Not got time for diagrams etc as in the old problems of the week but will be posting a few handicapping problems as we need some content. Will try and get a few more out but solutions may be slower than on the old problems.

First up, a good old fashioned 'take advantage of a league player' problem.

You are making your first forays into cash play, and are offered a match vs a regular from your bar league. You currently average a 60% win rate per individual game in that league over a large sample. The opponent averages a 85% win rate per individual game over a large sample. You have not seen them play for money before. They offer you matches for $100 with the following handicaps:

a) First to 10, rotating break nine ball, lag for first break with a 3 start.

b) First to 10, winner breaks US eight ball, flip for first break, 5 start.

c) First to 10, rotating break nine ball, lag for first break, no start but 3/1 on your money.

Should you accept any? Why?

I'm fairly new here- and haven't played league matches before so please excuse me if I'm asking a dumb question.

Surely the answer depends a LOT on the actual format of the league games? For example if they were best of 1 or best of 3 it's very different to a match of first to 10.

If individual game means just that- and not a match, then for sure you generally shouldn't take C- just run a few binomial tables and you can see how unlikely you are to win.

Some additional thoughts:

Option A: Definitely viable if the league is super strong, and everyone is capable of non-trivial % of break and run. But generally not a good option.

Option B: In 8 ball breaking is no where near as powerful as 9 ball (could even be -EV to break if we look at some stats which helps us tremendously). I would take this option given the choice since I can take a cautious strategy of blocking the 8 ball in particular- which guarantees that I'm -EV in any game, but gives me more chance overall vs a more skilled opponent which might edge it for me with my 5 start.

Option C: Not viable as said previously.

So would take option B over the other 2 but not sure if it is +EV.

Individual game would refer to one single rack. Overall standard of bar league play should be considered to be poor amateur at the low end, and high grade amateur (capable of relatively frequent clearances, sound tactical knowledge etc) at the other extreme.

3 start means you are winning 3 games to 0 before the first break, correct? I'm a very, very, very casual player so sorry but I like these types of threads. At first glance C seems bad to me and A and B seem close. I think we need to be a little better before I wouldn't rather have the other guy's action in all three though.

Again as a very casual and bad player, I think I like "A" better personally if it was in a league where I had those numbers. It's more attractive to me as a gambler anyway. Maybe that's the one you should offer to the fish if you're the 85% guy,

Yes, a 3 start means you start the match at 3-0 up.

Making a major assumption to simplify things - every break is a win at either 85% or 60%. I know this skews the logic pretty badly.

Looking at B: In a winner breaks format Villain runs 4 racks more than 50% of the time, and Hero runs 2 racks in a row only 36% of the time. At even money I think Hero loses the winner breaks format > %50 of the time even with 5 frames start.

The difference between A and C is minimal, without doing the math I think C is better than A by a small margin.

I'd pass on all 3 options.

I go for the eight ball. It's the easiest game, but he's offered you the biggest spot. Proviso is that he can maybe run racks with the winner breaks, but I wouldn't worry about that too much. If you win the first game or two, which is quite possible, then a big run of racks will be virtually his only way to win the set.

No, because you first have to figure the percentage of actually making a ball on the break, which is high, but not that high. If you break and don't make a ball, the odds of winning and individual game now favor your opponent. This is especially so at eight ball, but only marginally so at nine ball.

Changing my answer to B:

I have a recollection of Wamy saying he'd figured out out to skew his coin toss to be in his favour. With a 5 frame start and the break more than 50% of the time that looks a lot closer to profitable.

He's a "bar player" in your title...no way he puts more than a 1 pack together anyways. Take B every time.

I would refuse all 3.

a. Not enough of a spot. He will break and run more often than I will break and run and if I make a mistake, he'll most likely run out.

b. Seems really tempting but 8 ball gets harder towards the end of your run out. If I screw up in the end, all I've done is make his pattern easier.

c. I'll have to win 1 in 4 matches to break even. If it's individual racks at 3-1, I would take it but in a race to 10, I don't think I have 25%.

I've always felt money odds handicap is a trap. If a player is that much better than you, all you're doing by taking money odds is slowing down your loss rate.

League play and gambling are two different animals. Hypothetically based on your numbers however, b is the option I would choose. Odds on the money don't matter if you got no chance of winning the set, so c is out.

3 game handicap in 9 ball isn't that hard to overcome going to 10, plus the better player has a higher runout % than the other guy.

Soooo...This is actually more of a concept problem, designed to get players familiar with the information they can trust vs that they can't.

First up, the stats comparison. Although there are ways to calculate heads up equity in matches of two players from their respective averages vs a league, all of them rely on most players in the league being of similar ability for it to work. This is nearly never the case in bar leagues, and a very strong reason to be wary of any stat comparison in this spot. To see why, consider the following hypothetical:

A five player league, with one pro, one high grade player, you - a mid player, and two terrible players. The pro comes out with a near 100% average by year's end. The high grade player comes out with 75% (only losing to the pro), you out with a respectable looking 50% (beating the fish, but losing to the pro and the high grade player), and the two fish barely win a game (losing to everyone).

Although it looks from the numbers like you are closer to the mid player than to the fish, in reality the gap between you and the high grade player could well be larger than that between you and the fish, and in some cases (such as the above but with one lazy/drunk pro who drops a few games in the bar league, you and three fish) you may be close to dead even if the averages don't appear far out. In short, don't trust overall averages for making headsup comparison in one on one games of skill - this is as true for chess and backgammon as it is for tennis and cue sports. Someone 5% ahead of the field compared to you can easily be 99% ahead of you.

So, with this in mind, we move on to the next piece of information: The $100 offer. It is an often quoted piece of live poker wisdom that virtually no one bets much above a few hundred dollars without being a losing recreational gambler or quite savvy, and this wisdom extends right across gambling on the whole. 'Normal' players in a bar league will not be happy to play for $100 a match unless they are:

1) A big, losing gambler who loves action

2) An experienced gambler who knows he can beat you.

There is basically no middle ground. He either is very far ahead of you or there's not much in it.

With this in mind, lets look have a think about the handicaps:

a) A three start is not much in nine ball against someone better than you by a reasonable margin. Against an OK, bad gambling league player who is a bit more skilled than you you are probably are about break even to ahead. In case 1) you can't really win, in case 2) you are a little bit ahead. Big losses vs small wins are very rarely good in gambling.

b) 8 Ball can be a deceptive game for newcomers to pool, appearing overly hard when they first start, and then overly easy when they become better players. The reality is that 8 ball is not just a break and run out format for all but the very top players, but at the same time, it is a very tough game to win at vs a strong player.

However, a five start is a huge spot in a game like this between vaguely evenly matched players. It's also big enough that even if your opponent takes off his mask and is Efren Reyes you do still have some amount of equity - you only need to steal of couple of games here to put huge pressure on every shot of your opponent's. In option 1) you are a big favourite, in option 2) you are still OKish. Looks better.

c) If option a) was bad, option c) is even worse. If he is ahead of you by a long way even 6/1 is not good enough odds, and if he is just a bit of a degen gambler with some more skill than you, you are still quite a bit behind - and overall 3/1 is no where near the equity you need here. Don't even think about it.

So that's the overall evaluation. Play b) and ignore the rest right?

Well, not quite imo. Money pool with amateur gamblers is a game built on long relationships with players. Matches between a gambler who enjoys the action of a good player can last for very long periods if they don't get torn to pieces every night, and my take on this situation is generally to give a few bullets at any reasonable handicap (eg one you have some equity vs anyone) they are happy to go with.

As the situation is so polarised, you will either lose a few hundred dollars, learn a ton from a high grade gambler/player and get another notch of invaluable pressure match play experience; or you get a recreational gambler who does not know (or want to know) how to actually win who you could well win thousands from over time.


Solution: Take b) if offered all three, take a) if nothing else is going, and ignore c). Quit all of them if you are not winning after 3 bullets, possibly slightly more if playing b) and your break is running bad.