Thursday, December 20, 2012

Tournament deal analysis

Although it's not officially condoned by the casino, deal-making is pervasive in tournaments, and when I decided to start playing tournaments I knew that I would need to improve my understanding of this aspect of the game. As I've mentioned before, I think optimal deal-making is best viewed as an extension of sound poker strategy, even though I was originally reluctant to consider making deals. For this post, I'll quickly discuss the three deals that were under consideration in the tournament last week when I came in second place.

The Bubble Offer: The first deal offered came when we got down to eight players. The seventh place player would win nearly $1000, but eighth place gets nothing, so this is a rather severe bubble. It was suggested that we should all give $30 to whomever was knocked out next, essentially giving eighth place have a payout of $210.

A severe bubble like this creates a strategic advantage for the players with the biggest stacks. If the smaller stacks are playing optimally and mostly folding and waiting until one more player gets knocked out, the chip leaders can win all the blinds and antes hand after hand by simply putting everyone else's tournament lives at risk. As I said in my last post, the other players were playing far too recklessly, and so this effect was greatly diminished. However, the larger stacks still have some advantage to the extent that the other players realize they should be playing extra tight.

When the deal was offered, I was at or near the chip lead, and I refused the $30 bubble idea. My explanation to the other players was that, as the chip leader, I was clearly not going to be the next one knocked out, so it would make no sense for me to donate $30. I knew this made me look cheap and unsporting, but I didn't want to explain to my opponents the more subtle reason for my refusal: I didn't want to give up my strategic advantage against everyone as the table's chip leader. If the bubble gets $210 instead of $0, it's psychologically much easier to deal with, and so my opponents would not be as desperate to hang on to get into the money. In other words, I would not be able to steal the blinds and antes as easily. The other players, muttering about how cheap I was, agreed to make the deal without me. This didn't help my situation much (the bubble player would still be getting $180), so I objected that this was collusion against me. The floorman agreed. The players pointed out that there was nothing I could do to stop them. Indeed, I knocked out the next player before long and everyone gave the guy some money (I think one guy gave him $60 to cover my part). This is exactly the sort of awkward situation that made me dislike tournaments in the first place, as I mentioned in an earlier post about why I didn't play tournaments.

According to the other players, this $30 bubble deal is commonplace. I think I will continue to refuse it if I'm near the chip lead, but accept it otherwise. I wonder how long the other players will tolerate that!

Another option is to try to influence tournament policy to make something like this deal "official." If the eighth place player had been officially lined up to receive $400 of something, I could avoid the unpleasantness of needing to discuss under-the-table deals with poker players. Considering the strategy of trying to make more final tables but with smaller chip stacks that I discussed in my previous post, this extra payout place would also be advantageous to my EV if it were officially adopted. I think if I discussed the situation I experienced where the players all colluded against me (as the floorman agreed), the tournament administrators would consider making this change.

The proportional chop offer: The first deal of the traditional "chop" variety (where the rest of the money is split and the tournament is over) that was suggested was a proportional chop. This means that each player would get a proportion of the pot equal to the proportion of the remaining chips. I was well aware that this clearly favored the bigger stacks. In fact, it's easy to imagine the smallest stack(s) getting paid less than last place money and the biggest stack(s) getting paid more than first place money. It was not clear to me how exactly this would play out, but I was not about to be the lone holdout on this deal. At this point I had about 400K of the 1M chips in play, and there was about $14,000 left in the pot. This deal would have paid me about $5600, not far from the $6300 or so that was awarded to first place. I wasn't sure what my EV would be if I kept playing, but it seemed like it must be less than that. I simply started counting my chips and hoping everyone would go through with it. After about two minutes, one of the short stacks decided to back out, so the deal was off. (The defector happened to be one of the two people most upset with me for refusing to take the earlier Bubble Deal.) We continued playing.

I used an online calculator (which I don't trust because I found a logical inconsistency that suggested an EV of greater than first place money for someone holding 90% of the chips) that suggested my actual EV was $4340 at this point, assuming all players are equally skilled. If this were accurate, I guess my EV was closer to $4600 because I was almost certainly better than the average player at the table.

As I said before, the casino does not officially condone deals, although they do look the other way. This means that in order to end the tournament and make a deal, the players would have all had to go all-in blindly and have the dealer deal out hands until just one person was left. The casino would then hand out the official winnings to everyone based on where we were each knocked out, and it would be up to us to dole out the agreed-upon amounts. This requires a level of trust in other players that I'm not completely comfortable with. I do think it's pretty unlikely someone would have the guts to back out on a deal like this, but something similar did happen at the Bicycle Casino once (although not in a tournament*). In this case, whoever came in first would also have to fill out a tax form because it is IRS policy that anyone who wins over $5k needs to do that. I pay my taxes anyway, but this is still another unwanted complication. I'm also not entirely sure who would be doing the calculations. Together, these factors diminish the value of the chop somewhat - perhaps as much as 20% should be discounted from the EV of a chop to account for these concerns, but 10% seems more reasonable. Still, 80% of $5600 is still $4480, which is probably greater than the EV I would have by playing the tournament out. (I'm assuming the poker calculator was overestimating my EV as the chip leader. Perhaps my EV was actually around $4000)

Making the deal also has the added benefit of greatly lowering the volatility of our winnings. If we discount by 10% instead of 20%, it comes to $5040, so I do think the deal would have been well worth it considering all the above factors. As I will discuss below, however, there are still other factors yet to be considered. All told, I think the deal was worth it for me, but the fact that someone backed out was not the disaster for me that it seemed like at the time.

The First Place offer: After we had been playing with three players for about ten minutes, I had around 60% of the chips, and my younger opponent suggested a chop wherein I would take first place money (around $6300), and he and my older opponent would share second and third place (around $2400 each). I could hardly believe this offer - I couldn't lose! - but the older player did not seem at all interested, barely acknowledging that an offer had been made. We continued playing.

In retrospect, I think this older player, who later informed me he had trouble hearing, probably did not even realize a deal had been offered. The lesson I learned here is to be a little more assertive and persistent in pursuing lucrative deals. If this third player had still demurred after the offer was explained to him, as I expect he would have, I should have offered him $100 to take the deal, and been willing to go up to $500. I probably lost quite a bit of value with my passivity.


I mentioned that there were some factors worth considering that I skipped over in the above analysis. As a poker player, I have many objectives beyond just trying to make optimal strategic decisions by maximizing EV. When it comes to making deals to split the winnings at the end of tournaments, one objective in particular competes with my primary goal of maximizing profit: I would also really like to play the tournament out to the end because that would allow me to improve through experience. I learned quite a bit about my competitors at the Charles Town casino by playing out the three player and two player scenarios in the hour or two after The First Place Offer was passed over. In order to effectively balance these two considerations (immediate EV versus gaining valuable experience that will help my EV in the future), it would be helpful to put a monetary value on the otherwise qualitative value of this experience. I will explore the question of how to do this in a future post. I expect it will involve discounting the value of my future income, which is a standard practice in economic theory.

* One Bicycle Casino promotion was to give away about twelve keys to a car over the course of a day, eleven of which were fake. At the end of the day, all the keys would be tried and one of them would work and that person would win the car. The twelve people agreed that whoever won the car would give the others some amount of money, maybe $1000 each. The lady who won the car backed out.


Craig Berger said...

At the Bike, proportional deals are common, and if they are not officially sanctioned, they are sanctioned enough that the staff will stop the clock and do the math if they are convinced it is likely a deal will happen. I only agree to such a deal if I am one of the big stacks. If I am not, I say "knock me out, then make your deal." In general, I would rather play till the end. I have pretty good poker stamina, and I don't really like the idea of leaving any money on the table, even if probabilistically it's better for me to make the deal. If the deal is completely unsanctioned, I won't do it. I'm not trusting poker players I don't know to dole out winnings fairly or handle the tax/tip burden fairly. I also won't do a deal that doesn't end the tournament on the spot. That being said, I generally do agree to the "bubble" deal even though I know it's bad for me for the sake of goodwill.

Keith said...

Hi Craig, thanks for stopping by. When you tell the other players "knock me out, then make your deal," do they start to target you? That would hinder your ability to stick around for a better payout.

If they players all prefer a "bubble" deal, why don't casinos simply make a more forgiving bubble, essentially making the bubble deal official? Unofficial deals really screw with tournament strategy, and it's not fair to new players who don't know that the deals are to be expected. For example, it diminishes the strategic value of getting to the final table with a big stack.

Craig Berger said...

Nice to be back. I haven't experienced myself as being "targeted," and I don't necessarily know if it would hurt me if I did. The last time I said that, I ended up with the chip lead, at which point I did agree to a proportional deal. I have actually found that most of the times I have been at a final table, my opponents do not want to make a deal, which is fine with me.

Expanding the bubble would never work, because the players all want more. In fact, it used to be, after a bubble payout became commonplace, that players regularly lobbied for TWO bubble payouts, until the casino finally said enough was enough and would not allow players to entertain deals until the actual bubble.

Anonymous said...

I think it's really interesting how you note that extremely tight play around the bubble would be optimal. I've never seen this admitted anywhere else. I've read in so many places where players smugly note that superaggressive play around the bubble can pay off because others will fold, but they always write in a condescending way, suggesting that these players who are folding are idiots who are giving away money. Yours is the first time I've seen anyone treat the advantage a big stack can have near the bubble in a respectful, insightful, and frankly, correct manner.

I was thinking about something related to this recently, and I may have told you about it before, but I can't remember. It seems to me that players could mutually profit by playing unaggressively toward each other. I mean, suppose there are only 10 players left, and blinds are so high that everyone is basically a short stack, with like 5 big blinds left. The conventional wisdom seems to be to go all in whenever you're playing a hand in these situations. But suppose it's folded to you in the small blind and I'm in the big blind. If you just call rather than go all in, and if we then just check it down, it definitely benefits us both, compared to us going all in and one of getting eliminated. So, it might be a good tournament strategy, near the end, to kind of befriend the players to your left and right and, either implicitly or explicitly, suggest the benefits of playing softly against each other.

Keith said...

Thanks, Rick, "respectful, insightful, and correct" is pretty high praise! I suspect the tendency for other writers to be condescending has something to do with a selection bias. That is, players who have won more tournaments are more likely to have their opinions on tournaments published... and they are also more likely to have high opinions of themselves and their go-for-first-place strategies.

Also, most people just can't resist being condescending.

I really wish I knew of a good (free) payout equity calculator.

I think you are totally right about the implicit collusion on the blinds. It's an important point because that is such a common occurrence. However, without an explicit agreement I have a hard time believing my neighbors would be willing to check it down with me, and I'm not comfortable with making explicit agreements, which seems like cheating.