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Double21: EV Probability
In Don's excellent BJA he says "the more you play, the closer (on a % basis) your actual outcome will be to your expected outcome".
I think it is accurate to say that the more hours you play (all things else being equal; i.e system; game; bankroll and betting strategy)the more you converge on your ev. My question therefore is this: does the probability under these circumstances of exactly equalling your ev increase as you play more hours? In other words, given the same game, bankroll, system and betting strategy; is the probability of exactly equalling your ev (hourly ev times hours played) for 1000 hours greater than that of,say, 100 hours? It would seem to me that the more hours you play the higher this probability becomes, but I would like the opinion of the Masters!
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Don Schlesinger: Re: EV Probability
> I think it is accurate to say that the more
> hours you play (all things else being equal;
> i.e system; game; bankroll and betting
> strategy)the more you converge on your ev.
> My question therefore is this: does the
> probability under these circumstances of
> exactly equalling your ev increase as you
> play more hours? In other words, given the
> same game, bankroll, system and betting
> strategy; is the probability of exactly
> equalling your ev (hourly ev times hours
> played) for 1000 hours greater than that
> of,say, 100 hours? It would seem to me that
> the more hours you play the higher this
> probability becomes, but I would like the
> opinion of the Masters!
Short answer: no!
Think of it this way: Suppose you toss a coin ten times. You have a pretty good chance of getting five heads, your EV. But now suppose you toss that same coin ten million times. Now your chance of getting precisely five million heads is virtually zero.
So, you have to consider an interval around the EV and the percentage deviation from that mean result that I mentioned in the book. You can't talk about hitting a precise EV, as I explained above.
Don
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Franz Joseph: Re: EV Probability
Suppose that you toss a coin 20 times. It is fairly likely that the number of heads will not differ from ev by more than 10%, i.e. 9, 10 or 11 heads.
It is more likely with 200 tosses, i.e. from 90 to 110 heads.
It is a virtual certainty with 2,000,000 tosses, i.e. from 900,000 to 1,100,000 heads, as is from say 975,000 to 1,025,000 heads.
The above is a simplified statement of the law of large numbers, which is a truism.
That the number of heads obtained in n tosses approaches .5n as n increases is a FALACY, commonly called the law of averages.
See Allan Wilson's The Casino Gambler's Guide.
Don, can you explain the difference between the Weak Law of Large Numbers and the Strong Law of Large Numbers, especially as applied to blackjack?
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