Mathematics of Gambling: the Kelly Formula

[@gustavovaca8873]

One of the most useful and well explained videos I've ever found in KZbin...thank you!!!

[@csvaughen]

wow - thank you for such a positive response! So glad you found this interesting - I did this video so long ago, feel like I could add more now, actually I do have another more recent one here kzbin.info/www/bejne/Y2fMo5enhNSCY5o , it is a fun topic but my focus more recently has been rocket science and aerospace, no denying the attraction of looking for an edge though!

[@ammarorama]

absolutely fantastic video. kudos.

[@Beaches_south_of_L.A.]

I love this guy. You sir are a genius! I would follow you anywhere Mr. Christopher Vaughen!

[@kenhamasaka2524]

Thank you Mr. Vaughen, a very nice presentation of the Kelly Criterion. For further discussion is the representation of 'odds'. In your example, you use '2 to 1': that is 'race track odds': a dollar bet returns $3. Vegas odds are: '2 for 1': a dollar bet returns $2. Very different.

[@slickchukklez7191]

Excuse me, sir. Here in Las Vegas, a table bet that was presented as "2 for 1" would be a forfeit of the original bet(1) and a gain of twice the amount(2) It's a flat bet. If you win, you get your money back and get paid the equivalent of the original bet. -if presented as "2 to 1" the same amount is paid (2) without forfeiting the original bet. (1) (Much tastier)

[@IntermountainGoldRefiners]

This is really important retirement information and now I’m more interested in probability estimation skills.

[@csvaughen]

I'm glad you find it interesting, I would not recommend Kelly Formula for retirement planning. I would recommend "Fortune's Formula" by William Poundstone (on Amazon) to learn more about this formula in general and relation to investing

[@IntermountainGoldRefiners]

@@csvaughen Thanks for the tip, I'll go look at the formula and see what I can gather. I listen to a lot of investing pod casters and Kelley Criterion comes up once in awhile when trying to decide how to put on an investing position for sizing portfolios. Also being able to compound money with an edge is central to this conversation.

[@willykitheka7618]

Awesome stuff! Very interesting!!!

[@DramaticOgre]

lol all these formulas i learned about in algebra 2... never thought i'd be seeing them in a video about gambling

[@stefanmitrovic973]

Excellent Video! Forgive me for the intrusion, I am interested in your initial thoughts. Have you thought about - Rozardner Right Bet Reality (probably on Google)? It is a smashing one off product for highly winning sports betting system minus the hard work. Ive heard some incredible things about it and my friend Sam after a lifetime of fighting got great success with it.

[@shaofeima9755]

great video, I've been confused in the problem of fraction of bankroll in each bet, it helps me lot !

[@roberthuff3122]

Excellent and informative video. The multiple approaches e not 2.8 as the time subintervals go to infinity over the year.

[@msizibriancindi1459]

That was really interesting. This is something I can really use for my sport investing

[@chrisstraw5985]

"The Kelly Formula is only useful is we know the true probability of an event...." This was a pretty good youtube video presentation, but you have to agree that this comment at 35.53 basically renders the entire presentation useless as it is basically saying "The kelly formula is useless for sports gambling because no one will ever know the true probability of a sports event". Agree? OK, I am being harsh, and I think Kelly can be of use to a lot of people. If so, here are two thoughts to consider: 1. You cant calculate an accurate prob for a sports event, but you can try. If you keep losing then its "probable" that you are no good at it and need to quit or find someone that can. 2. The system may work best with an analyst working separate to a risk manager (the guy calculating the Kelly bet). This is because Kelly is going to produce some really aggressive outlays (percentage of bankroll), especially when you get down to $1.40 - $1.50 decimal odds. If you do both, you'll likely change either side (ie you estimated prob of a win or how much you are willing to bet). So basicially you should work out the probability of a team/horse etc winning and pass this onto the money manager/risk manager to place the bet without you knowing how much is going down.

[@csvaughen]

Thanks for your comments. My answer is this: We don't know the true probability for outcomes of sporting events, but we can do our best to estimate them. A professional, with a well designed model, can try to find an edge. Of course, that's the whole point. If you can find an edge, something other people don't see, the Kelly formula tells you how much to bet on that edge. No one knows the "true" probabilities for many outcomes that we model - like the weather, the stock market, politics, of course insurance.... but we have still built very good models for these outcomes. If you could build a better model, then you can find an edge.

[@nightlyslash8836]

great vid but you lost me when you uploaded information that is clearly unreadable. Why would you bother uploading this video? you have 10 min of viewable material. Then your making people try to make out the information. As far as sports betting. You both are clearly wrong as vegas has been a winner for EVER. lol there not guessing guys. they know down to the hundreth of a % which teach will win when and where. AKA why there lines are spot on. Again great start to the video but i expected a lot more after that 10 min mark man. Your better than this .

[@carlocanlas8730]

+Chris Straw Lovely Video clip! Apologies for chiming in, I am interested in your initial thoughts. Have you researched - Rozardner Right Bet Reality (just google it)? It is an awesome one off product for highly winning sports betting system without the hard work. Ive heard some extraordinary things about it and my GF got astronomical results with it.

[@danb6636]

He mentions at the the end Fortune's Formula, and I have to also agree that it is a great book, informative and entertaining as well. Highly recommended.

[@BrockPageProductions]

Listen guys I really liked this. Just keep up the great work!

[@blackballer3750]

You explained the basics really well. Well done!

[@Pedritox0953]

Great video!

[@prasadmahadik5684]

Very nice explanation! Thanks

[@polares8187]

Really well put video mate. Appreciate it.

[@SuperJaypatterson]

Very good, I just wish I could follow along and understand it.

[@csvaughen]

thanks, I can try answering any questions, this is a newer video on same topic kzbin.info/www/bejne/Y2fMo5enhNSCY5o

[@SphereofTime]

0:36 2 to 1 against

[@Kounomura]

There is already a certain asymmetry between winning and losing, a shift in the direction of loss even if I win the same percentage as I lose. If I start with $100 and gain 1% (101% = $101), then lose 1% (101*99%=99.99), the end result is -1Cent loss.

[@csvaughen]

yes, I've always found that result interesting, equal percent gains and losses cause a long term loss over time. Nevertheless, that does not change the results derived here.

[@saro4761]

Amazing Christopher Thanks

[@FunWiDofa]

Hello, Great Video ! Loved it. Answered many of my questions. However, I have a few more if you can help. In your example at around 26 mins mark, you talk about having 10 coinflips would make a bankroll go from 100$ to 180$. 1st) Are we talking about betting 25% of your current total or your total amount that you have ? 2nd) Does order matter ? if we lose 5 times first , then win 5 times in a row, will we have more money compared to another order?

[@zkowie]

How do you deal with bets that are currently in play? I'm imagining the case where you're betting a fraction of your current bankroll every time - so decreasing with each bet. If I now place 100 bets before any of them are settled, each with a true probability of success of 50% and lose half of bets with the highest betsize, and win half the bets with the lowest betsize, I'll be losing money like crazy. In this case a flat size would be optimal. It seems to me that Kelly only applies when each bet are given a return before the next bet is placed, is that correct?

[@csvaughen]

+Martin Skow Røed Yes, I think you are right, but if there are bets already in play, doesn't it just make sense bet the kelly fraction of the bankroll that remains, excluding those bets already in play?

[@zkowie]

+Christopher Vaughen That would seem like the rational scenario. However, when you then place on the true odds of 2 with a return of 3x until you exhaust your bankroll - there exists a lot of combinations where that would end up as not profitable. The extreme case is when you lose all the bigger bets and win all the smaller bets.

[@MrTinbuzzard]

Great video. My thanks to you.

[@ponzianomanning3071]

It sounds like you can't lose using the K% formula? But you certainly can, and people should know about it: If you have a run of consecutive losses early on in a series of bets you can bust. Losses often don't occur in convenient sequences. Take your example of 50/50 probability, and $2 pay-out; if you continue to bet 25% of your bankroll on every bet you eventually will go bust when a run of 4 consecutive losses occur, which will 6 out of 100 bets. Thats true no matter how much capital you've won: when you get a run of consecutive losses you can easily bust your bankroll. So at some point K% needs to be adjusted to K%/2 or 3 or 4... It's prudent to do that early on in a bet series to be safe. K% isn't a magical winning formula. Useful yes, very much so, but its aggressive so use it with caution.

[@adamtuck4898]

Would you still get the same return of 180% assuming 5 successful and 5 unsuccessful outcomes, if the order in which those outcomes occurred was different? i.e. would 3 wins 3 losses 2 wins 2 losses give you the same return as 5 straight wins then 5 straight losses? Mathematically it would seem so as you can just rearrange the expression but intuitively this outcome seems weird to me.

[@csvaughen]

+Adam Tuck Yes, the order doesn't matter. The mathematics provides a conclusion that seems counter-intuitive at first, but you can verify it is true. That's the beautiful thing about math, it can help you find the truth, even if it isn't obvious at first.... I've been wanting to make a new video to replace this one, your question is inspiring me to make another go at it...got a lot more I can say about this stuff... and I hope I can say better... we'll see...

[@adamtuck4898]

+Christopher Vaughen Thanks for the response, the video is very good, interesting, well explained, easy to follow and well planned out. You seem like you have a good channel, you should really have more subscribers.

[@hitendraspatil]

Nice one 👌👍

[@louisthurston3067]

Of course for all casino bets and 95% of sports bets with professional odds makers including racetracks , the Kelly formula has x=0%

[@madam_im_adam]

Really informative vid dude, whats your background? I'm about to start a data analytics major

[@csvaughen]

Thank you!! I majored in math for undergrad and grad school and now I teach math at a community college - data analytics sounds like a great thing to study

[@198317102788]

¿Quien puede traducir este interesante video al ESPAÑOL?

[@shaandrew]

I would be very grateful if someone could give me an opinion, could I substitute p for my probability of winning for a given strategy to estimate the return over time and to stake the correct amount of money to maximise profit. Rather than an estimate of the probability for a given race. For example substituting 0.85 for p. Which is my success rate when lay bets. Thanks Andrew

[@sushantchigadul3366]

Sir please can you say to me about number gambling like in USA cotton candy and in INDIA satta matka. Please sir i believe you will reply to me

[@MikeDaGreat2]

I have no clue why I'm watching this other than I have a gambling problem lol

[@chrisstraw5985]

You lost me a little at 17min. I couldnt help but think this section was a waste of time because you were assuming all odds for every bet were the same. In other words, you asked what is the true prob of winning a bet. But if the odds are $2 or $5 or $10, they are all going to be different because you'll likely win from any $10 bets far fewer times than winning $2 bets (which is why Kelly says only put 0.22% of the bankroll on if your estimated prob of winning is 10.2% and the odds you can secure are $10).

[@driversteve9345]

The title should have been labeled with Sports Gambling! I was hoping to see something about table games in casinos!

[@amalguptan6716]

You can still apply this to texas hold em by being a bit crafty

[@johndearden7931]

There is only one way to bet. Accumulated odds

[@nikmittica2631]

A $1 bet at odds of 2 to 1 does not return $3

[@chokurei38]

Nik Mittica includes the return of your stake . Semantics . Wins $2 returns 3

[@cristianmicu]

your 'derivation' has nothing to do with kelly criterion formula dykw?

[@alexgentry8761]

betting 2-1 odds with 10%... would'nt your BR increase by 5% which is half of 10% considering ur risking 2 for 1 so a 50% return on your 10%...

[@csvaughen]

When I say 2 to 1, I mean 2 to 1 against. That means if a $1 bet is correct, you get back $2 in profit, which means you collect $3 total. So you double the wager. If you wager 10% and you are correct, you get a 20% increase. If wrong, you lose 10%.

[@noneNone-mw1px]

In jesus name. The only equation for gambling is: 1_ big bankroll 2_ system 3_ patience 4_ target goal. 5_ no alcohol 6_ keep cool X hit and run = winning Other equations is bullshit. Amen

[@vasantpatel9321]

If u have soccer prediction....plz...msg me

[@csvaughen]

yeah, I wish!

[@tensevo]

Take home - Keep bets small and only place bets with better than 50% chance of winning.

[@tensevo]

...also increase and decrease bet size according to size of bankroll - v important - gambler bets more as his bankroll reduces to try and recover and results in financial ruin. Mathematician reduces bet size as his bankroll reduces.

[@pauloxxx7060]

lol

[@boystercaruthers2517]

Guys I make minimum $200 to $300 a day with sports betting at *TheSportsCash. Com* I Do recommend this website to all you guys who wants to earn their living with sports betting

[@kahloonng9702]

有联系方式吗？可以用中文教我吗？