I posted this which might have been in the wrong forum so I thought I post it in this forum since no replies on the other one.

Most suggest that betting lower average odds decreases variance. I always assumed this was correct but after reading a comment made in the sports betting forum where someone asked


To which someone replied



And then another reply contradicted that

Variance is maximized at break-even. As edge increases, variance decreases. That's how the math works. The highest variance bet is a coin flip.

If by "odds" you mean the probability of success (or failure), then nobody who understands it actually says that. A simple example is roulette. Betting red/black is the highest variance bet in the game. Betting single numbers is the lowest variance bet.

OK Thanks!!


So I first I wasn't sure if the post below might have been a troll.




So going by what you said and if I understand this correctly, its not a troll and he was correct when he said the previous posters were wrong.


OK here are a couple comments from betting articles online, I would appreciate if you or anyone could have a quick read; because this is often written in betting articles, in fact after doing a Google search, there was no articles that suggested betting shorter average odds produced higher variance, every article said the same thing, that if you wanted to lower variance bet shorter odds (even money etc), because betting bigger odds (Ten to One etc) increased variance.

First article

second article


So just to confirm both these articles are wrong? if so why is every betting article online saying the same thing as these two articles are?

You are confusing bankroll swings with variance. They might sometimes correlate but aren't the same thing.

The first quote above doesn't mention variance, but does accurately describe bankroll swings (and on a low variance bet). The second quote does mention variance, and the term is used incorrectly.

I'll leave it to someone else to explain or give you mathematical examples, as I'm at work now.

But think of betting a longshot bet like single number roulette. You expect to lose almost every time. And you do. So that's low variance from expectation. Conversely, when you bet on coin flips, you never breakeven on the bet, you only win or lose every time. But your expectation is to break even. So it's high variance from expectation. This is overly simplified obviously.

I understand TY.


I'm just wondering why all the articles though are writing the same incorrect information? I even spoke to some people I chat with regularly, and they also agree that the articles are correct and that betting shorter odds equals lower variance while betting longshots equals higher variance.

For example this article, and this is a massive article that got a lot of likes and people agreeing with it on social media.

Steps to reduce variance
Bet on lower odds ranges (E.g. < 3 )





And link to article http://www.blog.tradematesports.com/...oidlimitations

I’m pretty sure that what NewOldGuy is referring to is the variance of a Bernoulli variable, one in which there are only two outcomes, like win or lose, heads or tails. The variance for a sample of n independent trials is pq/n, where p is the probability of one of the outcomes and q = 1-p. the occurrence probability for the other outcome. (Binomial variance)

It is easy to show that the variance is maximized at p= ½. The sample article OP shows states that to reduce variance you should bet when odds are <3. Now if odds are defined as 100/p, this recommendation means that to reduce variance you should bet when p= 50% (odds=2), for example, which is absolutely not supportable.

I think these blog writers are just using variance to mean something other than what it means, something like, how long it takes on average for your cumulative result to be somewhere close to the expectation. It's true that this time (in # trials) is shorter for near-breakeven binomial bets (because wins and losses cancel each other out). But variance isn't lower.

This misuse of the word is all over the sports betting world apparently.

It is true that the variance of win/lose is the highest when the probability is 50/50. But that does not mean that you increase variance by betting lower odds. It would be true if you received an equal payout regardless of the odds - but you don't. You actually get a higher payout when you have higher odds.

So, a simple example can be done in Excel. Take two situations - in each case you are getting exactly the correct payout relative to the probability of success.

In one, you have a 50/50 chance of winning, and you will win $1 for each $1 you bet if you win. In the other, you have a 10% chance of winning, and you will win $9 for each $1 you bet. Suppose you play 10 times and everything goes according to probability. In the first instance you will win 5 times, and get $5, but lose 5 times and lose $5, thus breaking even. In the second, you will win once, winning $9, and lose 9 times, losing $9, thus breaking even.

Calculate the variance of 1,1,1,1,1,-1,-1,-1,-1,-1 and compare it to the variance of -1,-1,-1,-1,-1,-1,-1,-1,-1, +9.

You will find that the variance is much higher in the second one. If you looked at the results as simply WWWWWLLLLL vs LLLLLLLLLW - the first one will have higher variance. But when we are betting, the variance of wins and losses isn't nearly as relevant as the variance of money won or lost.

This is true. We can prove it mathematically in an even money bet.

This is not. Odds is referring to the payout. Games with a small risk to win high, infrequent rewards are higher variance than even money bets. Betting single numbers is higher variance than betting red/black. DDB is higher variance than JOB. No limit poker is higher variance than limit at the same blind level.

I stand corrected then, given that we are talking about the variance of the bankroll and not the variance of the win/loss result to expectation.

So just to confirm was the third reply correct or incorrect to the original question in the op

The answer depends on which variable you want the variance of. Both answers were correct as neither specified the variable. In poker we often talk about variance in relation to win/loss, particularly in this thread. In sports betting, as VBAces pointed out, the more important variable is the $ won or lost, as payouts are often asymmetrical.

Betting the same amount on a 51/49 bet versus a 90/10 bet could be a mistake, even with correct payouts. One bet or the other may allow for variance beyond the optimal, or the limit desired by the bettor.

If the wagering bet size is fixed, then the bettor should be limited to taking bets that are closer to optimal for bankroll growth, and declining bets that exceed a predetermined tolerance for variance.

If the money is ultimately what matters, then the size of the bet is the skill, if the odds are correctly determined.

From the poker perspective, if playing fixed limit poker a player who opens the action with a hand that has an established WR of .01 BB per hand would need other reasons to do so, beyond winning .01 BB, otherwise the experienced variance will be unpleasant and also lead to sub optimal bankroll growth.

In poker we also talk about variance in relation to $ won or lost. Why would we care about anything else?

Only in this subforum I suppose, there are lots of discussions about variance of other variables than $ won.

Specifically with respect to poker/gambling? Can you show an example? I don’t read this subforum a bunch.

Would you be able to post a formula showing this say even money vs ten to one?

$1000 bank, betting $10 odds vs betting $2 odds, both using Kelly both with the same edge of 10%.

The first example is $10 odds.
after 9 loses 1 win

1000 11
989 11
978 11
967 11
956 11
945 11
934 10
924 10
914 10
904 Finale bank



Second one is using $2 odds after 5 loses

1000 100
900 90
810 81
729 73
656 66

590 Finale bank

After 9 losing bets using Kelly, betting $10 odds the bank is $904, compared to betting $2 odds, where after 5 loses the bank is $590.


If you use this example, to me the swings seem much greater betting shorter odds vs betting longer odds, and swings and variance sound or seem the same, sort of, from a noob point of view. This part is where I'm still confused.