Management

Let’s suppose that you have studied up on the distribution tables, the binomial or Poisson charts, and have amassed your handicapping and research tools to predict the outcomes of horse races or sporting events, or in the alternative, you have studied up on card games like blackjack and Texas Hold’em, and are ready to go. You are aware of the anatomy of a bet, you are a Type II player, and you are clear about how to evaluate bets financially by com-paring their terms to the physical expectation of the contingent event. All of this jargon makes sense to you. Congratulations!

So . . . what are you going to bet on, and how much are you going to bet? This section asks and answers those questions. There is still a little arithmetic here, but very little math and science. In fact, there really are no rules, just principles or rules of thumb.

Basic Assumptions

1. Loss Minimization. The assumption for the rest of this treatment (except for those rare circumstances when it might be explicitly relaxed) is that the player is not emotionally involved with any of the propositions placed before or sought out by him or her. Rather, the question whether to bet on a proposition is determined by the principle of minimization of losses. The extreme case of this principle is when there is no edge for the bettor (i.e., if the edge is zero or negative). The optimal bet is zero. Pure and simple.

Suppose the bettor has a hunch about the outcome, but no clear understanding of the physi-cal probability of the contingent event. This is just a special case of the negative edge. In the face of ignorance, the optimal bet is still zero. (Put differently, if the bettor is no more informed than a coin toss would be, it is important to recall that the house vig alone will turn a 50% bet to a negative edge.) It is not shameful to be ignorant. We’re all ignorant, depending on what the subject is. The difference between ignorant (betting a hunch when you just don’t know the probabilities involved) and stupid (betting when you know the edge is zero or negative) is important. Ignorance can be remedied.

Once there is an edge for sure, then the question of how big a bet to make becomes a relevant one. This would relate more to profit maximization than minimization of losses.

2. The Role of Risk. Just as the optimal bet in a negative edge situation is zero, the theoretical optimal bet in the face of 100% certitude would be infinitely high. Obviously the size of the bankroll is one practical limit. Another is that nothing is really 100% certain. A third limit is that the betting system -- the house or the rules of the game – has betting limits, and even in extreme circumstances will just not accept a global “all in” bet. In between the zero edge and the sure thing, the amount of risk will influence how a bet should be constructed. In general, the bigger the edge, the more money should be invested in it, as the ROI or profit is closer to a practical maximum if more is bet as the edge is increases. As the edge plummets to zero, so should the size of the optimal bet.

It has been said over and over, but it’s central to the concept for a Type II player: what cre-ates the reward in the first place is a gap. This gap, when favorable, is an edge. The gap in question is between the player’s understanding of what is true versus the rewards offered for a bet, which reflects someone else’s understanding of what it true (or bluffing). The bigger the edge, and the more certain one is of the size of that edge, the less risk is involved in betting.

3. Staying Power. In the world of business, often the company than can stay in the fray the longest will win the contract or the market or whatever was being disputed. Staying power is an important strategic asset. Even if a proposition promises nearly 100% certitude, and even if the edge is enormous, no one will recommend risking the whole bank roll. (Well, almost no one.) Methodical gamblers have a “maximum bet” in their mind, usually ex-pressed as a percentage of the bankroll, that can be put at risk on a single betting proposi-tion. The concept is not too hard: Even if the chance of a payoff is high, it will not be 100%, so there’s a chance of a loss. If the bet is lost, how much bankroll will be left to keep going with? Even though the Type II bettor always bets on positive edges, random variation can cause a string of losses, which, in the long run should balance out so the final situation is a net positive. If this is not so, then there has been some negative-edge betting going on. The bankroll has to be big enough to make it to the long run. One way to make the bankroll more elastic for that purpose is to be disciplined about a maximum bet. Most gamblers talk about 2% or 3% of the bankroll, but the “correct” number for a given person depends on comfort levels and skill of play. For the novice, a 2% maximum bet is not a bad idea for starters.

4. Diversification. Stock brokers advise investors to diversify. This tends to even out secu-rities risk. Since risk and reward go hand in hand in that field, the idea is to make a blend of conservative and risky acquisitions, thus “stabilizing” risk and also making income more predictable. This principle is harder to apply in gaming. For one thing, if the bettor bets more when the risk is lower (the edge is higher), a different “mix” of assets is occurring than in the securities example. Moreover, if the wisdom of a bet depends on an accurate assessment of the risk (the physical risk), then it makes sense not to diversify, but rather to concentrate on that area of gaming in which the bettor has the most reliable skill is handi-capping or otherwise finding and calculating his or her edge. There is also a consideration of transactions costs. It takes the same amount of effort and expense to place a $200 as a $20 bet. So diversification can have an expense attached to it if the betting transactions are thinly sliced. Within all those limits, however, most gaming experts do recommend that a person make several appropriately-sized wagers rather than one big one, probably because the accuracy of the bettor’s appraisal of his or her edge is not always perfect, and some di-versification will help to iron that out.

These principles are not rules. They are simply considerations in deciding how to bet. They help a gambler maintain a certain calm and comfort as the wagers unfold. Consistent with this idea of “guideline” rather than “law”, most professional gamblers say that they have two criteria to help them decide when and how much to bet. This is the minimum profit-ability that’s worth the trouble of chasing (also called the minimum edge), and the mini-mum amount that is worth playing for (also called the minimum amount of winnings). The minimum bet, therefore, is not a number, but a variable. It is the amount required to bet in order to win the minimum amount of winnings.