This argument is incomplete. It doesn't discuss the fact that when the richer player loses, he loses a lot more money than the poorer player. That evens things out. I will try to find the time to read some of the longer ones.
I have to join the ranks of questioning big bankroll beating small bankroll only because of bankroll size. First, KenSmith’s statement: Now WumpieJr brings up a valid point: Monkeysystem brings to light the 50-50 coin toss argument. Now, let’s tie all these together with some numbers. From the article quoted by KenSmith: The probability for the guy having the $100 bankroll to win all the money from the guy with $10 is .909090909090. Therefore, the probability for the guy with the $10 bankroll to win the $100 from the other guy is: .090909090909 Now let’s calculate what happens after 10,000 sessions: Guy with $100 bankroll: 10,000 (sessions) * $10(win per session) * .909090909090 (Probability of winning) = $90,909.10 (expected wins) Guy with $10 bankroll: 10,000 (sessions) * $100(win per session) * .090909090909 (Probability of winning) = $90,909.10 (expected wins) WALLAH! They come out even. How about that! Surprise! Surprise!
I'm afraid you are countering one fallacious argument with another. There is no need to look for any evening-out factor. Whether the takings come from one high roller, or a succession of small players has no impact on the profitability of the game. All that counts is the total amount of 'action' and the underlying probabilities of the game. The only impact rich players might have is that if a small numer are making very large individual bets then their own short-term fluctuations in fortune might show up on the casino's balance sheet, rather than the smooth, predictable income that they would doubtless prefer.
London Colin, WumpieJr's comment was in reference to an article linked by RKuczek. In that article the premise is that two 2 people play until one loses all his bankroll. One starts with $10 the other with $100. All WumpieJr was saying is that since the odds are even, although the guy with the $100 bankroll will win more sessions, the guy with the $10 will win more per session. When this is calculated out, the winnings get evened out.
Okay, this is what does it for me. If you want to argue that a break even game is profitable, you need to show me just exactly how the casino wins more than 50% of the hands. If they can't do that, they break even. That's just pure math. So... how is it that they win more than 50% of the hands? I think the answer is that they don't, they break even. A separate argument is that players may be playing non-ideal strategy. Quite true, but that's a disctinct issue from the "gambler's ruin" one.
Oops. Sorry WumpieJr. I did look at the article, but I think I took your reference to 'this argument' to mean the words - - and 'the richer player' to be a generic rich player, rather than the one in the coin-flipping scenario. My wider point though is that applying this example to casino profits is flawed, not just because you can do the maths and show that when the $10 player ends a session by bankrupting his $100 opponent he wins more and so balances out the sessions in which the $100 player bankrupts him, but more importantly because the whole notion of dividing the action into sessions is pointless and misleading. It's all just one long game of the casino versus the rest of us.
Added to equation Getting back to the big increases in gamble losses at the BJ tables. The bankrolls will increase as the customers visiting have more disposable income. In a way its a method of customers shedding "excess" cash. These periods are economic events that peak during times of low unemployment and high cunsumer confidence. In other words there is more free money to throw around. At first I wanted to blame it all on 6:5 BJ, but there are many more things to consider economically. http://news.yahoo.com/s/ap/20070308/ap_on_bi_go_ec_fi/fed_household_finances_1
rough scenario Completely agree with London Colin (total action vs. total losses - no fragmenting). Looking back to ~12% hold I can offer this rough scenario: An average session length is 40 hands, an average bet is 1/10 of a buy-in. What is the average disadvantage? As you can see the total action comes to 40 * 1/10B = 4B (B is our buy-in) and if we (players) lose in average 0.12B during the average session then we lose in average 3% of our action.
LOL.... Just go sit at any BJ table in any casino for a few hours and you wont have to do any complicated math to understand why the casino is making so much money from this supposed low advantage game... It always amazes me at the truely dumb play I have witnessed....just when you think you have seen your last pair of tens split ...up steps a drunk girl or guy who is convinced you always double 12 (hey you gotta hit anyway) and then follows up these brilliant plays by splitting 5's ....yes 5's....against dealer ten up...??? Im surprized the casino made so little actually....Im playing green min tables while watching this and wondering where do I buy stock so that I can get some of this action.... Perfect play can reduce your disadvantage to 1/2 % or so but this type of poor play certainly multiplies that disadvantage by huge factors. Now add the poor game being offered today and even the skilled player is neutered....8 deck shoes and CSM plus dumb play = huge profit for the table games....now take away the dealer and pit salary and you get the one arm bandit profits ....now we are talking the serious money.... There is little question why its so hard to get the casinos to offer our little tournamnet game....
