Just saw this thread. Nice question, will try to answer from my point-of-view and the level of understanding I have.
First of all, there are three variables that user can control while playing dice game, namely: bet size (let say, B), multiplier (let say, P) and number of bets (let say, N). For a same bet size, there will be two values of P and N such that:
EV of (B * P1 * N1) = EV of (B * P2 * N2)
In other words, we can assume one of the variable to be constant for the calculation. Hence, there are two approaches we can use to find a strategy for minimizing variance, which are:
(i) Keeping P constant and trying various combinations of B and N.
(ii) Keeping N constant and trying various combinations of B and P.
I have sweet spot for 2.00x multiplier so I will be using the first approach for the further calculations using 2.00x as the constant value of P.
Now coming to the concept of variance. It is no rocket science to assume that higher the number of bets, lower will be the variance and closer will be the net gain/loss to the EV.
However, there is no possible way of finding the ideal viable bet size which will yield minimum variance considering restrictions of time and viability. We can't expect making 1 billion bets of 1 sat each, right? Hence, best strategy in my opinion is to make sectional bets. So rather than focusing on total wagered amount, focus on profit element. First step would be to choose the initial bet size, any method could be used but I think 'decimal distribution' would be best. The decimal distribution between the range of 1 sat and 10 BTC will be:
[0.00000001, 0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1, 1, 10]
excluding extremes from each side, final distribution:
[0.0000001, 0.000001, 0.00001, 0.0001, 0.001, 0.01, 0.1]
Taking the median value, 0.0001 BTC would be good starting point. Now, next step is to choose the number of sections. For total wager of 10 BTC, I think 100 sections would be appropriate.
Now starts the betting process:
Section 1: Make 1000 bets of 0.0001 BTC each. Total Wagered: 0.1 BTC (10/100). If the outcome is 'loss', move left of the distribution table for next section. If the outcome is 'profit', check whether profit is enough to cover the house edge of next section, if yes then move right of the distribution table, if no then repeat the next section with same bet size.
Now let see how section 2 will look in each of the three different scenarios:
Possibility One: Player wins less than 500 bets (say, 495 bets) in first section, hence ends in the loss of 0.001 BTC. Now he will move left of the distribution table and pick 0.00001 BTC as the bet size for the second section. Hence, total number of bets to be made: ((9.9 - 0.001) / 99) / 0.00001 = 9998.99 or 9999 bets of 0.00001 BTC each.
Possibility Two: Player wins between 500 and 505 bets (say, 502) in first section , hence ends in the profit of 0.0004 BTC. Since it is not enough to cover the house edge for next section, repeat second section with 0.0001 BTC bet size. Total number of bets to be made: ((9.9 + 0.0004) / 99) / 0.0001 = 1000.04 or 1000 bets of 0.0001 BTC each.
Possibility Three: Player wins more than 505 bets (say, 510) in first section , hence ends in the profit of 0.002 BTC. Now amount is enough to cover the house edge of next section so there is possibility to take higher risk to yield more profit so raise the bet size to 0.001. Total number of bets to be made: ((9.9 + 0.002) / 99) / 0.001 = 100.02 or 100 bets of 0.001 BTC each.
PS: Adjust profit/loss element in the remaining amount to calculate number of bets for the successive sections.
Some of the strategies suggest to double the bet size after each bet if the bet is lost while reset to the default bet size if the bet is won. However, that strategy is risky and should only be followed if player is looking to make profits. If our aim is just to end as nearer to EV as possible then the above strategy should work fine.
Topic: Minimizing variance on dice over X number of bets (Read 283 times)
Why are you asking that?
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
Given your name look at it like a bounty tournament. There is a one time shot at an additional prize for a hand, the Bounty (Prize for winning wagering contest), you will play a wider range but not just any 2 cards, so making a -EV decision (playing dice).I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
It's not a spot you would normally put yourself in but if you can study and create a strategy it can still be profitable by minimizing the variance as best you can but at the same time increasing the potential prize in the end. Like I said not shoving any 2 cards but maybe adding in some off suite connectors that are normally a losing decision in the long run.
Not much you can do put put in the work with that dice simulator and spreadsheet that's going on. Reading your original post it made me think of Pio solver for poker; that and the old show Deadliest Warrior. Run the simulations with as much known data, as possible. Then re-run the simulation itself numerous times to get a better idea of outlier results. It's gonna be some work but should give you a good understanding of sizing to use. Then if you get creative look at a mixed strategy, to figure out when it makes sense to adjust the multiplier based on your performance at say the half way point or any other point that the results might say is ideal to switch it up.
Given you will be limited in the number of bets I can't imagine that a static betting strategy would be the best strategy. That's why I think you'll want to come up with a "if this, than that" approach at a few intervals based on whether you are up or down to make adjustments based on that moment to try and right the path and limit your risk.
Why are you asking that?
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
Let's say there's a wagering contest, and to get first place comfortably, you'd have to wager 15 BTC for a 0.2BTC prize. Your EV would be 0.05BTC, but you could potentially lose a lot (or gain more profit) with variance. Minimizing it makes sense in scenarios such as a one time promotional wagering contest where you don't have more tries in later weeks/days for variance to even out.
Well there are some scenario's where it can be helpful. I unlocked a lot of deposit bonuses by playing like this. First get a decent profit and then just wager to unlock it. Where I played, you had one week to unlock it so there you could make a lot of small bets to do that. The more bets the closer you get to the house edge.
If it's to unlock bonuses, I do see more sense in it.
Why are you asking that?
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
Well there are some scenario's where it can be helpful. I unlocked a lot of deposit bonuses by playing like this. First get a decent profit and then just wager to unlock it. Where I played, you had one week to unlock it so there you could make a lot of small bets to do that. The more bets the closer you get to the house edge.
If you don't have that much time OP wants to find out what the best multiplier is to get as close to the 1% house edge.
Why are you asking that?
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
I don't see the point in minimizing variance.
By minimizing it, the only thing you can be sure of is that you will lose money.
If there is more variance, you are more likely to make money, although you are also more likely to lose more than you would by minimizing the variance.
As I say, I don't see it.
For me the best way is not to play EV- games. That way, you reduce the variance to 0 and make sure you don't lose money.
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Well, yeah. I don't think the chance is as big as you make it out to be, and again, the point of the thread is to figure out the best multiplier to reduce variance. I do like the choice of 1.25x as a multiplier; when I've needed to wager recently, I've usually gone somewhere in the range of 1.2-1.3. It feels like a better option than 1.01x to me since an unlucky streak wouldn't hurt as much. I'm very curious to know if it is actually better though.
I think the best way to reduce the variance is making more rolls instead of choosing the right mulitplier. Of course the bigger payout the smaller bets you need to make. The problem here is time. If you have all the time I think the best way to roll is just 1 sat on 2x and let it run forever. So you need to find a better way and as you said I also prefer 1.2-1.3 range so I normally do 1.25x.
Maybe you should try the simulate option in seunjies dicebot and see what settings will be the best.
As much as I would love to make more rolls, in certain cases, you are very limited on the number of bets you can make. For example, Stake has a weekly $5000 race that lasts 90 minutes, and the site will only allow so many rolls in that time period.
Thanks for the suggestion to use Dicebot's simulator, I'll take a look. Does it have functionality where it does a certain number of trials, and gives you the data on the standard deviation (or something similar) of the net profit/loss result?
In the simulate option you can set a balance and a number of rolls. At the end it shows the result.
I created a little spreadsheet to calculate the wagered amount and the house edge. The last line is the result of the simulation as shown above.
Link to the spreadsheet: https://drive.google.com/file/d/1cQda2NA2_v22KEa5c_kCH3wv2_ELt584/view?usp=sharing
I suggest you just make a few simulation per multiplier to calculate the average loss of it.
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Well, yeah. I don't think the chance is as big as you make it out to be, and again, the point of the thread is to figure out the best multiplier to reduce variance. I do like the choice of 1.25x as a multiplier; when I've needed to wager recently, I've usually gone somewhere in the range of 1.2-1.3. It feels like a better option than 1.01x to me since an unlucky streak wouldn't hurt as much. I'm very curious to know if it is actually better though.
I think the best way to reduce the variance is making more rolls instead of choosing the right mulitplier. Of course the bigger payout the smaller bets you need to make. The problem here is time. If you have all the time I think the best way to roll is just 1 sat on 2x and let it run forever. So you need to find a better way and as you said I also prefer 1.2-1.3 range so I normally do 1.25x.
Maybe you should try the simulate option in seunjies dicebot and see what settings will be the best.
As much as I would love to make more rolls, in certain cases, you are very limited on the number of bets you can make. For example, Stake has a weekly $5000 race that lasts 90 minutes, and the site will only allow so many rolls in that time period.
Thanks for the suggestion to use Dicebot's simulator, I'll take a look. Does it have functionality where it does a certain number of trials, and gives you the data on the standard deviation (or something similar) of the net profit/loss result?
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Well, yeah. I don't think the chance is as big as you make it out to be, and again, the point of the thread is to figure out the best multiplier to reduce variance. I do like the choice of 1.25x as a multiplier; when I've needed to wager recently, I've usually gone somewhere in the range of 1.2-1.3. It feels like a better option than 1.01x to me since an unlucky streak wouldn't hurt as much. I'm very curious to know if it is actually better though.
I think the best way to reduce the variance is making more rolls instead of choosing the right mulitplier. Of course the bigger payout the smaller bets you need to make. The problem here is time. If you have all the time I think the best way to roll is just 1 sat on 2x and let it run forever. So you need to find a better way and as you said I also prefer 1.2-1.3 range so I normally do 1.25x.
Maybe you should try the simulate option in seunjies dicebot and see what settings will be the best.
Very good question and I think it's for the statisticians, I don't know how else to calculate so always I go for the simple bet smallest qualifying amount at maximum chance, knowing I will lose around the house edge, but win a bigger prize. Is 5000 a restriction because of time? If so, isn't the best way to just divide 10BTC by 5000 at max chance?
5000 was just an arbitrary number I chose. It would take a decent chunk of time to wager on most sites, but I feel like the bet count is low enough for it to be viable to try to 'snipe' a wager competition.
I'm not too sure if 1.01x is the way to go, hence why I made this thread. For a smaller number of rolls, I think it is definitely not the way to go since a quick unlucky streak would really hurt.
Not sure about the maths to do it, but because you are restricted by number of bets, then it does seem most appropriate to bet:
that's 0.002 btc to get a 10 BTC wager amount.
But the real issue I think, starts at how much you think you need to wager. Because the expected loss is the house edge of wagered amount, not of your deposit. So if you can win the prize with 5 BTC wagered, then you should bet 0.001 btc over 5000 bets.
that's 0.002 btc to get a 10 BTC wager amount.
But the real issue I think, starts at how much you think you need to wager. Because the expected loss is the house edge of wagered amount, not of your deposit. So if you can win the prize with 5 BTC wagered, then you should bet 0.001 btc over 5000 bets.
Let's ignore how much you need to wager for now. The 0.002 BTC base bet makes a lot of sense as the right size, but the main thing I'm curious about is the optimal multiplier.
My strategy, if I had 10 BTC, would be to start on smallest bets on martingale for a bit. As an example, I'd go ultra cautious and eat up the early hours of wager contest with maybe a 10 satoshi base size (or even, 1 satoshi base size on 10 different tabs on auto if site allows, and most do). Set a max bet of 0.1 btc. That gives me roughly enough time to wager a million bets or 10 million bets before I bust on the max bet.
I'm not too sure how much I like the idea of martingale (even with conservative settings) for wagering. I feel like the goal with martingale is to turn a profit, and by increasing your chances of ending with a net profit in the end, you're also increasing the chance of ending with a larger loss.
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Well, yeah. I don't think the chance is as big as you make it out to be, and again, the point of the thread is to figure out the best multiplier to reduce variance. I do like the choice of 1.25x as a multiplier; when I've needed to wager recently, I've usually gone somewhere in the range of 1.2-1.3. It feels like a better option than 1.01x to me since an unlucky streak wouldn't hurt as much. I'm very curious to know if it is actually better though.
If so, isn't the best way to just divide 10BTC by 5000 at max chance?
Not sure about the maths to do it, but because you are restricted by number of bets, then it does seem most appropriate to bet:
that's 0.002 btc to get a 10 BTC wager amount.
But the real issue I think, starts at how much you think you need to wager. Because the expected loss is the house edge of wagered amount, not of your deposit. So if you can win the prize with 5 BTC wagered, then you should bet 0.001 btc over 5000 bets.
That's easy if it's a fixed target to win the prize that makes you +EV. Maximum number of rolls possible at min payout/max chance to win, to reach your wager target, for sure is the best way to minimise variance.
But wagering contests aren't a fixed target... And that's I think where it becomes a problem, because you can't know how much you need to win until it's closer to the end of the contest, though that's generally also where the whales lie in wait for the few hours. And your wager target may very well change as you and said whale(s) compete for the prize as the time runs down!
My strategy, if I had 10 BTC, would be to start on smallest bets on martingale for a bit. As an example, I'd go ultra cautious and eat up the early hours of wager contest with maybe a 10 satoshi base size (or even, 1 satoshi base size on 10 different tabs on auto if site allows, and most do). Set a max bet of 0.1 btc. That gives me roughly enough time to wager a million bets or 10 million bets before I bust on the max bet.
If I'm lucky, I get an additional close 0.1 btc, and a healthy start on wager, and then use that for a 1% boost on final stretch. If I get unlucky, I start the final stretch with 98% of my bankroll, but also already a good start on wager amount.
I sometimes do this to get VIP levels. Cautious martingale to about 1% of bankroll. Then spread that 1% profit out on smallest bets at min payout till it disappears. Repeat. I find, if you have a lot of time to kill on auto, this takes you up VIP levels with a bankroll punching above its weight.
I did this a lot for unlocking deposit bonuses. First get a nice profit and then just start wagering to unlock the bonus.
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Normally I did 1000sat bets on 1.25x and just let it run. At the end I could wager the correct amount and the loss wass ~1% like the house edge. The closer you want to come to the 1% the more bets you have to make. If you want to do it within 5000 rolls there is a big chance you won't come any close to the 1% house edge, both sides. So you can also be lucky and end up with a bigger balance then expected.
Very good question and I think it's for the statisticians, I don't know how else to calculate so always I go for the simple bet smallest qualifying amount at maximum chance, knowing I will lose around the house edge, but win a bigger prize. Is 5000 a restriction because of time? If so, isn't the best way to just divide 10BTC by 5000 at max chance?
Just a side note that I definitely am always trying to take advantage of promos myself but I think wagering contests are usually just for big whales, so +EV is actually only available to limited types of gamblers like me, where we look for contests and bonus... I am not a super big wagerer but if the promo is not too crazy in terms of wagering amounts, I go for it. Hard to find +EV that isn't about wagering contests though!
Just a side note that I definitely am always trying to take advantage of promos myself but I think wagering contests are usually just for big whales, so +EV is actually only available to limited types of gamblers like me, where we look for contests and bonus... I am not a super big wagerer but if the promo is not too crazy in terms of wagering amounts, I go for it. Hard to find +EV that isn't about wagering contests though!
For various reasons (wagering contests, VIP levels, wagering requirements, bet mining, etc), a player might wish to wager a certain amount with the goal of getting as close to EV as possible. You would often have time (and in effect, bet count) limits, meaning that you can't just decrease your bet size to stretch the wagering over as many bets as possible.
What would be the best way to minimize variance in terms of dice settings, over a certain number of bets? Does the multiplier vary significantly based on the number of bets? If we ignore extremes (obviously 9900x would be a poor choice to reduce variance), is there a significant difference between multipliers? (example: 1.5x vs 1.6x)
Anyone know if there's a good way to calculate this? If I wanted to get the optimal multiplier and bet sizing to wager 10 BTC (with an aim of losing 0.1 BTC assuming 1% house edge) in 5000 dice rolls, how would I do that/what would it be?
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What would be the best way to minimize variance in terms of dice settings, over a certain number of bets? Does the multiplier vary significantly based on the number of bets? If we ignore extremes (obviously 9900x would be a poor choice to reduce variance), is there a significant difference between multipliers? (example: 1.5x vs 1.6x)
Anyone know if there's a good way to calculate this? If I wanted to get the optimal multiplier and bet sizing to wager 10 BTC (with an aim of losing 0.1 BTC assuming 1% house edge) in 5000 dice rolls, how would I do that/what would it be?
Self-moderated to prevent spam
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