Bob wrote: "Over time, my actual results and my EV results will be fairly close. They will never (okay, extremely rarely) be EXACTLY the same, but close enough."
"Fairly close" is subjective. Percentage wise it becomes close, however, a real world gambler is subject to their bankroll and dollar amounts and the limitations of mortality and also the IRS. If you were to play a breakeven game, there would be no edge to either side, and the dollar standard deviation would always increase the more you played, $sd = $betsize x sqrt(variance x hands). This is why if you play a breakeven game with a limited bankroll against an opponent with an unlimited bankroll, you will eventually most likely go bust. Bust is the most likely end result, not breakeven. There is an increasingly smaller chance that you will survive, so that your average result will be breakeven, but the more you play, the more likely you are to go bust. If both you and your opponent have the same bankroll, then your odds are 50-50, half the time you go bust, the other half you've doubled up and busted your opponent. Again, breakeven is not the end result, although it is the average result.
Now, if you're playing with an edge, things change a bit. That's because edge (EV x hands) increases faster than sd (sqrt(variance x hands)) so that edge eventually equals and then exceeds sd, and the more you play, the greater are your chances of being ahead. So, assuming an infinite bankroll and an edge, the end result will be that you are ahead. Your average result will be the EV, but you will still have a distribution of possible dollar results around the average result.
The inflection point where the edge equals an sd has been called N0 or Nzero, not by me, I think a blackjack player coined the term. Since the IRS breaks your gambling career into individual years and you can't legally carry forward a losing year, you should select your play such that you at least exceed the Nzero for each calendar year. Canadians don't pay taxes on gambling, so there you need only plan to exceed Nzero for the duration of your career, assuming your goal is to quit ahead.
vpFREE Bank_NO http://www.west-point.org/users/usma1955/20228/V/Bank_NO.htm
vpFREE Bank_NO http://www.west-point.org/users/usma1955/20228/V/Bank_NO.htm Very early on, upon joining this board, iggy introduced a concept which he references in shorthand as "N0".
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Posted by: nightoftheiguana2000@yahoo.com
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