Chance and the market ( at least analysing chance is market related. Every market player should know the tenets of gambler's ruin.) I disagree that after ten heads the 11th toss has the same chance of coming up heads. I agree that runs do nothing to change the isolated event, but I disagree that is all that is being bet on. You have to bet on the total run, not on the event by event outcome. There is a time element to chance. Why does lurking by a non paying slot machine not work? Because it takes far too many reserves to test the theory. Testing the theory even with many machines that have been continously unsuccessfully tried to beyond the average payout time lag, is still subject to the the same overall chance.. tries times machines over average payout frequency is the same one machine or many, even on overdue machines...
What Scarne asserts is untrue:
1. Ed Thorpe did win the money he claimed he would in the time and with the 'reserve' betting fund he said he would need. Predicting outcome successfully, even with wrongly based theories, is a powerful arbiter of assessing scientific objectivity and validity.
2. it widely known that the methods he used of noting cards (that were less likely to favour the house and play progressed in a semi-Poincare scheme*) is mathematically sound statistics. In essence you count the number of times cards exceed a median card. This gives you the chance that as play progresses that fewer and fewer cards that favour the dealer will appear. That decks get depleted in this manner over time, given several outings allows every increasing stakes to be taken as play progresses. With an edge, however small, a cleanup is possible if you play a long time. Wins outnumber losses and stakes can be raised progressively, allowing a geometric accumulation of cash on a very small edge. If this did not work thent the Las Vegas houses themselves, working a mere 1% edge, would not exist. Las Vegas has fleeced suckers of 500 billion or more in cash since it started. Remember that brokers have a 3% fixed edge, win or lose, so they can afford to gamble a bit.
3. in fact the system he used is computer analyzable as real and there is a name for it in statistical analysis of chance. It is called mean variance mapping.
4. And the entire Blackjack system has been overhauled because of Thorpe, to ten deck, machine shuffled decks that are changed often.
5. Thorpe and Claude Shannon, the father of information theory whose discoveries led to predictive and adaptive digital signal processing, collaborated on a several schemes that contributed to the rise of the hedge fund system and computerized trading, which makes billions today for many trading institutions.
6. It is hardly likely that Shannon would have contributed to successful schemse with a mathematician whose ideas were unsound.
maa.org
* Poincare scheme. If you keep playing long enuff and doubling up you will win eventually.. given inexhaustible reserves of betting cash...
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