Pot odds

Pot odds is simply a term for the price you are getting laid by a bet. You can compare this to your assumed equity in the pot to make a judgement to continue or not. So

Pot odds = Bet amount / Total pot after the bet is called

If our equity is higher than the pot odds, we can call (assuming no further action possible, or at least that we realize our equity exactly). In the previous example, our equity was around 17%. If we assume our opponent is betting all-in on the turn here (and that our J high never beats his bluffs), we can calculate the maximum bet we can call directly from the above formula when the bet is X times the pot before the bet:

17% >= Bet / Total pot

or

17% >= (X*Pot before) / (Pot before*(2X + 1)

which can be written

17% >= X/(2X + 1)
=> X <= 0.25

In other words, with this equity, we can call the bet given the assumptions above if the bet is less than 25% of the pot.

The expression X / (2X + 1) can be used directly to compute a few pot odds that can be useful to know by heart. To call a bet of half pot, you need to be good 25% of the time, pot sized leads to 33% and twice the pot to 40%. As the bet gets larger and larger, the needed equity will approach 50% as most of the pot to win will be in the bet and less already in the pot.

You'll sometimes find pot odds expressed in ratios, like 3 : 1, but personally I find it easier to think about total pot and percentages directly, rather than going via ratios such as the one mentioned for a half pot sized bet.

Basic poker probabilities

Poker probabilities can be done naively even at the tables, just counting the cards and doing the percentages in your head. I still find this kind of fun and sort of effective, even if I will show you some useful shorthand methods below.

What I mean by naively is simply to divide the cards you believe will make you win the pot by the total cards you have not seen. Look at this example turn situation, where you are last to act with a bet before you:

Hero: J♠T♠
Board: K♦Q♥2♠3♣

If you get an ace or a nine here, you are winning (or splitting) the pot. There are four aces and four nines not accounted for, and 46 unknown cards. Thus, you have 8/46 or a bit over 17% chance of making your hand. 

A shorthand way of computing this is to count the cards, or outs, you have to make your hand. Each out accounts for a roughly 2% chance of making the hand. In this case the "outs shorthand" would indicate 16%, which is probably close enough in most cases. If you are guaranteed to see two cards, for instance when your opponent is all-in on the flop, you can use 4% (which is simply 2% twice, or a rough shorthand for 1/47+1/46, which is about 4,3%).

The term usually used in poker for this "chance of winning" is pot equity. With that in place, we are ready to look at two other basic concepts, namely pot odds and later implied odds.

7 gems of poker magic (or at least math)

I've always enjoyed the game of poker. And I've always loved math. But it is not until recently[1] I have begun to combine the two much. Doing this, I did not really find a simple tutorial suited for me (what I found was either way too basic, way too advanced or did not read really well). I also use the word tutorial for what I was looking for on purpose, even when I am trying to explain math concepts, I hope to do so in a very practical way.

For some of you this set of articles is still going to be too basic, but I also have an ambition to come back with some more advanced pieces later (for instance covering stuff I am discovering when playing around with poker bots and lately reading the old, but still good, Mathematics of Poker book), given I reach that level and also given that I find the time.

Anyway, on to what my so called 7 gems of poker math will cover:

- Basic poker probabilities
- Pot odds
- Open or not - do I have the best hand from this position?
- Implied odds and EV estimation
- Counting combos
- Basic and badass understanding of blockers
- Balance and board coverage

All the content will be for NLH (No Limit Texas Hold'em). I will not explain core poker rules or basic probabilities in the articles, but I will go through the example step by step with a certain degree of hand-holding (no pun intended). I hope I got the balance right and that some of you will enjoy it. For sure it will be a useful exercise for me to structure my thoughts enough to write out the pieces.

Hope this proves useful for someone, please shout out if you have comments or other feedback.

[1] - Well, this set of articles have been in a rough draft state for about five years, so it has been a little while now (and in fact other books have inspired my game more than the good old MoP mentioned above, but I decided to keep it and rather write a separate post on books later). Inspired by making day 2 of the WSOP Main Event at GG yesterday (after double-satelliting in, first USD50 into a USD500 satellite and then from the latter into the actual event), I decided that it would be better to get it out rather than waiting to find time to make it "so, so much better". So here it is!

The cereal entrepreneur

I follow the blog of Seth Godin and admire this thoughts on marketing etc. almost daily. I particularly liked the piece today called The cereal entrepreneur.

This section is worth remembering, I think: 

Every dollar not spent is a dollar you don’t need to raise. Eat cereal, not sushi.

Kind of relevant to us, as we just raised money for our product company (article in Norwegian). We'll continue to eat cereals and work hard. 

Hats off to Microsoft

This is a blog post I kind over never thought I'd write, as I thought of MS being stuck in the old world with Office products, Sharepoint and struggling even with the latest Windows versions. As an example I was testing Azure two years ago and it was very clunky and not really a serious contender to Amazon's AWS feature-wise.

Fast forward to today. Nadella's MS seems to be very real about being on all kinds of devices and Azure is elegant and efficient - I'd say very close to being on-par with AWS (which I also love, by the way), even for us that is basically mainly a Linux-based shop on the server side. And locally we see a quite new humbleness in the organization of the giant and a willingness to work with and help startups.

So hats off to Microsoft. Well done. Be sure to keep on improving.

Full disclosure: My firm has received some free usage of Azure via MS's Bizspark Plus program and this is the way I got to use Azure more again, but the sense of radical improvement is very real.

Startup valuation hype cycle

There is a lot of discussion in the startup community these days about if we are on the top of a hype or close to seeing a bubble burst. From my point of view, running a bootstrapped startup, it is not feeling like VCs are throwing seed money at you. At least not in Norway. But valuations for the "Unicorns", which are truly not common to see just like their fairytale counterparts - even if we forget it when we use them as samples and idols, are surely high.

Anyway, I wanted to share a super fun tongue-in-cheek "press release" from Basecamp. The entire thing reads well and if you are like me, it will give you many giggles, but this is my favorite part:

In order to increase the value of the company, Basecamp has decided to stop generating revenue. “When it comes to valuation, making money is a real obstacle. Our profitability has been a real drag on our valuation,” said Mr. Fried. “Once you have profits, it’s impossible to just make stuff up. That’s why we’re switching to a ‘freeconomics’ model. We’ll give away everything for free and let the market speculate about how much money we could make if we wanted to make money. That way, the sky’s the limit!”

Sounds like a brilliant plan! 

Get-set-go!

On Friday a blog post I wrote was posted on Innovation Norway's Gründerpulsen blog. It is in Norwegian and covers how to get a professional (cloud-based) infrastructure for your startup up and running in a week.

It touches on everything from email providers to PaaS, so it was a challenge to try to keep it relatively short. At least it is very to the point, mostly containing specific recommendation of tools (with links) in the different areas. Hope someone finds it useful!