1/ Fortune's Formula (William Poundstone)
"Even unlikely events must eventually come to pass. Therefore, anyone who accepts small risks of losing everything eventually _will_ lose everything. The compound return rate is acutely sensitive to fat tails."
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2/ "Looked at another way, a coin toss is physics. An event is random only when no one cares to predict it.
"Thorp discovered that he was able to guess approximately where the roulette ball would land: The wheel was slightly tilted. This made the ball favor the downhill side."
"Thorp discovered that he was able to guess approximately where the roulette ball would land: The wheel was slightly tilted. This made the ball favor the downhill side."
3/ "Money management is the tricky & all-important issue of how to extract the greatest profit from a favorable opportunity. You can be the world’s greatest poker player, but if you can’t manage your money, you’ll end up broke. Sadly, almost everyone goes broke in the long run."
4/ "Early in this random-walk chart, wealth hits zero (line marked “Bankrupt”). Had this happened in a casino, the gambler would be tapped out. The right part of the chart is therefore irrelevant. He’s out permanently.
"It is possible to go broke even with a positive edge."
"It is possible to go broke even with a positive edge."
5/ "A greedy better might be tempted to bet his entire bankroll on the basis of the inside tips. But tips are not sure things. Sooner or later, a favored horse will lose. The gambler who always stakes his entire bankroll will lose everything the first time a tip is wrong."
6/ "Kelly concluded that a gambler should be interested in compound return, measuring 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."
7/ Given zero transaction costs, "apportion your bets among horses according to your estimate of each one’s chance of winning.
"This way, you bet on every horse and will never be completely broke. If you believe War Admiral has a 24% chance to win, put 24% of your capital there.
"This way, you bet on every horse and will never be completely broke. If you believe War Admiral has a 24% chance to win, put 24% of your capital there.
8/ "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.
"The bets on the horses you think will lose are a valuable insurance policy.
"The bets on the horses you think will lose are a valuable insurance policy.
9/ " But “bet your beliefs” is of little use at a real track, as U.S. racetracks skim anywhere from 14-19% of the amount wagered.
"The Kelly formula says to bet edge/odds of your bankroll on each bet."
For a portfolio, Kelly sizing uses Sharpe ratios:
"The Kelly formula says to bet edge/odds of your bankroll on each bet."
For a portfolio, Kelly sizing uses Sharpe ratios:
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10/ "Elwyn Berlekamp, who worked for Kelly at Bell Labs, remembers Kelly saying that gambling and investment differ only by a minus sign. Favorable bets are called “investments.” Unfavorable bets constitute “gambling.” "
11/ "Shannon suggested that Thorp use Kelly’s formula to decide how much to bet on blackjack based on how favorable the deck was. Despite the theoretical protection against ruin, they realized that there are many variables in casino play."
12/ "In a moderately favorable situation, a card-counter might have a 51% chance of winning. The edge is 2%, so the Kelly formula says to bet 2% of the bankroll. (This estimate is not exact because of the features of splitting pairs and doubling down.)
13/ "They won $500 in 15 minutes at at a $500 maximum table. Then the dealer pressed the secret button.
"An army of unseen operatives inspected the play from behind miles of one-way mirrors. Dealers were expected to inform Smith when someone was winning too much too fast."
"An army of unseen operatives inspected the play from behind miles of one-way mirrors. Dealers were expected to inform Smith when someone was winning too much too fast."
14/ "Betting it all only works until you lose.
"The martingale, which requires doubling a wager at every bet lost, can lead to rapidly escalating losses.
"Although it takes a whole to get started, Kelly betting causes wealth to grow fastest by making optimal use of capital."
"The martingale, which requires doubling a wager at every bet lost, can lead to rapidly escalating losses.
"Although it takes a whole to get started, Kelly betting causes wealth to grow fastest by making optimal use of capital."
15/ "Betting twice Kelly ('overbet') is treacherous. Due to a lucky streak, overbettor was briefly the best-performing of the systems early on (the little volcano-shaped peak at lower left). Then the overbettor’s wealth fell back to nearly zero and stayed there for a long time.
16/ "Were the simulation continued indefinitely, the wealth of the twice-Kelly bettor would fall back to the original $1 or less an infinite number of times.
"The Kelly system manages money so that the bettor stays in the game long enough for the law of large numbers to work."
"The Kelly system manages money so that the bettor stays in the game long enough for the law of large numbers to work."
17/ "Card-counting may be the greatest shill ever invented. Not everyone who read Thorp’s book was able to apply the system consistently enough to gain an advantage. For every successful counter, there were hundreds who merely thought they could count cards successfully.
18/ "Card-counting got more attention than the more abstract Kelly formula.
"Those who skimmed Thorp’s book probably did not understand the importance of scaling bets to bankroll. It is a natural impulse to bet big when the deck is hot. For many, this must have been costly."
"Those who skimmed Thorp’s book probably did not understand the importance of scaling bets to bankroll. It is a natural impulse to bet big when the deck is hot. For many, this must have been costly."
19/ "Use of multiple decks makes counting less profitable. Because the end cards are never dealt, the concentrations of good cards that occasionally occur at the end of the deck never come into play.
"While playing at one Las Vegas strip casino, Thorp was offered a drink.
"While playing at one Las Vegas strip casino, Thorp was offered a drink.
20/ "He had problems concentrating and staggered up to his room. His eyes were dilated. It took about eight hours to wear off. The next day, Thorp returned and was offered another drink. He asked for water this time. “It tasted like they’d dumped a box of baking soda in it.
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