Information exists only when the sender is saying something that the recipient doesn’t already know and can’t predict. Because true information is unpredictable, it is essentially a series of random events like spins of a roulette wheel or rolls of dice.
The more improbable the message, the less “compressible” it is, and the more bandwidth it requires. This is Shannon’s point: the essence of a message is its improbability.
The gambler should measure success not in dollars but in percentage gain per race. The best strategy is one that offers the highest compound return consistent with no risk of going broke.
it is possible for a bettor to compound wealth at a certain maximum rate, with virtually no risk of ruin. The have-your-cake-and-eat-it-too feature of Shannon’s theory also applies to gambling.
The gamblers dilemma: if all odds are the same, you will win and lose at the same rate, but since you don’t have infinite money, you will eventually be stuck at zero and have to checkout the system
The systems to avoid the lose all dilemma of gamblers:
- Don’t bet!
- Double up until you win: 1 start, and each double will make your money back plus one dollar, but it can exponentially get you to the gamblers dilemma, unless you reserve say 10% not to go on the bet each time
- You bet is ALL horses, by percentage of the chances each has, based on your best bet. One of them HAS to win, so you will not go bankrupt EVER. In the long run, “bet your beliefs” will earn you the maximum possible compound return—provided that your assessment of the odds is more accurate than the public’s. But it only works if you don’t have to pay a fee for betting. And if you can in fact bet in ALL horses at the same time.
- The Kelly’s formula: edge / odd. Odds are what the public marketplace is telling you. This horse has 1 on 5 chances to win, therefor it gives you five times your money if you bet on him and he wins. The edge is the “inside trader” information only you have. If it is telling you this horse will win, and you trust it 30% due to equivocation or signal errors, and you bet $100, and the same horse and the same information can be applied in three bets in a row, you have the potential to triple your wager to $600, because of the 5 odds multiplier, and potentially lose $400 in the process, but you still up $100. In this case the edge is how much money you are going to make divided by how much money you bet: in other words $100 / $100 = 1. So plugging that in the final number: 1/5 , which means you bet 20% of your wager. The beauty is that even if the “inside information” was wrong, you won’t lose but 20% of your initial money. Notice that the only time you bet 100% of your initial wager is when your edge is perfect: meaning the winning horse information you possess is perfectly reliable, but you can still bet with imperfect odds, and automagically protect losing it all.
The “edge” doesn’t necessarily means cheating, it just means knowing more that the public, and assigning a decent level of equivocation to that knowledge, therefore preventing you from wagering all your money by this being a fraction, by definition.
The Kelly’s formula also guarantees the higher returns, because, as the money grows, so does the ratio of the bets. The Kelly system manages money so that the bettor stays in the game long enough, without having to bail due to hitting zero, for the law of large numbers to work (when large probabilities will eventually happen and win you the bucks)
You are unlikely to get an edge out of what you see in the news. The edge means information you have and most others don’t. It doesn’t mean illegally: your own research could be an edge. How good of an edge? your bets will tell you.