[Siegmund]

He's speaking somewhat loosely when he says "rolled the dice once" -- that is, almost your entire bankroll fluctuation for the trip is caused by that last roll.

Rather than "effective number of dice rolls," we usually just report the mean and standard deviation of a series of bets of differing sizes.

Simplifying from craps to betting on even-money coin flips:

10,000 independent fair $1 bets (standard deviation $1 each) add up to something that is, in effect, one fair bet with standard deviation $100.

Those 10,000 plus one million dollar bet make one fair bet with standard deviation $1000000.005.

Those 10,000 plus one $10 bet would have standard deviation $100.49, and those 10,000 plus one $100 bet would have standard deviation $141.42.

If you wish an "effective number," you can ask, "how many large bets could I have made, to get the same standard deviation in my outcome as I got by making the series of small bets followed by one large bet?" The answer is 1.00000001 million dollar bets, 2 $100 bets, or 101 $10 bets. In general, 1 + (numberof$1bets)/(sizeoflargebet^2).