Is it "better" to make a few large bets or many small bets

Hi all,
I have a mathematics/probability question or concern I want to run everyone.
There is a mathematical principle called the law of large numbers which basically states that given a large number of trials, the actual returns/results from a given bet should approach the calculated expected value.

what this means for any negative expectation game of chance, over the long run (many trials), you should lose, on average, an amount commensurate with the mathematically calculated expected value of a given bet type.
As a simple example, for a simple single unit craps pass line bet with no odds, the EV = ~ 0.98586. Or restated, the house edge is 1.41%.
What this means, in a truly random game of craps, is that if you made a large number of passline wagers over a long period of time, and no other bets, statistically, you should lose $1.41 for every $100 dollars wagered.
Now when people walk away winning a negative expectation wager, this is what mathematicians call "Variance".
Craps itself is a gambling game with a high variance. This is why you can experience "winning streaks", "losing streaks" and "choppy tables" with regards to any given wager or combined group of wagers.
As a customer at a casino, variance is your friend, and the law of large numbers is the Casino's friend.
Here is my question: Given all of the above, is it "better" to make a few very large wagers, accept the results (win or lose), and walk away, or is it better to make many smaller wagers?
I have asked this question on other forums, so I apologize to anyone who frequents multiple gambling discussion forums.

Quote: mainframe

Here is my question: Given all of the above, is it "better" to make a few very large wagers, accept the results (win or lose), and walk away, or is it better to make many smaller wagers?

If your sole goal is to win, then a few large wagers is superior to many small wagers. That's not my goal, especially when playing a negative EV game. I get in my car, drive 20 or so miles, and don't want to leave after three $1000 bets, win or lose. I want to enjoy the game, the chatter, the highs and lows, the drinks, the comped buffet, and spend some time there. If you have the money and can afford to lose those big bets, then the money you win from said bets should not make a difference for you either. If you are in some unique situation where you have $1000 but need $2000 to buy a pair of LaBoutin shoes, and the $1000 does you no good, then make 1 large bet. So it's either LaBoutin or barefoot.......

I personally woudnt be betting $1000 per bet regardless..I dont play at that level. But if my bankroll is $300 at a $10 craps or BJ table, and my goal is to win or go home, then I may every well place three bets total, for $100 each. I understand the entertainment aspect of gambling, and the energy, etc. I also would hate to win or lose quick and go home with a very far drive. But If I am in vegas for 5 days on business, and staying at a casino hotel maybe I'll play a few very short sessions after work since its right there in front of me, and its not going away for the duration of the trip:)

Here's an interesting and relevant "system" for you that discusses making a few large bets vs. a lot of smaller bets.

If you are in it strictly for the money aspect , then take your shot with larger size bets and 'hit n run'. This is fooling the variance and had proven to be the best way for me. There is a reason the casinos want you to stay and put in time.... and its not so they can comp you. If you want to stay and enjoy the excitement of the tables, etc then dont expect to come out on top too often.

You have to define ‘better’.

There is a compromise, where you can have a good time, have a low expected hourly loss, and maximize your probability of winning. It’s called 100x odds.

"small" or "large" is relative to your bankroll. A bankroll of $100 has small bets of $1 and large bets of $50 or $100. A bankroll of $10,000 has small bets of $100 and large bets of $5,000 or $10,000.

Assuming you play until you either win enough (say, double) or lose, then betting smaller means the total amount you wager, on average, is going to be higher. This is true regardless of the game and whether it's positive or negative EV.

For example, with a $100 bankroll at a slot machine, if you shove a $100 bill into a $100 slot machine, you get one spin (and don't spin again if you win, cash out any win even a tie). If the house edge is 8%, you lose an average of $8. But if you shove the $100 bill into a quarter machine and sit there for a long time until it's all gone or you win the balance up to $200 (much more likely the former), by the time you either walk away a loser or cash out at least $200, you will have wagered an average of much more than $100... maybe $1,000. If you wager $1,000 at an 8% edge slot machine, you lose an average of $80. $80 out of your $100 bankroll is 80 percent! Holy cow, how did the $8 loss at the $100 machine turn into an $80 loss at the quarter machine with the same 8% house edge? It's because you re-wagered your bankroll over and over and over.

At a positive expected value game, this is what you want to do (the Kelly betting method, ideally). But at a negative EV game, the best way to double your money is to bet all or half of your bankroll.

Alternatively, you could count the number of bets you make and limit it to equal your bankroll. This can be done at a machine with the player's club card if the points formula isn't too complex. For example, if you get 1 point per dollar, with a $100 bankroll, keep hitting spin until the number of points is exactly 100 more than what you started with. At a table game this would be tougher but can be done (just count from 1 to n, easy!). For example, a $100 bankroll at craps wagered $5 at a time is fine as long as you make 20 bets, no more, no less.

As with so many things in life, and particularly in gambling, it depends. And as already pointed out, define “better”.

For example, if you live 2 miles away from the casino, then the high variance hit-and-run aspect might be very appealing.

But if you’re someone like me, who has to drive for over an hour to get to a casino, or like I’m doing in 42 hours, jumping on a plane to go to Vegas, the hit-and-run is never an option.


On a sidenote, the first portion of your post was a little condescending. You’re on a gambling forum We know about high and low variance, house edge, “long run”, etc.

Thank you everyone for your thoughtful, insightful answers to my question regarding the value of "A few large bets vs. many small bets". I found TigerWu's link to a half-bankroll "hit and run" strategy authored by Michael Bluejay to be especially useful because it provided a few different "large wager, few bet" options in the event I just want to attempt a quick "hit and run" type of session.

Quote: DJTeddyBear

On a sidenote, the first portion of your post was a little condescending. You’re on a gambling forum We know about high and low variance, house edge, “long run”, etc.

DJTeddyBear- I apologize, it was not my intention to be condescending. I was trying to establish for forum members that I understood the basic mathematics of casino gambling before posing my question. Sometimes, extra exposition/background information as I wrote is unnecessary.

As far as my gambling goals/motivations: I guess they vary depending on the circumstances of a casino visit. The closest casino to my home is 1 hour 20 minutes. In that situation, I don't want to invest the time, energy, and gasoline to travel to that venue, only to play a single "double or nothing" even money, full bankroll wager.. In that situation, since its my "home casino", I'd be interested in accumulating tier credits/points/comps.
On the other hand, I only get out to Vegas once a year, if I am lucky..and its always on business. I don't feel the need to accumulate tier points with a casino operator that has no east-coast venues. I'd be willing to "stretch out" my gambling sessions at a Cesar's or MGM property because I have more than one opportunity to redeem comps per year. But It doesn't make sense for me to "stretch out" table-time at a Binion property, because they don't have east coast casinos (to my knowledge).

If I walk into a Vegas Casino that does not own properties that are driving distance from my home, my goal is typically to try to win some money rather then accumulate comp points. I guess in that case, I should try to find a place that has 100X or 20X craps odds, and play a minimum passline bet with max odds that would allow me to commit my total session bankroll. Or similarly, find a table with the most favorable Blackjack rules, and play a single hand or maybe 2-3 hands with a large fraction of my bankroll, then walk away.

When I had my Joker POker machine, there was a line to get on it sometimes on payday.
Most of the players put in $40-$100 and played for about $2.50 a spin. Most of them lost everything. One guy would load the game up to its $100 max bet and do one hand. About half the time he got his money back, most of the rest he lost it all but hit a straight or better and it's money for a quick vacation.
He hit a $100 4OAK at another bar and made a huge stink when they didn't pay him immediately.

Quote: billryan

When I had my Joker POker machine, there was a line to get on it sometimes on payday.
Most of the players put in $40-$100 and played for about $2.50 a spin. Most of them lost everything. One guy would load the game up to its $100 max bet and do one hand. About half the time he got his money back, most of the rest he lost it all but hit a straight or better and it's money for a quick vacation.
He hit a $100 4OAK at another bar and made a huge stink when they didn't pay him immediately.

He most likely didn't know what a handpay wait was at the time. He was presumably one of those people who think a big handpay is paid right away not knowing that they have to do verification to verify you are not on the 86/self exclusion list and do paperwork.

Quote: mainframe

... in that case, I should try to find a place that has 100X or 20X craps odds, and play a minimum passline bet with max odds that would allow me to commit my total session bankroll. Or similarly, find a table with the most favorable Blackjack rules, and play a single hand or maybe 2-3 hands with a large fraction of my bankroll, then walk away.

When you walk away having lost your bankroll it's cold comfort to think it was a smarter way to bet.

It's a tricky thing. Variance always goes both ways. For a given bankroll, the house edge is the same whether you break it up or bet it all at once, as you noted. So for the same total action [not a given, see below] it is entirely the matter of the Variance; I like to say betting it all at once or in large segments is a good way to increase your chances and also the best way to lose your money all at once .

It seems to me there is a gradient,

*the bankroll can be small bets constantly re-entered. In this case, a $200 bankroll yields a certain return, then that return is put through, then that return is put through, etc. So such betting actually means total action will be much more, $200 can be wind up being in the thousands as far as what was bet . We can see why this common way of betting gives the worst chances, in fact it no longer is a matter of the Variance but also a matter of increased total action going against a house edge. This gambler can potentially stay playing a long time though - what many want.

*the bankroll can be broken up into smaller bets, but restricting total action to that bankroll or something close to it. This makes the actual outcome closer to the EV than betting it all or in big segments. Hitting some goal like doubling your bankroll becomes less likely, but so does losing it all become less likely. Entertainment by playing long sessions is more limited.

*the bankroll is bet all at once or close to it. As a bonus this most likely this is the smallest EV, as total action is truly under control. Goals are more attainable as is the likelihood of being wiped out. Entertainment value of spending time playing at the casino is pretty much gone.

So I like to advise anyone to avoid the first type, then instead try to find a happy medium. I expect anyone doing what you are thinking about to give it up sooner or later. As others have noted, there is more than one reason players don't go to that extreme.

You want to make as few bets as possible that are -ev and as many bets as possible that are +ev.

I've changed how I play on my vegas trips.

For sports, when I go next month, if I'm betting on baseball, instead of betting $15 each on 5 games, I'll just make 2 plays and do $50 & $25. I'm picking my best plays, which should help my percentage, and all I need to do is hit my best play to make money.

When I'm playing pai gow, instead of playing 6 hours of $10-$15 pai gow, I'll play 3 hours of $25 pai gow. It increases variance which actually gives me a chance to win.

The more time you gamble, the larger chance you're going to lose on a trip/session.

Quote: FinsRule

You want to make as few bets as possible that are -ev and as many bets as possible that are +ev.

Where do you find those +EV bets?

No one deals with airport lines, airport groping and airplane cabin germ-laden air to go put their entire bankroll on ONE roll of the dice. Oh we all might dream of it but we are unlikely to do it. And if you lose, the wife and kids won't want to trek back home quite so promptly.

Its a question of moderation. Time spend gambling, eating, drinking, gawking, concerts, etc. Even sitting down to play a slot machine is a break from the craps table's pace and requirement that you stand.

Only the math types walk in to Benny Binion's place and put a quarter million on the line.

The answer depends on what you are trying to do.

If you are going to stop after a certain amount is bet, then it doesn't really matter.

If you are going to stop after either winning or losing a certain amount, then larger bets are better.

If you bet small, then the total amount of your bets to reach a target will end up being larger - and the more you actually bet overall, the more you expose to the house advantage.

You said it yourself - on the pass line in craps, "you should lose $1.41 for every $100 dollars wagered," so the total amount that you wager in your session (not the amount of each bet) should be as small as possible.

Quote: DJTeddyBear

Where do you find those +EV bets?

Bet more on the winning hands and less on the losing ones.

Quote: DJTeddyBear

Where do you find those +EV bets?

You’ve never made a +ev bet?? That’s sad DJ.

It's best to make many large bets

Well, this may be useful information for me, because I now want to start making money on NBA bets, it seems to me that this is relevant now.

Just going through a calculation:
$25 PL + $125 odds on the 6 or 8 pays a total of $175. 1.41% of $25 is 35 cents HA
$150 on the PB 6 or 8 pays $175. 1.51% of $150 is $2.27 HA. You'll be paying about 6.5X more in HA with the PB despite betting the same amount and winning the same amount.

As few Wagers as possible is the best thing in my opinion. Serves me well.

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Quote: ChumpChange

Just going through a calculation:
$25 PL + $125 odds on the 6 or 8 pays a total of $175. 1.41% of $25 is 35 cents HA
$150 on the PB 6 or 8 pays $175. 1.51% of $150 is $2.27 HA. You'll be paying about 6.5X more in HA with the PB despite betting the same amount and winning the same amount.

That's mainly because only 1/6th of the first bet is subject to HA.

Quote: marychap

Well, this may be useful information for me, because I now want to start making money on NBA bets, it seems to me that this is relevant now.

As far as I know, you can now find a betting calculator that will help you calculate everything you need. But, at the same time, it seems to me that even if you think, then after that, it is worth checking with the calculator to be accurate in your calculations. Otherwise, there is always a risk that you may make a mistake. Therefore, I do this: before each calculation, I first count myself, and if I have any doubts about this, then I use awhere I can keep my bet, coefficient, and so on. In short, there is no chance of error.