heavy wrote:
Suppose there was a casino with a BJ game with relatively decent rules that welcomed counters. The one caveat would be the old Benny Binion rule - your first bet is your limit. Knowing that you would be able to range your bets from table minimum to your personal max - how much would your first bet be?

JSTAT says:
In 1980 when I worked next door to Binions at The Mint. Word buzzed throughout the casino that someone scored big at Binions. I think it was $750,000 at roulette. One zero was taken out of play for the gambler, cutting down the house pc. The gambler came back again a few years later and bet $1,000,000. I think on the don't pass line. The point was 6 or 8 and it sevened out. He won again! The gambler later lost it all back and killed himself.

Betting $1,000,000(assuming a $300,000,000 bankroll)with the single deck rules then would have been a good play. If small cards came out with no aces, you would have the advantage the next hand. Charles Einstein had a theory in his book "Blackjack Hijack" that if you lost the first hand, the odds favor the second hand. Einstein assumed that losing hands constituted small cards therefore the big cards were due to come out. Any competent card counter can theoretically wipe out any casino with such an offer.

If you could get away with spreading $100-$1,000,000 at SD, you would eventually get into Archie Karras territory. Karras won $40,000,000 at craps by possibly sliding the dice. Jack Binion is rumoured to tell him to stop. Karras lost it all back. Casinos now put a speed bump in the middle of the table due to Karras. Karras was last seen on the 2008 WSOP Main Event on ESPN getting busted out.

JSTAT

Bringing Down The House in Blackjack 
Las Vegas