Gambling 101

If you’re goal is to win money (make a net profit) at gambling. In a game with a house edge, would you theoretically be better off placing a single bet of 500 units, or 500 bets of a single unit? Or would it make no difference over the long term?

Quote: Roberto21

If you’re goal is to win money (make a net profit) at gambling. In a game with a house edge, would you theoretically be better off placing a single bet of 500 units, or 500 bets of a single unit? Or would it make no difference over the long term?

Single bet of 500.

The smaller the bets, the more bets you are expected to make, and the more you expose to the house edge as a result.

And would it be the reverse logic if you had the edge? I.e. Bet smaller units and reduce variance?

If I play a MHB machine with an edge I know whether I bet minimum or maximum, the expected cost will be the same, but are you saying the optimal strategy would be to reduce your bet size as much as possible to see your edge materialise, so to speak, if one has a limited bankroll?

Quote: ThatDonGuy

Quote: Roberto21

If you’re goal is to win money (make a net profit) at gambling. In a game with a house edge, would you theoretically be better off placing a single bet of 500 units, or 500 bets of a single unit? Or would it make no difference over the long term?

Single bet of 500.

The smaller the bets, the more bets you are expected to make, and the more you expose to the house edge as a result.
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That is true, but there are other factors to be considered. One way to win in casinos or to reduce the house edge is thru the casino's own marketing department. For those offers, more frequent smaller bets may work better than a single bet.
With a $500 bet, you win it or you lose it but you end up giving the casino $500 in action( which is what they use to determine comps for the most part.)
If you make 500 $1 bets, you will most likely win about half of them so if you keep playing until you lose your $500 stake, you'll give the casino much more than $500 in action and you will get better comps.
I would say if you have $500 and never intend to play in the casino again, make a single $500 bet. If you intend to play on a regular basis, 500 $1 bets works better,
Some folks are lucky and overcome the math to win constantly. I'm not, so I need to resort to things like marketing offers to gain an advantage.

I'd break it up into 20 x 25 bet buy-ins, and try to double or nothing my money on each session.
A unit could be $25 so if you have 500 of those, you walked in with $12.5K. Take it easy and bet $25 a hand.

Quote: Roberto21

And would it be the reverse logic if you had the edge? I.e. Bet smaller units and reduce variance?

Yes, in theory. Of course, you have to take into account that it will take time to reach a final result.

However, my original answer was under the assumption that you would play until either you won $500 or lost your original $500. If your target is less than $500, your original bet should be your target; if you win, walk away, and if you lose, double the bet (yes, that is Martingaling, but it is justified in this case as you know you have a limit and have a chance to lose the entire bankroll). In other words, each bet should be the smaller of what you have left in your bankroll and the minimum needed to reach the target.

Quote: Roberto21

If I play a MHB machine with an edge I know whether I bet minimum or maximum, the expected cost will be the same, but are you saying the optimal strategy would be to reduce your bet size as much as possible to see your edge materialise, so to speak, if one has a limited bankroll?

This is a different problem. It depends on a number of things, like what is the probability of winning for different values of the progressive.

Would the house edge of the game play a factor in how you decide to break up your bankroll?

I set no specific target, I was just wondering in general if I would be more likely to be in the positive after a single
bet of $500 than 500 bets of $1 in a negative expectation game. As casino games can vary significantly in house edge, assume the example is for a slot machine with the same RTP for both scenarios (e.g. 1 $500 spin vs 500 $1 spins). Would I be more likely to walk out ahead after 1 spin of $500 or 500 spins of $1, over an infinite number of trials? I assume it would be equal probability over the long term? But in the short term I would be more likely to win with the single $500 bet, is that correct?

Quote: Roberto21

Would the house edge of the game play a factor in how you decide to break up your bankroll?
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I understand you are new and want to learn, but you need to learn to ask better, more specific questions.

It's more about the variance. If I play 625 hands of BJ, take the square root of that to get 25 (I know the math guys have an updated formula, but I'm stuck in the 1990's), so for 1 SD I'd expect to win or lose 25 bets. The HA would be 3 bets at 0.5%, so I'd be looking at (-28, +22). With 2 SD, it'd be +/-50 bets, so (-53, +47). At 3 SD, it'd be +/- 75 bets, so (-78, +72). The HA offsets what you can expect to win or lose. The higher the HA percentage, the worse the offset and the harder it is to stay above even. With the variance involved, I'd have to bring extra buy-ins if I'm on the losing end of it.

I’m not sure if my replies are getting posted in the right place, but my question “would the house edge of the game play a factor in how you decide to break up your bankroll?” Was in response to ChumpChange’s comment that they would split the 500 unit bankroll into 20 smaller bankrolls and aim to double their money with each bankroll for each session.

I apologise if these comments are being posted out of context. I am trying to reply specifically to each one.

Quote: Roberto21

I set no specific target, I was just wondering in general if I would be more likely to be in the positive after a single
bet of $500 than 500 bets of $1 in a negative expectation game. As casino games can vary significantly in house edge, assume the example is for a slot machine with the same RTP for both scenarios (e.g. 1 $500 spin vs 500 $1 spins). Would I be more likely to walk out ahead after 1 spin of $500 or 500 spins of $1, over an infinite number of trials? I assume it would be equal probability over the long term? But in the short term I would be more likely to win with the single $500 bet, is that correct?
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Slots are hard because there are an assortment of wins to be had on each spin.

Let's try roulette instead. Are you better off betting $500 on red once or betting $1 $500 times?

With a $500 bet on red, you will win about 48% of the time and lose about 52% of the time., so roughly 48 times out of 100 you walk away with $1000 and 52% you walk away with nothing.
With your 500 bets, you will walk away with $1,000 next to never, and if you stick to exactly 500 bets, you will walk away with zero next to never. Doing real simple math, you will see that in most circumstances you will win between 200 and 300 of your 500 bets the vast majority of the time and walk away after 500 $1 bets with between $200 and $800.
Which results are better? The single bet has you winning $1,000 almost half the time, but ending up broke the rest of the time.
The smaller bet means you never can win $1,000 but you also won't end up broke more than half the time.

Thanks for breaking it down like this. I’m sure I will appreciate it more when I get more skilled.

As for now, it’s good to know that the optimal strategy for a ploppy truly is ‘to go big or go home’, and it’s interesting to note how that changes when YOU have the edge. And bet sizing clearly gets pretty strategic when you have an edge, too. Thanks for the insight.

Quote: billryan

With a $500 bet on red, you will win about 48% of the time and lose about 52% of the time., so roughly 48 times out of 100 you walk away with $1000 and 52% you walk away with nothing.
With your 500 bets, you will walk away with $1,000 next to never, and if you stick to exactly 500 bets, you will walk away with zero next to never. Doing real simple math, you will see that in most circumstances you will win between 200 and 300 of your 500 bets the vast majority of the time and walk away after 500 $1 bets with between $200 and $800.
Which results are better? The single bet has you winning $1,000 almost half the time, but ending up broke the rest of the time.
The smaller bet means you never can win $1,000 but you also won't end up broke more than half the time.
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Mathematically, your expected value is the same either way. It's just that with one big bet you will never actually experience the calculated EV.

And to answer BillRyan's question, you have to decide your motivation. Are you playing for $$$ profit, then you'd need an edge, thus you are probably playing for amusement.
If it's amusement you desire, do you want the adrenaline rush and the potential boasting rights of one or a few BIG bets, or do you want a nice long session enjoying the ambiance, the free light refreshments and the chit chat with the dealer. The latter could be +ev. (light refreshments and ambiance have value)

Quote: Roberto21

Thanks for breaking it down like this. I’m sure I will appreciate it more when I get more skilled.

As for now, it’s good to know that the optimal strategy for a ploppy truly is ‘to go big or go home’, and it’s interesting to note how that changes when YOU have the edge. And bet sizing clearly gets pretty strategic when you have an edge, too. Thanks for the insight.
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If you have an edge, then there is an actual optimum answer, with the objective of growing your bankroll reliably and steadily enough... For that, research Kelly Criteria or Kelly Betting.
In a nutshell, with Kelly betting you wager a fixed percentage of your rolling bankroll that is proportional to your advantage.