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BGonline.org Forums
The Case Against Rebuys
Posted By: Daniel Murphy In Response To: The Case Against Rebuys (Eric Guedj)
Date: Tuesday, 13 April 2010, at 6:36 p.m.
Eric, thanks for participating in these discussions and good luck with your tournament.
On Level 1, the 'Double Rebuy Strategy' would give either players 7500 chips, or 75 points each.
Ok, and that seems like a lot of chips But after 10 games we're at level 2, and our two colluding double-rebuyers' 7,500 chip stacks are worth only 37.5 points. However, everyone who hasn't rebought has an average of only 12.5 points! Ten games later we're in level 3, and those buy-ins are worth 25 points and 8.33 points. Eight games later, level 4, and they're worth 15 points and 5 points. And at that point, although I may be wrong, I'm thinking that the double-rebuyers have made a good investment. It must be a whole lot easier in a money session to win five points more than your opponent, than to win 15 points more.
Of course, so far I've only mentioned the players' starting banks. Players may also win or lose chips during those games. We know what an average money game is worth. If we knew who the players in the tournament were, we'd be able to calculate approximately what their expectation(s) for Day 1 should be.
and if you happen to win every game ... (for instance the Day1 chip-leaders, with their fat stacks of 25.000 or more)
Well, winning just 10 games in a row is a rare event. But we might calculate how much
luckskillful play a "fat stack of 25,000" chips at the end of Day 1 would represent. A stack of 25,000 chips at the end of Day 1, without rebuying, means having won 22,500 chips. 10*100 + 10*200 + 8*300 + 8*500 = 9,400, and 9,400/36 = 261. The average point value for Day 1 games is 261 chips. And 22,500/261 = an average of 86 points.How likely is it that even a single player will have won 86 points in 36 games?
Another view: Typically, if your positive expectation in a money session is as much as 0.1 points per game, you're advantage is large. But a player winning 0.1 points per game in 36 Day 1 games at 261 chips per game will only gain 940 chips on Day 1. Winning a whopping 0.2 points per game would mean winning 1,880 chips. Players will have to do a whole lot better than that to accumulate 25,000 chips!
And note that the less likely it is that anyone will accumulate huge stacks on Day 1, the larger percentage of an average stack -- and better value -- that rebuy(s) represent.
Therefore, in every scenario where ROI is negative (typically for a strong player with a lot of chips in early levels)
I think it needs to be proved, not just asserted, that rebuying/add-ons have negative ROI for a strong player who is an early chip leader. I suppose you'd have to define "strong player" and "lot of chips" and consider the cost of the rebuy/add-on and size of the prize pool. But I'm inclined to think that "typically" there are actually many situations in which a strong playing early chip leader has positive equity on his rebuy/add-on.
Besides, there is another likely scenario: A weak player (or a qualified amateur) with just a few chips left might decide at the close of Day 1 that 2500 chips (5 points from Level 5) won't be enough for him to survive the next Level. Can someone convince such player that rebuying is a smart way to invest his money? Not so sure.
Well, "qualified amateur" qualifies quite a lot (did he even have positive ROI in his qualifier?), since a "weak player" is giving away equity the moment he sits down to play. However, it may still be sensible for this player to rebuy. Depends on the cost of the rebuy relative to the value of his expected percentage of the prize pool.
In all, it seems to me that the discussions about rebuying (that is, adding on) immediately lead to this conclusion: that rebuying at some point on Day 1 is positive for everyone except (A) the rare player who with extraordinary luck accumulates an absolutely massive early chip lead, and (B) some weak and losing players who from an equity standpoint had no business showing up for the tournament at all. In sum, I feel that the discussion has reinforced my original view that if I were to attend this tournament, I'd best think of it as one having a €1,440 (or €1,800) entry fee.
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