Table Minimums/Maximums

I hope that someone can answer this for me, because I imagine the answer is something simple that I am missing. In short, I do not understand why the Table Maximum is not the same as the House Maximum for every Table with only the minimums differing, at least, not in limited circumstances.

I have heard many people opine as to the reason for this, and I disagree with all reasons except the first, and the reasons/disagreements will follow:

1.) Limit the Spread for BJ Counters

A.) I agree with this one, because you don't want a BJ player to be spreading $5-$5000 depending on the favorability of the count. However, I partially disagree because this only applies to Blackjack and not the other games.

2.) Diminish the Probability of Success for Progression Systems

A.) I would still think that the casino would want players to be making a -EV bet, which they all are, even at the cost of them successfully winning one betting unit more often. For the same reasons that such systems are doomed to failure, (because the losses are devastating) the casino should encourage players to play these systems to their last dollar. It would seem that allowing such would increase variance at the table, but only in the casino's favor, the player (if Martingale) only stands to win one unit.

B.) If the player Martingales-Out due to the Table Maximum, he could theoretically switch tables to continue his Martingale. If he chooses not to, the casino may not win as money from him as they otherwise would have.

-I realize a story that John Scarne told in his, "New Complete Guide to Gambling," about a House getting shelled in Roulette by the Martingale essentially due to increasing the Maximum such that it gave the player an extra bet before bust, but the Odds are ALWAYS in the casino's favor. I believe in Scarne's story, it only gave him one extra bet before failure of the system.

3.) Seperate the Fleas from the Whales, Better Odds for Whales

-I believe it is the Table Minimum that succeeds in this area, not the Maximum.

4.) Discourage the Whales from Betting House Minimum

-They already could, by moving to the low table. It is the Minimum Bet that seperates people, not the maximum.

***So, with exception to the spread of a theoretically beatable game, I really don't see the reason why House Maximum is not the Table Max for games such as Craps, Roulette, and the like.

The basic reason is that while the casino wants -EV bets, they want them clustered around particular sizes, since they want their own SD/EV as low as possible. They're not there to gamble. They don't want a pit's entire week sunk by a few lucky bets, nor when someone with deep pockets is chipping away by Martingale at a $5 table is it any help that sooner or later he'll have a bad run. That thinking only works as long as the spread is kept under control. (You illustrated this to me once when you pointed out that my strategy, while it had +EV, would lose in the majority of cases, regardless of time.) It's the same reason they're more likely to waive a table/house maximum once they know you'll be back for more.

" -I realize a story that John Scarne told in his, "New Complete Guide to Gambling," about a House getting shelled in Roulette by the Martingale essentially due to increasing the Maximum such that it gave the player an extra bet before bust, but the Odds are ALWAYS in the casino's favor. I believe in Scarne's



The main reason for different limits is you want your best people at the higher limit tables.

There are not that many great dealers like Paigowdan on a casino's payroll.


OMG More than one Dan, no way, the universe would split !

Quote: Mission146

1.) Limit the Spread for BJ Counters

A.) I agree with this one, because you don't want a BJ player to be spreading $5-$5000 depending on the favorability of the count. However, I partially disagree because this only applies to Blackjack and not the other games.

I don't agree with this one. Even a $5 table max resembles an infinite spread if the player simply passes (or leaves) on his -EV bets.

I think maybe Paigowdan could speak to this the best. But my impression is that the house likes to keep it's top people on high limit games. So a $5 table with say a $500 max...doesn't worry them much if at all. But they feel like they could get hurt at a $100min $10,000 max table. There are only so many people you really trust in any business, those people work the big money games.

Quote: 24Bingo

They don't want a pit's entire week sunk by a few lucky bets,

The casino has cash flow issues just like any other business. House advantage doesn't mean that much when someone is laying monster bets. You would necessarily want your big betters in one place for many reasons. You can take better care of the elite dealers, you can have your best dealers, and you can have concentrated surveillance in case you are being scammed.

One story that the young owners of the Golden Nugget told was regarding the September 2004 play of a big time whale. They realized that their craps dealers weren't experienced enough to keep up with the frantic pace set by the whale. Finally the owner gave up, and he encouraged the dealers to meet the pace , even if it meant making a mistake every so often.

It is also widely believed that casinos set the ratio of the maximum to minimum bet to protect themselves against Martingale players. Nothing could be further from the truth. Casinos love Martingale players. Any player who firmly believes in any betting system will play longer at a table. Ultimately that is good for the casino. There is the old joke where a casino paid to have signs hung in the hotel rooms. The sign said, "If you want to gamble, walk over to our casino; If you have a system then call us and we'll send a limo".

The ratio is just a byproduct of not wanting to set the minimum too low so that the EV is not worth the cost of manning the table, and not wanting to set the maximum too high, since the casino doesn't want to deal with the potential deviation.

I have a totally different reason, although I don't know how true it might be.

As I understand it, casinos need to have cash on hand for every chip on the casino floor. Therefore, every open table must have cash in the cage to cover every chip in their rack.

Tables with higher maximums need more higher value chips on hand.

So if every table were to allow high-limit wagers, the chips on the floor would exceed the cash on hand.



A second reason is much more simple. Chip distribution within the rack.

On the low limit tables, there are lots of whites and reds, some greens and blacks and maybe just a few of another color or two.

At the high limit tables, the rack is much more colorful, and there may not even be any white chips. Maybe no red chips either!

It seems that I am being presented with:

1.) Dealers you Trust Play with Big Bucks

-I would agree with this one and say I see the logic behind that. You wouldn't want a break-in dealer to make a payout mistake on Craps, Roulette, or what have you on a $1,000+ bet.

2.) Cash on Hand

-Maybe. I could see where this could be a problem for smaller time casinos, especially.

3.) Chip Rack Distribution

-Maybe, but I really don't see it as much of functional problem. You would assume your whales would still play higher minimums, better Rules, so you wouldn't have to keep too many other chips there.

4.) Scared of the Martingale, Variance, Standard Deviation

-This is where we may get into a bit of semantics. I look at the Martingale/Labouchere/Other Systems as one bet if a player is truly committed to following the system. He's not making a bet based on odds, but rather a bet based on probability. For a $5-Min/$500-Max Table and Martingale player, if committed, he's making one bet $5-$10-$20-$40-$80-$160-$320 (Total: $635) that he will not lose seven turns in a row. The difference is that he does not have to put the whole $635 up at once, and sometimes, not at all.

I know some people will disagree with the way I look at it, but if the Martingale player is committed, it is effectively one bet, $635 to profit $5, in my opinion.

In Roulette, for example, he is putting up a $635 wager on:

20/38 * 20/38 * 20/38 * 20/38 * 20/38 * 20/38 * 20/38 = 0.01118728735197 = 1- 0.01118728735197 = .98881271264803 or 98.8813%

PROBABILITY that he sees Red/Black/Even/Odd/1st 18/Last 18---within seven spins.

I'm just representing this from the Martingale-Player's standpoint, just for the record. Everybody here knows that the probability of the event is 98.8813% BEFORE it actually lands on something he is not betting on that first spin. After that, you can knock one of those 20/38's from the equation because it is irrelevant. The Odds of hitting an Even Money bet (Assuming two zeroes) will ALWAYS be 18/38.

The only variance in increasing the Table Minimum favors the casino, because the player always bucks 18:38 Odds. Besides, the player could theoretically just move to a higher limit Table if his Marty is busted, intuitively, though, I'm guessing he won't.

However, no matter how you cut it, the player always stands to only profit $5.00 per wager.

I could see this possibly being a problem if every player went in there with the intention of going $5.00 win and out, but regardless of the inherent worthlessness of the Martingale System, it's difficult to fathom anyone being stupid enough to venture $635 (potentially) or what have you just to win $5.00. In fact, just to win $500, the player has to run 100 successful Martingales, the guarantee of which being a 100% probability of success, which, literally, cannot happen. Probability theory also has the Martingale getting busted before the 100th attempt, even regardless of a probable win rate of 99%+.

In short, I just don't think anyone fears the Martingale. In fact, in the $5-$500 Limit case, the Martingale must succeed 127 times before one failure...just to be even.

I hope I didn't miss anything. I would usually open another window and respond to posts one-by-one, but I'm on my laptop...which is thoroughly opposed to having more than one window open at a time...lol

24Bingo,

If I recall, your strategy had -EV, since +EV is impossible, it just had a positive win rate.

Quote: Mission146

In short, I just don't think anyone fears the Martingale. In fact, in the $5-$500 Limit case, the Martingale must succeed 127 times before one failure...just to be even.

Although$5-$500 is often the table limits at a smallish casino in Vegas. It has always seemed to me that casinos should have tables with the following limits:
(1) $5-$320 (max/min=64 =2^6)
(2) $5-$640 (max/min=128 =2^7)
(3) $5-$1280 (max/min=256 =2^8)
Especially with roulette since blackjack frequently requires doubling your bet (or possibly redoubling). These table limits would specifically encourage the Martingale delusion.

For roulette:
On average in case 1, the player will play 97 times before he loses 6 in a row.
On average in case 2, the player will play 186 times before he loses 7 in a row.
On average in case 3, the player will play 356 times before he loses 8 in a row.

Of course these are only the average numbers. You could lose 6,7, or 8 in a row immediately.

But in any case, the player who reaches the average, will still be unhappy with his winnings, which have probably failed to double his bankroll, and will keep on playing.

Quote: Mission146

24Bingo,

If I recall, your strategy had -EV, since +EV is impossible, it just had a positive win rate.

Um... it was the exact opposite of that. We were discussing a +EV game.

Mission -

I LOVE your commitment / one bet of $635 to win $5 theory. It really sums it up nicely.

And I agree that martingales / systems is not the reason casinos have the max limit.



Paco -

Your spreads make sense on paper, but would never fly simply because people in general expect to see round numbers. That's why a $5 table generally has a $500 or $1,000 max (or sometimes even $250).

I thought that was the point - if they don't see round numbers, they'll ask why, and get the answer from the "smarts."

Quote: pacomartin

But in any case, the player who reaches the average, will still be unhappy with his winnings, which have probably failed to double his bankroll, and will keep on playing.

What you're missing is that these people, at least the ones who are really committed, and not just on a whim trying to recoup their losses, think they're making money. They're probably not going to go all the way up to try to double their money, but they're going to go a ways, and at a table where everyone else is betting $10, that's a pest the books don't need.

If they go up to another table when they cross the threshold, great! If they win, the loss gets swallowed up in the high-roller pits, and if they lose, hooray! But they don't need to be screwing up the games they set up for the working schlubs.

" I thought that was the point - if they don't see round numbers, they'll ask why, and get the answer from the "smarts.""

No, they will just go to another casino who is not trying to cheat them. LOL

Quote: DJTeddyBear

A second reason is much more simple. Chip distribution within the rack.

On the low limit tables, there are lots of whites and reds, some greens and blacks and maybe just a few of another color or two.

At the high limit tables, the rack is much more colorful, and there may not even be any white chips. Maybe no red chips either!

This is the point I was going to make. Some of the other reasons have their own logical sense to them, but the ability to pay the winners without running out of chips is the only reason I know to be true.

I tend to disagree a little bit with the last sentence (maybe no red/white) because, at least where I work, there's always red and white on every table because you need it to pay off unusual bets when they win. For example, just because I might have no white chips in my rack doesn't mean someone can't walk up with some and cap his purple/black/green/whatever bet with a few whites. I don't know why they do it, but they do. Maybe it's some kind of lucky talisman thing, or maybe they want to stump the dealer if they get a blackjack.

The only time I can think of a particular low value chip not being on a table is on a carnival game where the chip wouldn't be eligible to be wagered on it's own and wouldn't be part of any winning pay out. That can cause a minor problem when someone uses a stack of them to obtain a minimum bet, or tosses it out as a toke bet.

I'm not a dealer, so I wasn't sure about the reds & whites.

I just recall on at least one episode of High Stakes Poker, a player had gone all-in, and when counting it out, he was about to include his reds and greens when the other player commented that those don't play - they're only for tips.

But the rack / distribution thing is an important factor.

Quote: 24Bingo

Um... it was the exact opposite of that. We were discussing a +EV game.

Right...I'm sorry, I was thinking of a different discussion with someone else. I believe it was Craps-Related.

Quote: DJTeddyBear

Mission -

I LOVE your commitment / one bet of $635 to win $5 theory. It really sums it up nicely.

And I agree that martingales / systems is not the reason casinos have the max limit.



Paco -

Your spreads make sense on paper, but would never fly simply because people in general expect to see round numbers. That's why a $5 table generally has a $500 or $1,000 max (or sometimes even $250).

I agree with the entirety of this post, however, I appreciate Paco's inclusion of the Martingale failure rate in his post.

I also appreciate the compliment, DJTeddyBear, thank you.

Quote: DJTeddyBear

Paco -

Your spreads make sense on paper, but would never fly simply because people in general expect to see round numbers. That's why a $5 table generally has a $500 or $1,000 max (or sometimes even $250).

The maximum amount can be a factor of two or anything over that. The main point is that if your max/min spread permits you to double 6 times, then if you play to the point where you are expected to lose 6 in a row, odds are very high that you won't even have doubled your investment.

If the table permits you to double your bet 7 times, then your bankroll must be twice as high.The average length of play is roughly twice as long. You will (on average) find you have increased your bankroll by the same percentage.

I was trying to figure out how the casino could encourage Martingale play. One way is to explicitely call attention to it by setting the maximums to a power of two. Another way would be to

Paco and DJTed hit on two good points. I'm not sure if the casino REALLY needs cash to cover every chip on the floor, however they do want to be able to cover them all in case someone wins a lot and wants cash.

The other thing is cash flow. Profits from slots are 10X that of tables where I work, so a big loss from tables will be made up for on slots. But they don't want that to happen. There are days when the tables lose money, but this is usually just a couple times a year, and obviously plenty more times where tables make a lot more than usual. But what they DEFINITELY don't want to happen, is have a loss that's so huge, it might take six months to make up.

Example: Look at Mississippi Stud. Our max is $25. If someone is playing that, gets AK suited, and decides to bet full 3X on each street, and hits the Royal, they'll get 125,000. Our casino won't even pay that, since max aggregate payout is 25,000 (which I think is stupid, if you don't want someone to win that much, don't allow them to bet that much. If it happens, you'll really piss off that player and alienate them, why would you want to do that to one of your biggest players?). Even if they do a realistic betting structure, 1x, 2x, then 3x on the final street. That's still 87,000(and still over max aggregate)

Now, imagine $1000 maximum bet. If a player is playing that, and gets KQ suited, bets 1x, 2x, 3x. They'll win 3.5 million. Considering tables make about 25,000 a day, that's 4-5 months before they make up the loss. Even Quads is 240,000 which would take, theoretically, ten days to make up.

For my casino, there aren't enough big players coming in consistently to help offset one big player winning a lot.



On a parallel to that, my dad once asked if a couple of people came in and won a million dollars each, would I see a cut in my pay. I told him no, but then went on to say it would be pretty much impossible for that to happen. You would have to bet absolute max on craps and have an incredibly awesome roll, or several incredible rolls to make a million dollars (just assuming right side playing). You would have to have at least $33,000 to start with (they allow 10X odds). Of course I haven't really thought about other games, like roulette, where it might be easier, because my dad was asking specifically about craps.

EWJones,

I appreciate the informative post, but my OP did not concern the existence of a Maximum to begin with, the necessity of that I clearly see, just the relationship between the Table Minimum and Table Maximum. It was an excellent post, all the same.

How significant are whales that the casinos really plan around them? It would seem like strip casinos have an upper middle class demographic in mind and downtown casinos have a senior citizen demographic in mind.

I find the maximum being both a way to control the variance and limit risk with dealers to be the most plausible answers. It would be interesting to know the actual answer from the people who make these decisions though.

The relationship of Minimum/Maximum is IMHO;

1.) The Minimum establishes the financial risk needed to operate the table break-even/profit. Blackjack minimums are going up due to the low house edge/counting. The drop hs been less than it was over time due to increased knowledge of the game. Craps OTOH, has increased more slowly, due to no Customer strategy. Video Poker is a different beast all-together, in that the payout % can be changed to suit the denomination. Generally 25c VP has declined from 99.5% to 97.5% over the years. Slots ditto, with new, lower denominations with multiple pay-lines. Single to 5-line machines are basically progressives or defunct. I like to think that Craps and Roulette are the two games where low-rollers and high-rollers can exist at the same table. Historically, this was part of the "culture" of such gaming. Blackjack used to be that way, but the House has tightened up on Counters. VP and Slots are heads-up gaming, and has no such culture.

2.) Maximum bet is the typical limit on financial risk the House wants in a Community gambit. Rarely does one see a table-limit with an action restriction (Re: $25 - $2000 with a $10,000 cap on Blackjack) unless some gimmick bet is availible, and then only upon the gimmick bet (Carribean Stud for example). Frankly, gimmick bets with payout caps are poorly designed bets ( Re: Ultimate Texas Hold'em has a 500 to 1 payout on a Royal... but usually the cap is placed at 10 Grand outside of Vegas... thats a $20 bet. Ditto for Carrib. Stud)

If I were running a Casino I'd probably break up Blackjack into 3 sets of limits... $10 to 100, $25 to $250, and $100 to $1000. Craps would use pinkies ($2.50 chips) and have a $2.50 to $500 limit with 10x Pass Line and 6-8-10x Donts (Place 12x odds on any point). Pinkies allow 1/2 standard wagering on points (4/10 $2.50 pays $4.50... 5/9 $2.50 pays $3.50... 6/8 $3 pays $3.50)

Quote: 98Clubs

Blackjack minimums are going up due to the low house edge/counting. The drop hs been less than it was over time due to increased knowledge of the game.

My conspiracy theorist side often wonders if S17 BJ is not just a loss leader for casinos. Attract the one spouse who will play with BS and not really lose a ton to the HE but bring along the other spouse who may throw away 4-5x as much on slots while waiting.

Thats a good theory, and quite true. Unfortuneately, in most Casinos, that BJ minimum bet is $25, and the spouse is dropping $2 a bet much faster.