splendor: get the egde over the dealer

[Greasy John]

> Pick any number of hands. After that many
> hands you will be behind on the average.
> There is a common misunderstanding with the
> concept of infinity that causes what some
> people see as a contradiction that doesn't,
> in fact, exist. The odds are the odds and
> infinity doesn't change them.

> And this doesn't include the fact that you
> would have to bring an infinite bankroll
> that would cost you an infinite amount of
> money in interest even in one second of
> time.

But while a double-up progression is folly in the long term, in the short term, watch out! Suppose someone like Bill Gates wanted to wager on the flip of a coin with the intention of making $1,000,000. And lets say that he were to use his $65 billion fortune (approximate assumption) to do it. By betting $1,000,000 a flip and using a double-up progression after a loss, he would have to loose, I believe, 16 coin tosses in a row. The odds of this happening are approximately 32,000:1. Yes, he would be behind at anytime during the progression until he wins a flip, and yes he would ultimately loose his fortune if he plays continually. But if his goal is just to win $1,000,000 and quit, the odds are approximately 32,000 to one of success.(My math may be somewhat off but I believe it's close.)

There are 65,000 millions in a billion. An analogy for the common man would be to bet $1 and if a loss occurs double-up until there is a win.

The very reason why casinos employ table limits is to pevent progressions from being successful in the short term. Casinos would rather grind out their vig and not be prone to large fluctuations. That is why the casinos would probably not welcome a hypothetical game against Bill Gates as laid out above. And that's why if playing blackjack I'd take "even money" with a $50,000 wager in a neutral count.

Even Benny Binion who would "take any bet" would insist that "your first bet will be your limit."

Just as no one with an expendable $65,000 bankroll would have the goal of a $1 win, neither would Bill Gates chase a $1,000,000 win with his fortune. If we assume only a meger 2% annual rate of return on $65 billion, the amount of interest lost on a per diem basis is $3,500,000. But it wouldn't take all day to play 16 hands of blackjack. Too bad though, I hear Bill Gates plays blackjack for only $5 a hand.

[Norm Wattenberger]

To risk $65B to win a relatively tiny bit of money. For the odds to be as you propose, the entire $65B must be put at risk. And remember, 32,000 to one can happen. Lottery odds vastly higher occur all the time.

[Don Schlesinger]

> To risk $65B to win a relatively tiny bit of
> money. For the odds to be as you propose,
> the entire $65B must be put at risk. And
> remember, 32,000 to one can happen. Lottery
> odds vastly higher occur all the time.

Precisely. Suppose Gates has $65 billion and our writer has a fortune of $650,000. That means Bill has 100,000 times as much money. Bill playing for a mill is like our poster's playing to win $10!!

What's the point???

Don

[humble]

There may be some point because rumour has it that William Gates does play blackjack, and at a mere $5.00 a hand.

[ET Fan]

Suppose Gates has access to computer software that predicts the future far more accurately than the smartest humans. (Not that far-fetched. If anyone has it, he does, and I don't think he'd share it with the public.) Suppose he's put his faith in their prediction that a given casino will triple or quadruple in value in a few years time. But suppose the casino ownership is all tied up, because of the compact or license in that particular state. Gate's lawyers have determined the only legal way he can get the casino is to win it in a bet.

All of a sudden, the progression becomes a positive EV play, and the only thing preventing the takeover is the table limit. The only thing really incredible in the hypo is the lack of table limits. Which is sort of the point. I think GJ was trying to point a possible reason the casinos have table limits.

Another reason that comes to mind is to discourage very, very sophisticated advantage plays that would require many millions of dollars in R&D. First, you hire a team of lawyers to find the loopholes ... (how far away does that EMP equipment have to be ... suppose you're in a neighboring state and aim it at a casino right on the border ... how about surgically altering vision, so you can see microscopic spots on the backs of cards ... this is not science fiction! It's being done in labs. It's just very, very expensive -- for now.)

ETF

> Precisely. Suppose Gates has $65 billion and
> our writer has a fortune of $650,000. That
> means Bill has 100,000 times as much money.
> Bill playing for a mill is like our poster's
> playing to win $10!!

> What's the point???

> Don

[qboy]

On a related note (and I hope not one addressed elsewhere), if I have an infinite bankroll, doesn't winning $X leave my bankroll unchanged?

> The whole problem of doubling strategies and
> similar is the problem of so-called local
> martingales in probability theory. In fact,
> this problem in more general setting is so
> complicated that it has been subject of
> scientific research for the last perhaps 100
> years, and very extensive research in
> financial mathematics for the last 20 years.

> A martingale is such a process where the
> expected value cannot change regardless of
> "betting" (or investment)
> strategy. A local martingale is a similar
> concept, except one is constrained in
> investment strategies. One possible
> constraint is arbitrary but finite wealth
> (bankroll) for investment strategies. As
> soon as there is no limit, the expected
> value does indeed change. Different kinds of
> "doubling strategies" in
> complicated models cause major theoretical
> problems.

> Any doubling strategy is in fact a valid
> winning strategy if the player has no
> constraints for bet sizes. The problem is
> that no constraint means absolutely no
> constraint. As soon as one has a limit of
> maximum 100 billion bet size, then the
> doubling strategy is invalid and loses in
> the long run. The existence of table limits
> does not take place because of doubling
> strategies. Casinos use table limits for
> their own risk management purposes.

> Regards,

> Karel

[Norm Wattenberger]

> Suppose Gates has access to computer
> software that predicts the future far more
> accurately than the smartest humans. (Not
> that far-fetched. If anyone has it, he does,

Gates can't even get Windows to work.

BJStats

[Norm Wattenberger]

> On a related note (and I hope not one
> addressed elsewhere), if I have an infinite
> bankroll, doesn't winning $X leave my
> bankroll unchanged?

Yes (outside of transfinite math.) And in this case, you could lose an infinite amount.

[C]

"On a related note (and I hope not one addressed elsewhere) if I have an infinite bankroll, doesn't winning $X leave my bankroll unchanged?"

[Geoff Hall]

> Yes (outside of transfinite math.) And in
> this case, you could lose an infinite
> amount.

The problem with using infinite limits is that they cause paradoxes all over the place.

For example, say you were offered 2 envelopes, both containing cash with 1 envelope having twice as much as the other.

You pick envelope A which has $1000 inside and are now given the choice to swap. You know that envelope B has either $500 or $2000 so you can gain $1000 or lose $500 by swapping. Therefore you swap for envelope B.

However, this means that you would always swap regardless of the amount found in your chosen envelope. A paradoxical situation caused by having infinite limits placed on the amounts inside the 2 envelopes.

Geoff

[Parker]

> Gates can't even get Windows to work.

Game, set, match.

:-)

[PunkEye]

> Gates can't even get Windows to work.
Sometimes you guys can be just hilarious!

[Sun Runner]

> Game, set, match.
> :-)

Surely you jest.
You guys are hilarious.

His $65 Billion speaks for itself.