would you rebuy?

[Mackie]

limit he tourney, $45 buy-in $10 entry gets you T600. Start at 15-30 limit and appx. double every 20 minutes. 66 players. Pays 9. Final table no limit. There is one optional rebuy, another $45 gets you T1000 more. Rebuy option expires at the start of the 4th round (100-200).

Would you always take the rebuy no matter what? How much would you need at the end of round 3 to pass on the rebuy?

Last night at the end of round 3 I had T3400, my table was playing pretty loose with a couple of bad players still in, but was likely to break soon. For $45 I could increase my stack from T3400 to T4400. Worth it or no?

[Bozeman]

Yup, definitely.

Craig

[Jimbo]

It would be nice to know several things first:
1) How many players have been knocked out?
2) What is the current average stack size?
3) How many total rebuys are common in this tourney?

Without this info I would say not to rebuy. You essentially paid $45 for T3400 in chips. Now you would be paying $45 for T1000 more chips. Seems like a poor investment decision.

[Mackie]

1) not many, usually at least 90% make it to the first break (following round 3). I didn't count but I'd say certainly fewer than 5 players were gone.

2) current avg would be about 1800, because...

3) Usually nearly everone rebuys. 95% rebuys is common. Sometimes it's 100%.

[Bozeman]

Just because a rebuy is not as good an investment as an original buyin (in this particular case it still is better than the original investment) doesn't make it a bad deal. As poker players, we are not looking only for AA, we are looking for any situation with positive EV. Unless you are already in the money, or you are abysmally worse than the competition, an add on here will be a +EV investment.

Craig

[Greg (FossilMan)]

Very fuzzy thinking.

Let's look at an analogy. I have two paintings for sale in my gallery, both are priced at $1000. The first is actually a Manet, and really worth $1000000. The second is actually a Smith, and really worth $4000. You have plenty of money in your pocket. What do you do?

Here, the question isn't whether or not paying $45 will double his return on the first $45 he paid. The question is whether the chips he can rebuy are worth more or less than the $45 price he has to pay for them. Since we don't know his skill relative to the field, we have to assume he's average. If that's the case, these chips are clearly worth more than the $45 price tag, and he should buy them.

With that big of a difference in price per chip (2/3 more chips for the rebuy at the same price), I could never have enough chips in my stack that I wouldn't rebuy. In fact, why even wait until the end of the rebuy period? I would rebuy on the first hand and get it over with. Plus, if I start to run low on the first buyin, I won't have to worry about running out of chips in the middle of a hand where I want more action.

Later, Greg Raymer (FossilMan)

[Mackie]

"The question is whether the chips he can rebuy are worth more or less than the $45 price he has to pay for them"

Clearly, if I have an average stack and I'm an average player, the answer is yes, because as you noted I get them at a "discount" compared to the original buy-in. But there is a conflicting concept - that each additional chip in your stack decreases in value as you stack grows bigger, and increases in value as your stack grows smaller. Would they ever decrease in value enough to overtake the discount?
The only tournament book I own, TPFAP, does not address this scenario, and I'm wondering if there is a math model in existance that can be used to calculate this.

[Bozeman]

The decrease in chip value is not very large in general and is quite small here for 3 reasons:

1)At the addon point, you are a long way from the money

2)He only has less than 4 times an addon

3)It's not a supersatelite, so the prize money differences between positions are significant.

You are correct that tournament payouts adjust the value of these new chips, but the stack size would probably have to be about 30 times the addon for this factor to offset the 3/2 increase in chips/money.

Craig

[Jimbo]

Sorry to disagree with a tournament expert but I do. No way I rebuy under his circumstances!!! Your painting analogy was very nice though! /forums/images/icons/wink.gif

[Greg (FossilMan)]

I'm glad you're in disagreement. Without it, there would be no debate, and no fun.

But please explain then why you disagree. Why do you think my position is mistaken?

Just making a guess here, but are you active in the stock market?

Later, Greg Raymer (FossilMan)

[Jimbo]

Hi Greg,

I was going to elaborate in my first response but the site went "bonkers" and I wasn't even sure that it got posted in the first place. It did before I had time to edit and add my reasoning. First yes I am quite active in the stock market. I have a personal account. I am the account manager for a ten person high risk investment group and have a 401k. Why do you ask?

Now, Your painting analogy is flawed, primarily because you are able to resell your painting for more than your purchase price and the chips you buy will always be worth less than their purchase price relative to all the other chips in the tournament. I prefer the milk analogy. My family drinks 1 gallon of milk per week, this is all we need. Now if I am able to buy the first carton of milk for $1.50 but a 2nd gallon of milk later the same day for $1.00 it seems like a good deal except now I have more milk than I need. Since it is also illegal in my state to resell this milk I am stuck with paying 66.666% more for milk than I needed. Now it may ocassionally arise that company comes over and it would have been prudent to have acquired the extra milk but so long as I do not expect that to happen more often than every other week it makes sense not to buy the extra milk.

Additionally you assumed that he was an average player and using the info I had available I (more correctly) assumed he was above average due to his relative stack size. After all what other info did we have to evaluate? After his next post stating the average size stack was T1800 and he had T3400 I certainly would not rebuy. At this time he has $45 invested with an above average chip stack even after all the other players rebuy and is getting nearly 2 to 1 on his money. I am searching for justification for your opinion and can only surmise that you like to play fast and loose early which I consider acceptable but not prudent tournament strategy in this particular tournament.

[Greg (FossilMan)]

I ask about the stock market because your opinion on this subject reflects what I call "ROI thinking". In the stock market it is very important to always consider the ROI for any investment you might make. After all, there are practically unlimited investing opportunities, and since your money has to be somewhere, it is primarily your job to locate the best of these opportunities. ROI is the main driver of your decisions, with tolerance for risk being a significant modulator of those decisions.

With a poker bankroll, most of the time your money is just sitting there doing nothing. ROI is not really a consideration at all. What really matters is the expected return per unit time, with the risk of ruin to your bankroll being the primary reason to opt for a less-than-maximum hourly return decision.

So, finally to rebuys. I did not reread our original poster's message, so I forget the details. Instead I am going to use some details I am very familiar with, the Tuesday night NLH tourney at Foxwoods. The original buyin is $25 (+10 vig) for T200. Anytime during the first 3 levels, if you have T200 or less, you may buy T200 for $20. At the end of the 3rd level, no matter what your chip count, you may buy T200 for $20 or T400 for $40.

From long experience I know that when you add up the total prize pool, the average cost per unit of T200 is about $21.50. Therefore, in theory, when you add-on for $20, you are getting chips worth about $21.50, for a profit of $1.50.

It is my position that if you are an average player, you will make that $1.50 in profit when you add-on almost no matter how big your stack has become. At the time you buy these chips you are still very far from the money, and even if you have a stack of T3000 you still have no more than 5% of all the chips in play. As such, the concept that chips are worth less in a big stack really isn't relevant yet, as the chips you add to your stack probably have at least 99% of the value they would have if added to an average sized stack. So, while the chips might not be worth $21.50, they are worth at least $21.47 or so.

As for skill level, if you are a better than average player, the chips are worth MORE in your stack, and therefore you should be MORE inclined to add-on than otherwise. If a truly horrible player spends $20 to addon, they might have an expected return of only a couple of dollars. To balance that out, it must be that the better players have a return of much more than $20 (or $21.50 in this case) for each addon.

Bottom line summary: I think that for an average player in this event, if they addon T400, they will be paying $40 for chips worth $43. If they are a well above average player, they will be paying $40 for chips worth something like $50-80 in their stack. And, since that $40 will sit in your pocket doing nothing if you don't use it, the fact that it reduces your overall ROI is unimportant, as it certainly increases your total average return.

Of course, the implication is, if you are a below average player, it is -EV to addon. But, of course, this is no surprise, since it is by definition -EV for this person to play at all.

Later, Greg Raymer (FossilMan)

[Jimbo]

Thanks for the excellent explanation Greg. I just have two questions. If you win the tournament with no rebuys haven't you done better than if you spent $100 on rebuys? This is where I am becoming confused. The converse is also somewhat perplexing. If you get put out with a single buyin 5 times it is the same cost as the entry plus 4 rebuys (minus any vig) and you lose less. Now does having 4 rebuys make you 5 times as likely to win? If not I would never rebuy. Please explain to me where I am going awry with my logic.

Thanks in advance,

[Bozeman]

When you win the tourney, you will get at least ten times the buy-in, sometimes much more. So while the difference in ROI is between 1000%x and 500%x, the difference in EV is only between 9x and 8x. When you factor in the greater than 20% increase in your chance of winning the addon gives, it's a definite deal. As Greg said, total ROI is not the important measure, because your addon money would be getting 0% ROI if you left it in your pocket. In the case of 4 extra buyins vs. 4 rebuys, you will buy more entertainment if you are a losing player, but if you are a good player the decrease in SD is minimal, and you pass on +EV situations. You do not need to have the 5 times increase in EV, you need only for each rebuy bought to increase the EV greater than it's cost. In the original situation, this is a no-brainer because the addon gives 50% more chips/$ than the original buyin.

Craig

[Bozeman]

Oops, wanted to correct that this tourney gives 67% more chips/$ on the addon wrt the buyin.

[Myrtle]

Jimbo………In your milk analogy you stated.... “but a 2nd gallon of milk later the same day for $1.00 it seems like a good deal except now I have more milk than I need”.

Is it on this point that perhaps you’re logic is a bit fuzzy?

I would simply ask “Do you EVER have more chips than you NEED in a NL tournament?”

I don’t think so......or is my thinking fuzzy?

[Jimbo]

Yes it is easy to have more chips than you need in a tourney. It does not matter if at the end you have all the chips in the tournament whether or not you have 1000 chips or 1,000,000 chips. The prize remains the same after the rebuy period has ended. There is little difference if you have 2 times the average stack or 2.5 times the average stack as in Mackies example above. It is early in the tourney, you are the table chip leader and cannot be busted on any one hand by anyone else at your table.

[Mackie]

I ended up deciding to take the rebuy after initially deciding not to. I think what happened may help show in real life terms why it was a good idea. The rebuy was for T1000. My stack never got below that amount, however, at the final table following a beat I was down to T3400, with the blinds at 1000-2000 (no limit at this point). I picked up pocket tens UTG and moved in. I was called by the worst player at the table who tabled aces. I started to put my coat on to go collect 8th place money when I spiked a ten on the turn to double through. A couple hands later in the small blind I almost doubled through again with AK, eliminating a player with AQ whom I had outstacked by T400. At this point I had T11200, a slightly better than average stack. Had I not taken the rebuy, I would have had T7600, a below average stack, AND the player I knocked out with AQ would still be in with T1600. Now obviously things may have played out differently because some decisions are based on stack size but I think the point is valid.

[Jimbo]

Bozeman you said "When you factor in the greater than 20% increase in your chance of winning the addon gives, it's a definite deal. As Greg said, total ROI is not the important..... First of all the addon does not give you a 20% greater chance to win the tournament. All that will give you a 20% better chance to win would be a sudden 20% increase in your skill. This is a common fallacy that chip position is correlated to your chances of winning. If this was true in the WSOP every players odds would be the same on day one which is obviously not the case. Secondly ROI is not important as to whether or not your money is earning anything by sitting in your pocket but if you have a chance to win $1000 by spending $20 or virtually the same chance to win $1015 by spending $100 why would you choose the latter? It appears that we disagree on how much your chance of winning the tournament increases by rebuying and adding on. I feel it is negligible and you and Greg feel it is very important.

Now let's take a simple case and assume I agree that in a single rebuy tourney that making the rebuy increases your chance to win by 20%. There are 10 players in this tourney who paid $20 each to enter (no juice) and 5 of them rebuy (including you) and one of them are out of the tourney. The tourney is structured for simplicity that 100% goes to first place. You got T1000 for your initial entry and T2000 for your rebuy for $20. Now here is what happened you went from having 10% equity in a $200 prize for a value of $20 to a 13.333% equity in a prize valued at $300 for a value of $39.99. Nearly the same ratio so all you did was break even, even if we assume for some reason that your rebuy magically gave you 20% more equity and hurt ever other player in the tournament which makes no sense to me to begin with. Now assume that not rebuying costs me 20% equity. Now using the same numbers as above except that the prize pool is now only $280 (without my rebuy) I have an 8.888% equity in the prize which offers me a value of $24.89 for my initial investment of $20. Obviously a much better deal even assuming I lost 20% equity by not making the rebuy.

Now it is certainly possible that I am all wet in my evaluation but I do think it is unlikely that your scenario of increasing your chances of winning the tournament goes up by 20% is correct either.

Allow me to add two more scenarios to my above mini-tourney example. At the end of the rebuy period one player is still out but you have 9,992 chips and the other 8 players left have 1 chip each. They will all rebuy for $20 and get T2000 more chips but should you? Now assume you are one of the players with one chip, should you rebuy here? Just a parting thought.......

[Jimbo]

I hate to break this to you Mackie but if you do not spike the ten your rebuy meant nada. This is the ultimate in results oriented thinking. Just beacuse you did rebuy and had a good result is irrelevant when determining if the rebuy was a good decision before you know what will happen in the tourney. At any rate congratulations on the good showing in the tournament.

[BoredAtheist]

Greg,

I won't dispute whether the rebuy is correct in the original post, as this seems to be a very complicated issue. But I really feel that your blanket statement of "always rebuy" is incorrect. Take this contrived example:

You're in a tournament with one million players. Entry is $22 and gets you T1000. You are allowed a single rebuy, T1000 for $20, at any time during the tournament. You are at the final table with 100M chips (average for the table). The blinds are 1M/2M. Would you rebuy in this situation?

[Mackie]

If I don't rebuy I still have a below average stack after doubling through twice and fail to knock out the player with AQ. Is that worth the $45? I don't really know.

Of course if I don't hit the ten the rebuy is irrelavent. It could also have been irrelavent if that player didn't happen to get dealt aces on the same hand I get tens. What I'm looking for is some general methodology to help estimate when taking the rebuy is +EV. In this particular tourney it potentially made a significant difference.

[ohkanada]

Certainly increasing your chips by 20% does not give you a 20% increase chance in winning. Assuming equal skill the more chips you have the more likely you will win. In a perfect world, if you have 35% of the chips you would have a 35% chance to win. But even given that we are not all equal the more chips (percentage wise) you have the more likely you will win. Of course an extra 5% of chips means more to Greg than a newbie but it still improves the newbies chance in winning.

The addon gives you more chips. The percentage may not increase much if any if all other players also take the addon. But if you don't take the addon and others do, then the percentage will drop and therefore you are hurting your position.

In a NL tourney that extra 1000 can easily double or triple in 1 hand. In a limit tourney at lower limits it is harder to use that addon at one time but it is still important in the later stages.

One tourney where I had a tough choice was when I was able to triple my initial stack without taking the rebuy. At the break I have the option to make that rebuy and do the addon. Everyone else at my table is taking any outstanding rebuys and the addon so if I don't, I fall behind plus the one player with a bigger stack is also taking both. I would have been happy to save the $200 but decided to take them and was rewarded in the end.

One tourney where i probably shouldn't have taken the rebuy is when I had started with 1000 and was at about 11k at the rebuy stage. The rebuy only gave me another 1000 so percentage wise it wasn't much. Although in this case it was only $20.

Ken Poklitar

[Bozeman]

"First of all the addon does not give you a 20% greater chance to win the tournament...This is a common fallacy that chip position is correlated to your chances of winning. If this was true in the WSOP every players odds would be the same on day one which is obviously not the case."

You are making a felonious comparison here. Yes, 1000 chips are worth a different amount to me than you, but for each of us a 29% increase in stack size is a more than 20% increase in winning chance (probably > 28% for a typical tournament). Why do you think it is a fallacy that chip position correlates with winning chances? It is true that it is not the only factor that correlates with winning chance, but that does not negate it's correlation. There may be a few unusual circumstances, like players who play better with a small stack, but by and large this correlation is effectively perfect. Even if you only have .01% cahnce of winning, doubling your stack will significantly increase this chance.

But maybe I should let Greg explain it because he is clearer and more respected,
Craig

[Jimbo]

Bozeman I respect your opinion a great deal, certainly no less than Gregs. I simply disagree with your logic and showed why with my example. I would not care if you were David Sklansky simply saying something is so does not make it true unless you can show me calculations that justify your position. Until you choose to do that I am forced to believe my position is correct.

[Myrtle]

Jimbo,

If there were two players seated at the table, both with equal playing ability.....

One had T2000 & the other had T2500 and you HAD to bet on
one of them only, upon whom would you place your bet and why?

[Jimbo]

I would bet on whoever was the better player. If they were equal I would bet on the player with more chips unless the blinds were at say 200/400 then I would bet on whoever had the button. So the 500 extra chips becomes marginal very easily. We are not discussing heads up but 10 to 100 players where your itty bitty additional amount of chips makes little difference.

[Greg (FossilMan)]

I am completely at a loss to understand your comment. "First of all the addon does not give you a 20% greater chance to win the tournament. All that will give you a 20% better chance to win would be a sudden 20% increase in your skill. This is a common fallacy that chip position is correlated to your chances of winning."

Also, in your hypothetical you do the math of a rebuy giving you a 20% increase in the chances of winning. Well, in your hypo the rebuy gave the player a 200% increase in stack size, so I would certainly hope it would give them a LOT more than a 20% increase in win rate. Like, 200%?

This lack of agreement on the value of stack size is clearly the base cause of our disagreement in this thread.

I am going to start a new thread, since this one is getting a bit long.

Later, Greg Raymer (FossilMan)