Shen Zhiyi was holding the tea cup, his eyes moved from Zhao Chen's cards to his face.
"So you brought us to the casino today to teach us a lesson?"
"I'll take you to play. Let me tell you a story."
Zhao Chen pushed the chips in front of the dealer, and he lost this round.
"What is that Kelly Criterion you just said?" Su Wantang asked.
"Kelly Criterion is a method of calculating the optimal betting ratio when the odds and winning rate are known.
The formula is f equals (bp minus q) divided by b, where f is the proportion of the bankroll that should be bet, b is the odds, p is the winning rate, and q is the losing rate.
For example, if the odds are one to one and the winning rate is 55%,
Then the optimal betting ratio is (one times 0.55 minus 0.45) divided by one,
It is equal to 0.1, which is 10% of the total funds.
Thorp uses a simplified version of Kelly Criterion at the gaming table--
The bet amount is adjusted according to the high card density of the remaining card pile. The more high cards there are, the larger the bet is.
He used the same logic in Wall Street and Hedge Fund - adjusting positions based on market signals and risk-return ratio.
The core idea of Kelly Criterion is that you only bet when the expected value is positive, and the proportion of bets cannot exceed the optimal proportion.
If it exceeds the optimal ratio, the long-term growth rate will decrease. If it is lower than the optimal ratio, the growth will be too slow.
Only by placing bets exactly as Kelly Criterion can the long-term maximum growth rate of your funds be achieved."
The dealer dealt another round of cards.
Zhao Chen looked at the hole cards and did the math in his head--
"Hachi. Place your bet."
He pushed the chips onto the table.
The dealer dealt the cards, and in the end Zhao Chen had 18 points and the dealer had 20 points, and he lost.
"But you lost the game just now." Su Wantang said.
"Yes. But the single result is not important.
The important thing is that you make decisions based on correct expectations every time you place a bet.
If you continue to bet in a situation with positive expected value, there may be fluctuations in the short term, but you will definitely win in the long term.
This is what casinos make money from - they don't need to win every hand, they just need to keep operating under their own rules of positive expected value.
In blackjack, the house edge is only about 0.5 percent.
This advantage is small, but with casinos opening hundreds of tables every day and running millions of games every year, a 0.5% advantage can turn into a stable profit with a huge sample size.
What Thorp did was to reverse his expected value from minus 0.5 to plus 1.5 through card counting--
From a person harvested by the casino, to a person harvesting the casino."
He took them to another table and continued placing bets.
This time he used five chips and won.
Played another round and lost.
I played another round, blackjack, and won 1.5 times.
Su Wantang was watching the chips circulating on the table and suddenly asked--
"Are you counting cards?"
"It doesn't count. The cards on this table are randomly shuffled, and the shuffler replaces the pile with a new card every round. There is no point in counting the cards.
I'm just telling the story of Thorp, not to win money."
He pushed the last few chips to Su Wantang and Shen Zhiyi,
"You guys try it. Everyone plays a round. If I lose, it's mine. If I win, it's yours."
Su Wantang sat in Zhao Chen's seat, and Shen Zhiyi sat down next to her.
The dealer reshuffled the cards and dealt them. Su Wantang looked at the hole cards, calculated them in his mind, and placed a bet as Zhao Chen taught her just now.
At seventeen o'clock, trading is suspended.
The banker lost at nineteen o'clock.
Shen Zhiyi took the chips and placed the same bet.
The dealer dealt the cards and she got an ace and an eight.
Zhao Chen said beside him - "At nineteen o'clock, trading will be suspended."
The dealer turned over seventeen points, the dealer asked for a card, turned over twenty-three, and busted the card. Shen Zhiyi won.
She put the winning chips on the table and did not continue to bet.
Zhao Chen looked at her and smiled.
"Is this your first time winning money at a casino?"
"This is also my first time in a casino." Shen Zhiyi put the chips in his pocket, stood up and walked next to him.
Zhao Chen also stood up and put away the remaining chips.
He led them away from the gaming table area, past the flashing slot machines and the noisy crowd, and walked to the promenade outside the casino.
Las Vegas The night wind blows from the direction of the desert, dry and warm, carrying the water vapor from the fountain show in the distance.
The New York-New York roller coaster roared overhead, and the passengers on the car screamed and hung upside down from the neon track.
Su Wantang walked on his left, and Shen Zhiyi walked on his right.
The three people walked slowly along the walking path of Las Vegas Boulevard, the floor tiles under their feet were illuminated by the lights.
The fountain of Bellagio is performing in the distance, and the water column rises to the highest point amid the sound of music and then breaks into a white mist.
"The story you told about Thorp today is not just for the sake of telling Thorp." Su Wantang turned her head and looked at him.
"I'm thinking about something.
Thorp can bring the mathematics of the gambling table into Wall Street,
It's because he believes that the market is like people. As long as the sample size is large enough, the probability will be on his side.
Regardless of the casino or the fund, the underlying logic is the same - find a system with positive expected value, and then place your bet according to Kelly Criterion."
"What is the difference between what you do on Era Vanguard and what Thorp does on the gaming table?"
"There's no difference. It's just that my card table is bigger than his."
Zhao Chen took Zisha Pot out of the soft cloth bag, sat down on the stone bench next to the corridor, and poured a cup of tea.
Su Wantang and Shen Zhiyi sat down next to him. The night sky of Las Vegas spread overhead,
The neon halo drowned out the stars, and only a few of the brightest ones were still faintly visible.
Zhao Chen picked up the tea cup and took a sip.
"Thorp proved mathematically that the dealer can be defeated.
But Beat the Dealer's method is not cheating, it's about understanding probability better than the dealer.
The same goes for investment. The way to beat the market is not to Inside Information, but to understand value better than the market."
Las Vegas The night wind blows continuously from the direction of the desert, carrying dry warmth and water vapor from the fountain show in the distance.
Su Wantang and Shen Zhiyi sat on either side of him. The three of them faced the fountain lights of Bellagio in the distance, like three quiet silhouettes placed in the same picture.
Tourists passing in front of them occasionally turn their heads and glance--
There are very few people sitting on the roadside drinking tea on the Las Vegas Strip, and even fewer people sitting with three people together without talking or playing with their mobile phones.
"Thorp is a professor of mathematics. But he's not the only one who has turned his academic background into an investing advantage."
Zhao Chen picked up the tea cup and took a sip, his eyes fell on the water column of the fountain in the distance.
"In Wall Street, for a long time, physicists and mathematicians were the least popular groups.
Analysts who graduated from business schools feel that they do not understand finance, and traders feel that they do not understand the market.
But what happened later proved that it was precisely those people who were considered to be 'uninformed about finance' who established Wall Street's most profitable fund."