A math term? Need advice....
You can never say "the dealer will bust in X hands" if (a) the dealer does not always bust, and (b) each hand is independent. For any series of independent trials with a probability p < 1 of outcome A happening, and with probability 1-p of outcome B happening, there is a non-zero (but vanishing) probability of either A or B *never* happening. Therefore, you can never say that A or B *will* happen. As likely as it may be, it's never guaranteed. The only time it is guaranteed is when the event happens every time anyway.
None of the above applies to dependent events, like drawing cards from a deck without putting them back. If you have a single shuffled deck and you start picking cards from it and setting them aside, there is a 100% chance you will draw the ace of spades. However, if you put the drawn card back and reshuffle each time, there is a small chance you will *never* draw the ace of spades. These two scenarios are called "selection without replacement" and "selection with replacement", respectively, and probability theory can answer many questions about how these scenarios behave over time.
Quote: MathExtremist"Will" is improper. What you want to say is "there is an X% probability of the dealer having busted within N hands." Or, "with a 90% confidence, after N hands the actual results should be within +/- X% of the EV"
You can never say "the dealer will bust in X hands" if (a) the dealer does not always bust, and (b) each hand is independent. For any series of independent trials with a probability p < 1 of outcome A happening, and with probability 1-p of outcome B happening, there is a non-zero (but vanishing) probability of either A or B *never* happening. Therefore, you can never say that A or B *will* happen. As likely as it may be, it's never guaranteed. The only time it is guaranteed is when the event happens every time anyway.
None of the above applies to dependent events, like drawing cards from a deck without putting them back. If you have a single shuffled deck and you start picking cards from it and setting them aside, there is a 100% chance you will draw the ace of spades. However, if you put the drawn card back and reshuffle each time, there is a small chance you will *never* draw the ace of spades. These two scenarios are called "selection without replacement" and "selection with replacement", respectively, and probability theory can answer many questions about how these scenarios behave over time.
Mr. jjj doesn't understand these sorts of analyses---for one thing, he doesn't believe in mathematics.
Expectation is used in the mathematical sense.
Quote: mrjjjMaybe I'm not asking right? According to the current stats (not future events) a dealer will bust ON AVERAGE once every ***** hands. How would I word that without knowing the stats? Ken
The dealer busts roughly every 3.5 hands on average. I'm not quite sure what you mean by "word that without knowing the stats".
You can find detailed statistics for the dealer probabilities on the Wizard's blackjack appendix 2b page.
The latter part of the question makes it clear that you are looking for a statistical answer.
Quote: mrjjjOk thanks. Lets say I did not know it is 3.5 but I do know, the dealers do bust (of course). How would I word that WITHOUT knowing its 3.5 Ken
That's when you'd use a statement like "The dealers bust every X hands on average." X is used as an unknown constant.
"The dealer is expected to hit every X hands".
This discussion reminds me a story about a physicist and a mathematician traveling across Scotland, and seeing a black sheep by the road. The physicist wrote in his diary "The sheep in Scotland are black.", and the mathematician wrote "there is at least one sheep in Scotland, that is black on at least one side".
