Suboptimal Bets, Liquidity Traps & Real Estate
Suppose that two insane billionaires offer you great bets. Billionaire A has a 70% chance of winning (double your bet) and 30% chance of losing (lose your bet). Billionaire B isn’t quite as insane … you have a 2/3rds chance of winning. Being Billionaires, they’ll take whatever stakes you can scrap together.
But A has a catch. It’s a single event. B, on the other hand, is willing to make three tries. Like all Billionaires, they are insanely jealous and suspicious of each other, so if you bet with one, the other won’t deal with you.
The best bet, in terms of expected value, is to wager as much as you can afford to lose on A. But a much better long term strategy is to take that amount, divide it into 3 piles, and place three wagers with B. That’s because your odds of going broke are 30% with A, and a mere 1/27th (under 4%) with B. Of course, your “Ideal” Billionaire would give you some odds (not much, say a 51% of winning) and then take as many bets as you care to place. (Of course, better odds are still better, but you get the point).
The public, by the way, is the ideal billionaire for Las Vegas, State Lotteries, and the like.
But if you generalized the insane billionaires, so that they allowed N bets, you could figure out what the ideal betting strategy would be. You want to grow your bankroll, but the I.B. will go on hot streaks, so you don’t want to bet too much on each bet. But if you bet too little, it takes too many bets (which may take up your time, or risk I.B. getting bored with you and leaving). I believe Poker Theoreticians have solved this problem, assuming you have some Expected Value for your time playing.
Anyway, I was thinking about Acquire, and it occurs to me that you are trying to solve the same basic problem. All the chains will appreciate, but you can only place so many bets at a time. Placing a big bet (3 shares) on company A precludes you from betting big on B. Worse yet, each bet doesn’t resolve instantly, so if your money stays tied up, not only do you have to decide between A and B, you have to worry that either A or B may preclude you from taking bets C, D and E down the road. You’ve run into a liquidity trap — good investments and no money. You lose.
Of course, games aren’t the real world. If I earn a crushing 20% per year safe investment, I don’t lose because someone else squeaked out 22%. But in a game you do. Winner takes all. The net result is that, if your first bet won bigger than everyone elses, you can switch to the slightly lower, but much less swingy return on investment. The worst your early investments failed, the more volatile high-risk/high-reward bets you take later on. If you aren’t winning, betting all of your money hoping for a merger before your next purchase is reasonable.
Of course, in the actual game you probably don’t assign numbers, just a gut feel (“Imperial will fold into American pretty soon and I can take 2nd place, or I could lock up world wide, which will likely be 31+ by the end of the game…”), but the idea holds.
More idly, I was thinking that Acquire had everyone a big winner, but if you assume it represents ~40 years of business (say, 1910 to 1950). You start with $5.5k (I think), and end with ~$50k (if you win), but by the inflation calculator that has a real value of about $20k of starting value, which is a nice steady three and a quarter percent real rate of return!