Easy math puzzles

We talk about risk of ruin only when the edge is greater than zero.

Quote: lilredrooster

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Blackjack Puzzle

"You go to Vegas over a long weekend to play a single-deck blackjack game with a 0% edge ($500 minimum). You decide to play 1,200 hands but you will quit if you bust or double your initial bankroll before reaching 1200 hands.

What size bankroll should you bring to give yourself a 1/3 chance of busting, 1/3 chance of doubling and 1/3 chance of finishing the 1200 hands without busting or doubling?

Assume a standard deviation of 1.1547, flat betting $500 one hand at a time and perfect basic strategy to realize the 0% edge"


we all know that the house edge against basic strategy is not 0 - the puzzle is set that way intentionally

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blackjack Hall of Fame member and author Don Schlesinger solved the puzzle in another forum

this is what he wrote:

" I'm going to give you a very elegant solution that doesn't rely on calculators With SD = 1.1547, the total SD for 1,200 hands is 1.1547 * 1200^0.5 = 40 units exactly. To have 33.33% probability as the END POINT solution (doubling or going broke), using my "bumping into the barrier concept" (see BJA, p. 124, second full paragraph) you need exactly half of that value or 16.67% probability of busting or going broke IF you're guaranteed to get to play all 1,200 hands. If you look at cumulative normal tables, you'll see that, to lose enough to go broke, we have to lose 0.97 standard deviations, which has probability 16.6%. So, we're looking for B/40 = 0.97, whence B = 38.8 units, or $19,400. QED. No fancy math, no calculators!"

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What did I say above?

Quote: aceside

What did I say above?

you implied the puzzle was not worthwhile because the edge was set at zero
Don found the puzzle interesting and decided to solve it just as it was setup (with the edge at zero)
it's a mathematical puzzle - it wasn't set up to reflect the real world of blackjack - it was set up to challenge a person's math skills
so Don obviously didn't agree with your comment

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Don has dismissed me many times. He probably thinks I am assside. What matters is your math derivation.

Quote: aceside

We talk about risk of ruin only when the edge is greater than zero.
link to original post

Wrong. There is a RoR in any scenario with variance, including scenarios with a player advantage.

Also worth noting that games with <0.5% house edge (the only games worth playing) are close enough to 0% to use the RoR calculations for 0%