Two Rebuy Related Questions

Tourney Structure: NLHE, T1000 for $60, 2 T1000 rebuys for $50 each. Each rebuy taken after the break (1 hour) gets you T1500 for $50 (I refer to this as "the rich get richer" structure). Blinds start at 25-50 and double every 20 minutes until tourney ends.


It would be nice to just coast for the first hour to try and get the double rebuy bonus, but the speed of the blinds doesn't allow you to do this. You must win at least one or two hands in the first hour to get the bonus.


First situation: This is the first time this casino has spread this tourney, and only 14 people buy in, two tables of 7 each. By the begining of the 3rd round, we're down to 6 handed and blinds are 100-200. I have T550, UTG, and push in with AKs and lose to big stack with JJ. I rebuy, and get QJs in the BB. Loose, clueless player with large stack raises only T200 on button and I reluctantly call. Flop comes J high, 1 of my suit, I push in (T600) and she calls me and wins with KJ.


So now I'm in the SB and looking at taking my last rebuy. Normally I don't even think about it, but in this particular situation, short handed, high blinds I declined. Comments?


Second situation: We're within a couple of minutes of the end of the 3rd round, I've taken one rebuy, and I'm down to T100 after posting the T100 SB. Two limpers to me and I get AKs. I effectively looked at this situation as having to lay 600 to win 700 against 3 other players, so I mucked. Comments? Would you play _any_ hand here?


-Oz-

Let me get this straight - you are allowed two rebuys which you can take at any time. However if you save a rebuy until after the first hour, you get 1500 instead of 1000 ? And do you have to have zero chips left to rebuy ?


Interesting. It's not poker, but it's interesting all the same ! For example it seems correct for you to pass the AK in the last case. AA (maybe KK) is probably OK getting 7-6 vs 3 opponents.


As for overall strategy, well, if this is the first time this slightly bizarre structure has been offered, who knows it might be the last, and so not worth thinking about ! It would seem to be correct to tighten up during the first hour as rebuying effectively loses you 500 chips. However you can put pressure on your opponents to fold during the first hour as they don't want to rebuy either. Although that depends how clueless they are :-).


Anyway if I have grasped it right I think you should take the 1500 rebuy any time you can, even if the blinds are high.


Good luck,


Andy.

It might even be correct to walk if you lose your first lot of chips during the first hour, especially early on. Even though the first buy-in costs $10 extra, you are losing 500 chips which is worth between $16.67 and $25 compared to any opponent who does not rebuy in the first hour.

Depends on your edge compared to the field.


Andy.

If this is the tourney that I think it is, change the "after" to "at" in 'Each rebuy taken after the break (1 hour) gets you T1500 for $50'.


No rebuys after the break ends.

You get 2 rebuys or add-on ($50 each). You can take them with any amount of chips.


If you make it to the break without using both rebuys, you can add on and get T1500 each.


For strategy:

If you take the first rebuy early, do not take the second rebuy right before the break. After the break everyone else will have lots of chips, you will have 1000 and the blinds will be 100-200.


If you are planning to use the add-ons and are low on chips, right before the break be sure to consider the potential gain/loss for going all-in. If you go all in w/ 200 chips you may stand to gain ~200 if you win the hand and lose 700 if you lose.


The above paragraph doesn't apply to the last hand of the 3rd round, so keep track of the time and listen tournament director to call "finish the hand you are on." If you bust out on this hand you can still get full value on the rebuys.


Hopefully other people have more thoughts here. For example,

If you have both rebuys available, how many chips should you have before declining the add-ons?

(Assume a 40/30/20/10 payout w/ max 44 entrants.)


Would there me an amount where it would be best to take only 1 add-on?


Cazz

> Two limpers to me and I get AKs. I effectively looked at this situation as having to lay 600 to win 700


Only if you would be forced to rebuy. Since you didn't rebuy in the situation before, why not call but only continue if you win the hand? Since I assume that most ppl. will make one or two T1500 addons, you don't lose much by quitting as the chips get devalued anyway. But let's look into this in more detail:


Let's say that 1/3 of the cupons will be used on T1000 rebuys and 2/3 on T1500 addons. Let's further assume the the entry fee is $10, so only $50 of your buy-in will make it into the prize pool. The equity of one chip is then $200/(1000+1/3*2000+2/3*3000) = 5.45 cents.


Also, let's say that your AKs is a 40% favorite to win the hand (41.4% vs. 3 random hands).


1. you muck and addon for T1500:


cost: $50, chips T1600, equity $87, EV = $27


2. you move in and rebuy no matter what


cost: $50, chips 0.4*T2300+0.6*T1000, equity $83, EV = $23


3. you move in and quit when you lose


cost: 0.4*$50, chips 0.4*T2300, equity $50, EV = $30


If profit per hour is relevant to you, than this all-or-nothing strategy is even more attractive as it will not only save you money, but also saves your time. (Unless you dominate the remaining field by a considerable margin, in which case at some point it will become better to muck).


cu


Ignatius

Please excuse my inexact description. Cazz has the rebuy/add-on structure correct. This is, as far as I know, the only casino spread tournament in Colorado (was at Bullwhackers, now at Harvey's). I dislike this stucture immensly, but sometimes i just can't stand it and just have to chase my tourney jones /images/smile.gif


-Oz-

I'm glad someone pointed out another option, but my math and yours are not adding up.


Problem one: Your EV calcs are off (87-50 = 27? and 83-50 = 23?)

Using 5.45 cents per chip I get


1. you muck and addon for T1500: EV = $37

2. you move in and rebuy no matter what: EV = $33

3. you move in and quit when you lose: EV = $30


(Option 1 is best)


Problem 2: I think you calculated the chip value incorrectly. Buy-in is $50 (ingnoring $10 to the house). Rebuys are $50 each.

Using your distribution I get

one chip = $150/(1000 + 2*(1/3 *1000 + 2/3*1500)) = 4.1 cents


Using this value

1. you muck and addon for T1500: EV = $15.45

2. you move in and rebuy no matter what: EV = $12.18

3. you move in and quit when you lose: EV = $17.64


Option 3 is best, like in your post.


The original buy-in and early rebuys cost 5 cents a chip. Late rebuys (add-ons) cost 3.33 cents a chip.


Since every has to take the original, the lowest possible chip value is 3.75 cents if all players take 2 add-ons at the break. The highest possible value is 5.0 cents, if no one takes the 1500 add-on. (5.45 cents a chip is not in the valid range).


At the extremes the results are:

5 cents

Option 1 EV = $30.00

Option 2 EV = $26.00

Option 3 EV = $26.00


3.75 cents

Option 1 EV = $10.00

Option 2 EV = $7.00

Option 3 EV = $14.50


BTW the cross-over point for options 1 and 3 is ~4.2 cents and option 2 is only tied for the second best option at the one extreme. Its the worst option (except for mucking and not rebuying) over the entire range.


A couple of things

1) As the chips decrease in value, taking the 1000 chip rebuy becomes more and more -EV.

2) With any of the options the field has a big effect on the EV of the situation. For nearly all chip values the difference between EV is $4 or less for options 1 and 3. The diffenece in EV due to the distribution of rebuys is ~$20. The best situation is when no one else takes the 1500 chip add-ons.

3) The EV from chip buying will be based on how much better you do than the "average" player. If the average is 1 early rebuy and 1 add-on, and you do the same you should be neutral (-$10 for the admin fee). If the average is *worse* than this, you take a negative EV unless you get to the break without using a rebuy.


Cazz

> but my math and yours are not adding up.


Ooops, that's putting it mildly! - I guess I really shouldn't post math related stuff after a 12h drinking session ...


I'm glad you still came to the same conclusions, though.


cu


Ignatius

You would probably have to have at least 15-20% of all the chips in play in your stack before it would become mathematically incorrect to take both rebuys when getting T1500 apiece.


Later, Greg Raymer (FossilMan)