I'm not sure if counting on set over set as your main source of profit is a sustainable strategy.

This, you're running really ****ing hot.

Uh-oh.

Especially when the guy with the flush wipes you both out...

One thing to keep in mind is that the kelly criterion gives you the *optimal* amount to bet to maximize your expected bankroll growth. It is not intended to be an upper bound. If you have a logarithmic utility of money (kelly criterion), it is probably still worth taking bets with an edge that are for more than kelly would suggest for your bankroll, as long as they aren't a *lot* larger than the kelly amount. A quick log utility estimator in Excel shows that with a bankroll of 20k, the 1000 bet with a 51.25%edge is ok, just not as good for you as a 500 bet (which is close to your optimal bet size).

If you are an aggressive gambler, the Kelly criterion represents the bullseye of amount to bet, and there's a reasonably wide range that offers similar expected utility. For instance, with a 20k bankroll, your 2.5% edge bet has a utility adjusted gain of $6.25 at $500 which is right around the kelly criterion bet. Betting $300 has a utility adjusted gain of $5.25 which is nearly as much. Betting $700 also has a utility adjusted gain of $5.25. Betting $1000 starts getting dicey, cutting your adjusted gain to roughly zero.

Generally the utility adjusted amount rises gradually with your bet, until it plateaus near the kelly amount, then comes down slightly at first, and starts going over a cliff usually somewhere around double the kelly amount.

This all assumes you have roughly logarithmic utility of money which should be relatively close to accurate for a very aggressive investor or an advantage gambler, but will be much too risk-loving for the typical person.

It's worth putting together a spreadsheet to analyze props like this. It isn't hard. Here's the formula I used:

Start by converting your bet to an EV equivalent bet of win X n% of the time, and lose X 1-n% of the time.

ln is the natural logarithm function in excel etc.

pwin is the probability (between 0 and 1) of winning the bet
bet is the bet amount
bankroll is your bankroll

util-adjusted-EV == exp( pwin*ln(bankroll+bet) + (1-pwin)*ln(bankroll-bet) ) - bankroll

Utility adjusted EV is basically logarithmic utils converted back into dollar units. For very small bets relative to your bankroll, this will be very close to linear EV (what we're normally talking about when we say EV).

The primary function of good bankroll management is to keep your bets at sizes where your utility of money function is close enough to linear that standard EV calcs are close enough. If you put too much money on the table your utility of money function starts to become important, and you become exploitable by people whose utility at those stakes is still close to linear (scared money).

For crazy prop-land, it's a good idea to have a sense of your real utility of money function, and what kinds of bets/edges will maximize it, or at least be in range of maximizing it.

Short answer: your 1k bets are not terrible and probably don't hurt you much unless you have a hard bankroll or are more risk-averse than a typical poker player.

Only bring 5bi with me when I'm away at school bc I don't like bringing my entire roll when I can't play consistently. Just a mental thing, and playing under rolled is not fun. Some semesters I only get to play 10-20 hrs bc I lose a few bi and just call it off for the semester. Luckily this semester I'm on a 15bi upswing and it helps pad my roll when I get home. Just always make sure I'm in a situation to make more than I can lose, but starting from scratch is going to be extremely difficult.

I hate to break it to you, but it's pretty much a degen cliche. I think they've even made some movies. Every gambler's dream is to run 1 buyin into a fortune.

And since it's not crazy to start with 1-2 buyins as a rec gambler with a day job, I am quite sure that a fair number of poker pros have done exactly that. Since I started playing live after a 5 year poker break, I'm currently +1040 off an original buyin of $80. I've yet to have a single down session. I've had plenty of down sessions at *play money* online, but so far my worst live sessions this year have been about break even.

Sometimes you run good.

Hey Mes, by optimal I thought that meant the statistically fastest way to grow your bankroll while minimizing risk of ruin. By definition how could you be better than optimal?

Haven't grinded thru teh maths yet since its late and I'm about to eat some steak

yeah no ****, like getting a 200xbb stack in is easy in a 3bet pot, 300xbb plus is a bit more difficult. some people can't ****ing read between the lines.

11T, Kelly is NOT the fastest way to grow your bankroll, that's a common misconception. Kelly is not even the fraction of your bankroll to wager (rather, it is equal to the fraction of your bankroll to wager in special circumstances -- and in most gambling situations those circumstances are satisfied, but in things like trading markets, Kelly is no longer a fraction in most casees).

Regardless, The Kelly Criterion maximizes the leverage factor to apply to a stake asymptotically -- as the number of plays apprach infinity. For example, if you have a positive expectation play, that's maximized by wagering 100% of your stake. AIf you were to quit at two plays, the expected optimal fraction is somewhere between 1.0 and the asymptotic "fraction" (and again, one needs to be careful using he Kelly Criterion here because that only equals the fraction in special cases, and never results ina value less than the asymptotic fraction, which we all know can be trouble). So the fastest way to reach a specific goal is either have a target in terms of number of plays you will encounter, and find what is the optimal fraction with regard to that, OR, to have a specific upper goal on the stake, iterate to that value of number of plays and corresponding optimal fraction for that number of plays which results in the least number of plays.

Lastly, and this may be a value, a fraction of your stake that is more germane to what you are trying to do than the growth optimal fraction. Rather than wager the growth optimal fraction (or Kelly Leverage Factor, the two are likely equal in this instance on this thread) is to wager that point to the left, that point which is less than the grwoth optimal fraction where the function of growth with respect to percent of stake wagered flips from being concave up to concave down -- the inflection point left of growth optimal which represents that amount of your stake to risk where marginal increase in gain is maximized with respect to marginal increase in risk. The math behind this for those who are interested is at http://papers.ssrn.com/sol3/papers.c...act_id=2230874

-Ralph Vince

Thank you for your reply and I just saved your paper in my drop box for later, it looks interesting.

On the Kelly wiki it seems clear that the Kelly betting strategy is iterative and not for infinite runs. Is this correct or am I thinking about it wrong? I do understand that it is best to bet to the left of the inflection point and not to the right with respect to gambling but how can it be correct to wager 100% of your stake (as in bankroll?) for a positive expectation play or is this with respect to investing where the risk of losing all of your money is much less and not a 1k flip with a 50 dollar overlay.

With investing etc. you aren't likely to lose all of the money you risk (unlike gambling) which is where I am guessing a lot of the mathemagical differences come in?

I can think of two distinctions:

There is a difference in modeling an event with only two outcomes (win all or lose all) vs. an event where you may have a range of outcomes from a risk of ruin perspective.

The other thing is, in gambling, presumably, you're making the same bet over and over again (at least for Kelly criterion purposes). You're running it 20 times with the same deck for instance. That really isn't exactly replicable in the investment world. You can theoretically do it but it's basically impossible from a real-world perspective, since you won't find 20 investments that are exactly the same. You have to fit them to a distribution.

The Kelly criterion is more accurate for the discrete gambling problem than for investing, IMO.

Wow, a lot of great replies to my prop bet question. Thanks so far.

And on a side note, a reg with whom I play sometimes was doing 500 coin flips the other day. And he ended up getting another reg to give him 5% overlay on a 2500 coin flip.

Assuming that this reg happens to have a 50k poker bankroll separate from his life bankroll, and also probably has a 50/hour win rate, is the 2500 coin flip bet with 5% overlay +EV or -EV?

I'm ball parking that it is quite +EV to do it like once and quite -EV to do it twice

that kind of sounds ridiculous but it makes sense to me, like as a one time risk it isn't too "risky" but if you would run the event over and over again without having a large enough bankroll the short term variance could easily be too great and you don't hit the long run quick enough to realize your edge.

I'm up like 7k in the last 100 hours

COME AT ME BROS

^nh 11t. I'm up just over $2,400 in my last 4 session totalling 13hrs.

[x] sustainable. ;-)

FFFFUUUUUUUUU

in all seriousness, I had a pretty long stretch of running like trash combined with playing poorly here and there and confidence is rising.

However, I know I can play much much better than I am.

11t, not to one-up you here or anything, but I just played my 100th hour at my local casino this weekend and I'm now up $11,880, all at 2/5. I'm playing better now than I was when I started but am still making plenty of mistakes. I shipped 500 last night on a horribly played hand when it should have been obvious my opp had a set. Ugh. Still ended up 550 in 5 hours.

[ ] sustainable


55 hours played at my other casino and I'm up $170 total.

[ ] sustainable

must be nice to run like god

It really is. I'm terrified of the impending cliff.

that's unsustainable haha.

Love the $1 book sandwiched in there.

If u guys have a 23k life and poker roll and play 1-3, 2-5 everyday and a massive whale (complete spewtard that consistently does 8-9k at 2-5, 20+ in higher games) was sat at a 10-25 game with a 10k min sitdown and a seat open would you take the seat?? All other seats are filled with a mixture of high stakes (5-10-10-25) pros and old reg 5-10 nits. This whale is already stuck 40k and in full gamble mode, if not at what stage would you take this opportunity? This is based on a real situation

If I was a pro and that was all the money I had, I'd be an idiot to sit in that game.

I'd shot take there with like a 100k poker/life roll.

Probably not since you will hate life if you lose half of your savings in one night. You would also want to reload if you lose a few hands which would be pretty risky with $23k total. x2 on $100k minimum life roll to sit in that game.

This is very different from being able to play the whale HU. Let's say that the table is half high-stakes pros and half 5-10 nits. As a 1-3/2-5 player, you are probably not as good as at least 2-4 other players at the table, on par with maybe two or three of them, and better than the whale and maybe another player or two. Does that sound like an +EV situation for you? And on top of that, you can assume that every time the whale is involved in a hand, there probably will be a pro who is going to put massive pressure on you in an attempt to isolate the whale.

We don't make money being better than one player at the table; we make money by being better than most/all of the players at the table. I can't imagine risking 40% of just my recreational poker roll to play in this game, much less 40% of a poker+life roll.