Need Re-Buy Help for First Limit Hold'em Tournament

[Dulcharnon]

I will be playing my first tournament this coming weeek and I have a few questions concerning the re-buy. The rules of the tournament only allow re-buys if you have less than or equal to the initial amount of chips. Here the tournament buy-in is $35 for T500, the re-buy is $15 for T500, and the add-on is $20 for T1000. According to the rules, I may re-buy at the start of the tournament since I only have T500. <font color="blue">Hence, my question is whether or not I should re-buy on entering the tournament to start out with T1000 or should I wait until later to re-buy?</font color> I believe that there is only one re-buy and only one add-on. Furthermore, the add-on is only available for the first three rounds of the tournament, there are 10 rounds in all. Any help would be greatly appreciated. Thank you in advance for you consideration and prompt reply to my query.

[Ignatius]

Given the enormous discount you get on the rebuy and the addon, this format is practically a $70 event. It would be an error not to always rebuy and addon at the first opportunity.

[Greg (FossilMan)]

Actually, I think that this question is a bit more complex than Ignatius' reply would indicate.

Of the $35 for the initial T500, how much is vig, and how much goes into the prize pool? This is important, as I consider the vig separately when determining rebuy strategy.

Let's pretend it's $25 into the prize pool, and $10 to the house. That means $25 for the first T500, $15 for T500 rebuys, and $20 for T1000 addons. The question I need to answer is how many of each will the field likely take?

Let's guess that of 100 initial entrants, there were 95 addons and 200 rebuys. That is a total of $7400 for T245,000, or an average of T33.1/$1. Since a rebuy costs $15 for T500, a price of T33.3/$1, you should take all available rebuys, since you get slightly more chips per dollar than the average of the field. Wow, that's pretty close.

However, if we change the situation just a little, such as the initial buyin is $20 + $15, or $20 to the prize pool and $15 to the vig, we now have the same T245,000 in play, and a prize pool of $6900, or T35.5/$1. At this price, your rebuys get you LESS chips than average, and you should be that much less inclined to take them.

The complicating factor here is the extremely cheap price of the addon. Thus, even though the rebuy is much cheaper than the original buyin, the addon is so much cheaper still, and dilutes the average value of a chip so much, that rebuys can be money-losers to an average player.

That is another factor. All of the above assumes you are an average or break-even player in the field. If you are below average, then every rebuy and addon is worth even less in your stack. Of course, if you're a winning player, each chip is worth more in your stack. As such, winning players should be more inclined to take rebuys and addons, and losing players less inclined.

Later, Greg Raymer (FossilMan)

[**MR.MANHATTAN**]

any info on the tourney at the orleans in vegas???? 20$/10$ rebuy.....1 addon..?

[Ignatius]

My answer assumed that there is just one rebuy and one addon allowed per person, as Dulcharnon mentioned in his post (that's why I considered it to be a $70 event).
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Still, I think your vig-argument is misleading. If you enter the event, then you better are already confident that you can overcome the vig or you're playing poker for other reasons than to make money. So the question is not: "does taking a rebuy get me more additional equity than it costs to rebuy?" but rather "does taking a rebuy improve my equity/investment ratio?". And that investment of course also has to include the vig.
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For the format in question, that means: If you only take the addon you get T1500 chips for $55 (T27.27/$). If you take infinite rebuys you get (T33.33/$). How many rebuys/addons the other take is important to decide whether you intend to enter the tourney or not, as it decides the eventual prize pool and number of chips on the final table and thus the equity of a single chip and consequently the necessary edge you need to overcome the vig. But once you're in there, all you should be concerned is to get chips for the lowest price, and this decision _only_ depends on the format and not on the rebuy stragtegies of the other players.
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Depending on the format this can mean to never rebuy (e.g. in "free" tourneys where you only pay a small vig for your initial chips and the casino gurantees a minimum prize pool), to only rebuy when necessary (when there is a huge discount on the addon but only a small or no discount for the rebuys) or to rebuy at every opportunity (when the rebuy-chips are cheaper than the combined chip-price determined by the entry-fee+the addon).
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In the format Dulcharnon mentioned, clearly the latter is the case, so assuming there are unlimited rebuys, he should rebuy as often as possible.

[Greg (FossilMan)]

You're right, I missed the part about there being only 1 rebuy. However, that's OK, because the math just needs to be adjusted a bit to take that into account.

The big issue with only 1 rebuy is to make sure that you survive to the point where the addon is offered, since that is the absolute cheapest chance to buy chips. In that case, I would not rebuy unless I went broke, in order to increase my chances of surviving until the addon is offered.

I must disagree with your statement: "So the question is not: "does taking a rebuy get me more additional equity than it costs to rebuy?" but rather "does taking a rebuy improve my equity/investment ratio?"."

So, let's say you make an investment where you pay $1 to have a 1 in 1000 shot at $500 (such as the daily pick 3 lottery things in many states). Now I offer you a chance to increase your investment from $1 to a total of $5, and that if you now win, instead of $500 you will win $3000. This new deal has just increased your return on investment from -50% to -40%, but you obviously shouldn't make it. You just put up $4 more with an EV of $2.50, or lost an additional $1.50 with that bet in terms of expectation. However, since this bet is not as bad as your original bet, it did improve your equity/investment ratio I believe.

If you are an average player, as these discussions assume (from my end), then clearly you are losing the vig, and breaking even on the rest. Of course, if I don't think my edge over the field is high enough to overcome the vig, I don't enter a tourney, but that is difficult to factor into these rebuy discussions, without having to do a lot more work. That's why I commented that if you're a winning player, you should take a rebuy or addon that looks slightly bad mathematically, because those chips will be worth more than you pay for them IN YOUR STACK.

Later, Greg Raymer (FossilMan)

[Ignatius]

You're right about the "going broke and miss the addon" thing. In thos cases it is indeed better to save your last rebuy and take it immediately before the addon if it's profitable to do so (and you stack isn't already so huge that the levelling effects of the payout structure have to be considered).
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As for your lottery example, we're using different examples here. I assume that anyone playing to make money has already made sure that he is able to overcome the vig, while you assume an average player. However, the only (financial) advice to the latter is not to play at all and any further advice is pointless, at it will only affect the rate at which he will lose his money (which usually is limited by the amount he is willing to spend on his poker entertainment, anyway).
But for a winning player, reducing his inital handicap form 50% to 40% directly translates into 10% of additional profit.
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but that is difficult to factor into these rebuy discussions, without having to do a lot more work.
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I think that the opposite is true: While it might be difficult to find out for sure whether you are indeed capable of beating a certain tourney, once this fact
is established, the optimal rebuy stragegy is almost completely determined by the structure of the event and independent of your actual edge. (It does get complicated if you don't want to optimize only your ROI, but also your playing time and also take factors like tournament points of payout structure into account ...)

[Greg (FossilMan)]

Oh my GOD! Not ROI!

I don't take that into account at all, not even a little bit, and I don't think any tourney player should. The only time I can imagine it being proper to do so is if you're thinking about backing a tourney player, or some such.

First thing, if your bankroll isn't readily renewable, is to make sure you're not playing so big that your risk of ruin is too high. After you've done that, make the plays that maximize profit, not ROI.

I've seen other folks make a very spurious ROI argument with respect to rebuy tourneys. Here's an example. Original buy-in is $100 + 20 for T500. Rebuys are available only if you go broke, and cost $100 for T500. Since this is the same price (minus vig), they are essentially neutral decisions.

However, at the end of the rebuy period, you can take an addon and pay $100 for T1000. Here is where I see mistakes. Somebody will argue with me that since they have amassed a large stack of T5000 during the rebuy period, and only paid the original $120, that they shouldn't take the addon because it will lower their ROI. In their mind, they've paid $100 or $120 for T5000, and therefore it is a bad deal to pay $100 more for only T1000. Ugh, hate it!

However, from the point of view of ROI only, I guess they are correct. However, who cares about ROI? If they can pay $100 for $200 worth of chips, they are making themselves $100 in expectation, as I see it.

Later, Greg Raymer (FossilMan)

[Ignatius]

OK, I think I better understand your reasoning now! To clarify: with ROI, I meant your avg. EV per tourney in relation you typical investment in a tourney (which depends on your rebuy strategy). It does not mean to optimize your per-torney-ROI for whatever your current stacksize happens to be - this would be as stupid as quitting a profitable game just because you happend to pull a giant pot and don't want to spoil your ROI for the session.
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But I think your argument goes deeper than that and is probably a good illustration of the different mindsets of a pro (like yourself) and a mere recreational player (like me): e.g. each Monday my local cardroom offers a "free" torney where you get T4000 for a $4 vig, unlimited rebuys are T4000 for $20 and the addon in T10000 for $20. Only the rebuys and addons contribute to the prize-pool ($2000 guaranteed by the casino).
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At HE and Pineapple, I make a net EV of about $30 in those events by playing a strict freezout strategy (i.e. never rebuy, never addon) for a ROI of about 750%. I guestimate that in the cases when I make it to the break (about 40% of the times) the equity of the addon would be worth about $30 to me, so an addon-strategy would increase my EV to $30+0.4*($30-$20) = $34 yet decrease my ROI to $34/($4+0.4*$20) = 283%. Yet I choose not to, as the 13% increase in net EV simply doesn't seem to be worth the more than 2.5-fold increase in variance.
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And this is exactly where bankroll comes into play: As, in the context of a poker tourney, ROI is basically the ratio between EV and SD, the nearer you go to the limit of your bankroll, the more variance becomes an issue and you will have to pass on profitable propositions if you are unable to take the swings. As a recreational player, I adopt a smilar attitude, albait for different reasons: Without a formal bankroll I cannot bring myself to view money merely as a tool, so as long as the cash isn't changed into chips, when given a choice, I tend to prefer a high ROI over a more marginal, but more profitable (in terms of EV) proposition.

[Dulcharnon]

I am sorry I did not mention the "vig". The entry fee or vig in this case is $5. This means that $5 goes to the house and $30 goes to the prize pool. Furthermore, all re-buys and add-ons go the prize pool. In any case, this is just what the flyer states. Thank you all for your prompt and helpful replies.