From my understanding, in no-limit games, one would want to only have some fraction of ones bankroll in chips on the table, so that one can re-buy after losing an all-in bluff. (I would guess that this fraction should be determined by the Kelly criterion or something.)
On the other hand, from browsing Wikipedia, it seems like many poker tournaments prohibit or limit re-buying after going bust. This would indicate that one has limited amounts of opportunity to get familiar with the strategy of the opponents (which could very well change once the stakes change).
(Of course, Kelly is kind of brutal with regard to gambling. In a zero sum game, the average edge is zero, so at least one participant should not be playing even from an EV perspective. But even under the generous assumption that you are 50% more likely than chance to win a 50 participant elimination tournament (e.g. because a third of the participants are actively trying to lose) (so your EV is 0.5 the buy-in) Kelly tells you to wager about 1% of your bankroll. So if the buy-in is 10k$ you would have to be a millionaire.)
Yeah, you need an enormous bankroll to play $10,000 tournaments. What a lot of pros do is sell action. Let’s say you’re highly skilled and have a, say, 125% expected return on investment. If you find someone with a big bankroll and they’re convinced of your skills, you can you sell them your action at a markup somewhere between 1 and 1.2 to incentivize them to make a profit. I’d say something like 1.1 markup is fairest, so you’re paying them a good prize to weather the variance for you. At 1.1 markup, they pay 1.1x whatever it costs you to buy into the tournament. You can sell a large part of your action but not quite all of it to keep an incentive to play well (if you sold everything at $11,000, you could, if you were shady, just pocket the extra $1,000, go out early on purpose, and register the next tournament where you sold action for another round of instant profit).
So, let’s say they paid you $8,800 to get 80% of your winnings, so they make an expected profit of ($8,000 * 1.25) - $8,000, which is $1,200. And then you yourself still have 20% of your own action, for which you only paid $1,200 (since you got $800 from the 1.1 markup and you invest that into your tournament). Now, you’re only in for $1,200 of your own money, but you have 20% of the tournament, so you’d already be highly profitable if you were just breaking even. In addition, as we stipulated, you have an edge on the field expecting 125% ROI, so in expectation, that $1,200 is worth $2,000*1.25, which is $2,500. This still comes with a lot of variance, but your ROI is now so high that Kelly allows you to play a big tournament in this way even if your net worth is <$100k.
(This analysis simplified things assuming there’s no casino fee. In reality, if a tournament is advertized as a $10k tournament, the buy in tends to be more like $10,500, and $500 is just the casino fee that doesn’t go into the prize pool. This makes edges considerably smaller.)
Regarding busting a tournament with a risky bluff: In the comment above I was assuming we’re playing cash game where chips are equivalent to real dollars and you can leave the table at any point. In tournaments, at least if they are not “winner takes it all” format (which they almost never are), there’s additional expected value in playing a little more conservative than the strategy “maximizing expected value in chips.” Namely, you have to figure out how “having lots of chips” translates into “probabilities of making various pay jumps.” If you’re close to the money, or close to a big pay jump when you’re already in the money (and at a big final table, every pay jump tends to be huge!), you actually make money by folding, since every time you fold, there’s a chance that some other player will go out (either behind you at your table, or at some other table in a tournament where there are still many tables playing). If someone else goes out and you make the pay jump, you get more money without having to risk your stack. So, in tournaments, you gotta be more selective with the big bluffs for multiples of what is already in the pot, especially if you think you have an edge on the field and if the pay jumps are close.
Thanks, this is interesting.
From my understanding, in no-limit games, one would want to only have some fraction of ones bankroll in chips on the table, so that one can re-buy after losing an all-in bluff. (I would guess that this fraction should be determined by the Kelly criterion or something.)
On the other hand, from browsing Wikipedia, it seems like many poker tournaments prohibit or limit re-buying after going bust. This would indicate that one has limited amounts of opportunity to get familiar with the strategy of the opponents (which could very well change once the stakes change).
(Of course, Kelly is kind of brutal with regard to gambling. In a zero sum game, the average edge is zero, so at least one participant should not be playing even from an EV perspective. But even under the generous assumption that you are 50% more likely than chance to win a 50 participant elimination tournament (e.g. because a third of the participants are actively trying to lose) (so your EV is 0.5 the buy-in) Kelly tells you to wager about 1% of your bankroll. So if the buy-in is 10k$ you would have to be a millionaire.)
Yeah, you need an enormous bankroll to play $10,000 tournaments. What a lot of pros do is sell action. Let’s say you’re highly skilled and have a, say, 125% expected return on investment. If you find someone with a big bankroll and they’re convinced of your skills, you can you sell them your action at a markup somewhere between 1 and 1.2 to incentivize them to make a profit. I’d say something like 1.1 markup is fairest, so you’re paying them a good prize to weather the variance for you. At 1.1 markup, they pay 1.1x whatever it costs you to buy into the tournament. You can sell a large part of your action but not quite all of it to keep an incentive to play well (if you sold everything at $11,000, you could, if you were shady, just pocket the extra $1,000, go out early on purpose, and register the next tournament where you sold action for another round of instant profit).
So, let’s say they paid you $8,800 to get 80% of your winnings, so they make an expected profit of ($8,000 * 1.25) - $8,000, which is $1,200. And then you yourself still have 20% of your own action, for which you only paid $1,200 (since you got $800 from the 1.1 markup and you invest that into your tournament). Now, you’re only in for $1,200 of your own money, but you have 20% of the tournament, so you’d already be highly profitable if you were just breaking even. In addition, as we stipulated, you have an edge on the field expecting 125% ROI, so in expectation, that $1,200 is worth $2,000*1.25, which is $2,500. This still comes with a lot of variance, but your ROI is now so high that Kelly allows you to play a big tournament in this way even if your net worth is <$100k.
(This analysis simplified things assuming there’s no casino fee. In reality, if a tournament is advertized as a $10k tournament, the buy in tends to be more like $10,500, and $500 is just the casino fee that doesn’t go into the prize pool. This makes edges considerably smaller.)
Regarding busting a tournament with a risky bluff: In the comment above I was assuming we’re playing cash game where chips are equivalent to real dollars and you can leave the table at any point. In tournaments, at least if they are not “winner takes it all” format (which they almost never are), there’s additional expected value in playing a little more conservative than the strategy “maximizing expected value in chips.” Namely, you have to figure out how “having lots of chips” translates into “probabilities of making various pay jumps.” If you’re close to the money, or close to a big pay jump when you’re already in the money (and at a big final table, every pay jump tends to be huge!), you actually make money by folding, since every time you fold, there’s a chance that some other player will go out (either behind you at your table, or at some other table in a tournament where there are still many tables playing). If someone else goes out and you make the pay jump, you get more money without having to risk your stack. So, in tournaments, you gotta be more selective with the big bluffs for multiples of what is already in the pot, especially if you think you have an edge on the field and if the pay jumps are close.