How Crunching Numbers Made Me a Fortune in Poker

How Crunching Numbers Made Me a Fortune in Poker

Today’s #HOTD is a throwback to an epic session I played in Ivey’s Room at the Aria Resort & Casino. There’s something about playing there that brings out the kid inside me; the one who read ‘The Professor, Banker and Suicide King’ as a 16 year old on a camping trip, dreaming about one day playing on the biggest stage in the world.

Most instead dream of the WSOP Main Event and bracelets, but to me there’s no thrill like high stakes poker, where a normal first place tournament prize could be won and lost in a single hand, a single mistake, a single great read.

While today’s hand review is one of those fairly big monsters, it’s more about the normality of hand that made it worth telling. It’s a hand that without careful insight could be chalked up as standard and without much further thought.

That’s precisely why it’s so interesting.

A great example of how an otherwise trivial decision to fold could be turned into a profitable call through some in depth analysis and number crunching.

My plan to check at showdown turned astray when my opponent came out firing. His small bet size however gave me just the right price I needed to call. Had he bet bigger, say the size of the pot, I’d have a much tougher choice and would have likely folded.

I don’t believe this to be a long-term mistake on his part. What he expects my calling range to be shouldn’t change based on how big he bets (he can’t expect me to hero call with two red kings). Therefore betting half pot he gives himself a much better price on his bluffs.

His logic was likely, ‘if my opponent is going to fold regardless of my bet size then why waste more money when I’m caught?’

And he was right. It’s a brilliant play. 

We both played it well, but in the end somebody has to win. I may have won the hand, but that doesn’t mean I was correct to call. 

I know ahead of time that by calling the river I’m going to lose my fair share of the time, but to find out how often I had to do some math. As always, I ran the numbers afterwards to confirm if my hypothesis was correct.

I started by giving my opponent a range of hands he would be betting the river with. You’ll notice his range is fairly narrow and I discounted hands he could theoretically hold such as sets (QQ, JJ, 77 and 66). I did this because he would likely check the river with those hands. 

In other words, his checking range is much different than his value betting range.

1. ENTIRE RIVER RANGE

This is a screenshot of every hand he could have on the river, before he acts.

2. RIVER BETTING RANGE

As we already discussed however, once he bets the river his range changes dramatically. This screenshot is my estimation of the hands he actually bets the river with, which of course is all that really matters.

Hands like sets, two pair and small flushes would almost always check (since they can’t expect to get called by worse), so I discounted them from his range. I also discounted certain combinations of one pair hands that he wouldn’t bluff with 100% of the time. This is a more advanced way of doing hand analysis, but I felt it was important to share here as it dramatically affects the equities. Missing this key step could turn a losing call into a profitable one and vise versa.

Let’s take a hand like KJ off suit for example and analyze how our opponent would play it on the river.

There are 6 combos of KJ off suit which he could hold, 3 of which contain a club in it. I assumed he would value bet these 100% of the time.

Of the 3 combinations of bluffs (KJ with no club), I assumed he’d only bluff with 2 of them, and that with the other 1 he would simply check and hope to win at showdown. Which combos he would check or bet with is arbitrary and irreverent for our analysis, nor can we know this for certain.

The end result is the same (my two kings wins vs. all of them). The point of the exercise is to estimate what percentage of the time he turns his KJ into a bluff. As is always the case with hand range analysis you want to be conservative in your analysis so that you come to the correct conclusion about how you should play the hand.

In our example I estimated him to be bluffing with 2 out of the 3 possible combos, or 2/3 of the time.

RESULTS

Since I’m getting 3:1 (calling $25,000 to win $75,000) I only need to be right 25% of the time (or have 25% equity vs. his range) to justify calling.

To be sure I was in fact being conservative (ensuring I was justified by calling), I gave him every single combination of nut flush and several king high flushes. In reality this is simply not true because some of the time he’d check raise the flop with these hands or go for a check raise on the river.

Still, even a conservative analysis shows I have 50% percent equity, making this a clearly profitable call.

Just how profitable? For curiosity sake I ran the numbers. To do so I simply took the difference in my equity vs. his range and the equity I need to call, and then multiplied it by the amount of his bet.

PROFIT OF CALLING (50% EQUITY – 25% POT ODDS) X $25,000 = $6,250

If my analysis is correct, $6,250 is the amount I’ll profit each time I make this call.

That’s why you always run the numbers. Because decisions like these are for real money And you can’t afford not to. 

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Alec

Alec Torelli
Welcome! I'm Alec Torelli, founder of Conscious Poker, a training site dedicated to transforming good players into great ones by providing the best poker strategy and mindset content. I've been a professional poker player for 15 years and have over $1,500,000 in tournament winnings and millions more in both live and online cash games. On this site, I share the lessons I learned during my poker career to help you crush the games, optimize your bankroll, make winning decisions and achieve your poker goals.

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