To: WSFAlist at keithlynch.net Date: Sun, 9 Mar 2003 13:23:03 -0500 Subject: [WSFA] Re: math problem From: ronkean at juno.com Reply-To: WSFA members <WSFAlist at keithlynch.net> On Sat, 8 Mar 2003 10:07:07 -0500 Eric Jablow <erjablow at netacc.net> writes: > Let's restrict this to one bettor and one casino. Furthermore, > restrict it to one fair game and one stake. That is, the bettor > has a dollars, the house has b dollars. each wager is 1 dollar, > and the odds are 50-50. Assume that the bettor keeps playing > until one side goes broke. > > Then, with probability 1, one side does go broke. With > probability a/(a+b), the bettor wins and ends up with a+b > dollars. With probability b/(a+b), the house wins and gets all > the bettor's money. I'm not sure how this helps with the > particular problem, and I'm not sure the problem is well > defined. It depends on how many games the bettor may make in a > day. That analysis sounds right, given the stated assumptions. If two players play a 50-50 game of pure chance against each other until one loses his stake, each player's probability of being the winner at the end is proportionate to their stake. The player with the bigger stake has an advantage. The situation I was describing is a bit more complicated than just having two parties playing against each other. The casino provides slot machines with a 100% payout ratio, so the casino, by definition, must break even in the long run on the game itself. At least it seems that way to me. Also, the players, in the aggregate, must break even in the long run, because of the 100% payout. To give a specific example of how there might be a winning strategy available to a player, suppose that the casino has 1,000 customers per day. 990 of them bring $10 to play with for that day, and they have the habit of playing until they lose all of the $10 stake, including whatever winnings they may have gained that day, or until the casino closes. Most of them will lose their $10 before the day is over, and leave the casino. It seems likely that those 990 players, by the end of the day, will have stood an aggregate net loss of perhaps $5,000, or more. That $5,000 has to go somewhere. If it does not go to the casino, then presumably it goes to the other 10 players. The other 10 players bring a much larger stake, say, $1,000 each, and the size of their stakes distinguishes them from the $10 customers. It seems that if the $10 players lose in the aggregate on a particular day, then the $1,000 players must win in the aggregate on that day, even if they don't use a 'quit when you're ahead' strategy. Typically, the $1,000 players should win about $500 per day. I suppose the catch is that a $1,000 player will eventually hit a long run of bad luck, and lose all of the accumulated winnings of the previous days. So the real difference between the $10 players and the $1,000 players lies in how long it takes to lose all of their money. It just takes a lot longer for that to happen to the $1,000 players. But most of the $1,000 players will have the opportunity to quit while ahead, at some point. So it comes back to the winning strategy being to quit when you're ahead, as Ted said. > > In the end, it is a social issue. I believe that it is unethical > for a government to get money by encouraging people to gamble. > Governments that do this tell their citizens that the way to get > ahead in life is to gamble, not to work, not to study, not to > improve their lives. They tell their citizens to act against > their own interests. Consider the Virginia lottery commercial > where "Lady Luck" upbraids a couple for only betting when the > odds are good. > > If society needs to raise money for worthy causes, raise taxes > democratically. Or cut down on the services that it wants to > pay for. If people bet on the lottery because they feel that > they have no other legal and moral way to succeed, then help > create the conditions where they can try to succeed. > In Maryland, the main political argument in favor of slot machines is that it will provide a several hundred million dollar quick fix for the budget deficit. Additional arguments in favor include the point that thousands of Marylanders want to have access to slot machines without having to go to Delaware, Atlantic City, or West Virginia, and many of those Marylanders are already playing slots in neighboring states, fattening their state coffers with money which could be going to Maryland state revenue. Practically no one would claim that casino gambling is good for society. It is plain that if the present slot machine proposal is approved in Maryland, the net result will be to transfer several hundred million dollars a year from slot players mainly to gambling operators and to the State of Maryland. If some people enjoy casino games and can easily afford to lose what money they lose, there would seem to be little harm in them indulging in that pastime. But casino gambling holds much greater danger to compulsive gamblers than a lottery. Lottery players have to wait hours or days for the result of their bet, whereas casino players can bet just as fast as they can feed money into a slot machine, or as fast as the croupier can spin the roulette wheel or the blackjack dealer can deal successive hands. Few lottery players would spend a thousand dollars per day on lottery tickets, but a gambler who enters a casino with a thousand dollars can lose it all in less than an hour. One point that tends to get lost in the debates over gambling is that in almost all states in the U.S. where gambling is legally allowed, it is as a monopoly or quasi-monopoly under government license, with mandated high profit margins to allow for what amounts to a special high tax on gambling for the benefit of the government. The alternative of opening gambling to the free market is never seriously considered. In theory, if gambling were a competitive business, taxed like any other retail business such as restaurants and beauty salons, competition should drive profit margins to a minimum, and the government would not be in the business of encouraging people to gamble. Ron Kean . ________________________________________________________________ Only $9.95 per month!