Chip Race Question

[Hedge Henderson]

You have four players with spare $5 chips, and you're replacing them with $25 chips.

Suppose player one has two $5 chips, the rest have three or four. Dealing one card per chip to each player, player one happens to get, say, and ace and a king and none of the other players receive a card higher than a queen. Does player one receive two $25 chips, or do you skip to the highest card among the players who have yet to receive a $25 chip?

[Bozeman]

Skip, no one should get more than one chip.

[CrisBrown]

Hi Hedge,

We usually just round, and give $10 chips where necessary to fill gaps. E.g.: Blinds reach $25/50 (so no more need for $5 chips), and Players A, B, and C have 21, 19, and 17 $5 chips respectively. Player A would get 4x$25 chips; B would get 3x$25 and 2x$10 chips; C would get 3x$25 and 1x$10 chips. Note that A loses $5 in the exchange, and that no one can lose more than $5 in this system. That is negligible given the chip stacks (starting $1500).

Cris

[Stew]

You should skip, no player should get more than one chip.

PS: Don't do what Chris is recommending, the whole point is you are getting rid of all chips smaller than the small blind. If you were going to change out for ten dollar chips, just let everyone keep the fives.

[Ignatius]

There are two fair ways to do it: either all chips go the one with the highest card or each of the top cards gets a single chip.
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There's also an unfair way to do it which unfortunately seems to get increasingly common, which is to only consider the highest card of each player so that no one can get more than one chip. This hurts the guys with many odd chips and favors those with only one. If this method should be practice in your cardroom, it makes sense to make slightly marginal plays (like completing the SB when you would usually fold) in order to get a single odd chip.
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For illustration, consider a 7 handed table where six players have a single odd chip and one has 4 for a total of ten. With either of the fair methods, the EV for each player is zero, however with the "one chip to a player" rule, the EV of the 4-chip guy is
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EV[4] = 5*((1-C(6,2)/C(10,2))-4 = -2/3 = -0.67
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while for the single chip holders EV[1] = 1/9 = 0.11.

[Hedge Henderson]

Thanks for the replies, folks. We've held six tournaments with my home game group so far and that problem has only come up in one chip race. I did it that time as Ignatius second method suggested. Fortunately for me, the player who complains loudest and longest about every chip race was the player who received two chips.

I wanted to have a rule in place in case that problem came up again. While Ignatius' methods are technically more fair over the long run, most players won't see it that way, and it would take a loooooooong time for things to even out. I'll go with the skip method.

[Greg (FossilMan)]

Go back in time a few years, and pretty much every room ran their chip races with the single highest card getting all the chips.

When the TDA was created a few years ago, they instituted a rule where nobody can win more than one chip. Thus, if there are 3 chips to be won, the person with the highest card gets a chip. You then remove all of their cards from the table. Look around, the highest card remaining gets the second chip. Repeat.

I used to see a couple of rooms that didn't race at all. They just rounded up. If the T5 chips were coming off the table, you got a T25 chip whether you had 1, 2, 3, or 4 of the T5 chips.

I think all methods are acceptable, except for the old winner-take-all method, as that could often be too much of a boon for the lucky player. When I first moved to CT, I was in the $500 limit HE tourney at the World Poker Finals, with the T100 chips being raced off the table. I had just taken a bad beat, and had T600, so only 1 odd chip. Everybody else at my table had 3 or 4 odd chips. I won the race and T3000. With the blinds about to go to T500/1000, that obviously had a huge impact on my chances. I went on to win $22,000 in a 3-way deal.

Later, Greg Raymer (FossilMan)

[Bozeman]

Since they are odd chips, I think it is more fair to keep the SD low than to have 0 EV, which is why I like the current standard. If you don't, people can gain full chips instead of gaining or losing just a fraction of a chip. The fairest way, in my opinion, would be to have races between groups that added up to one chip. One way to do this would be to remove the lowest 5-x cards when you give a chip to the player with x cards (assuming the new small chip equals 5 old small chips), though I expect to never see this. As it is, the difference is always less than one raced out chip, which seems quite reasonable.

Craig

[Ignatius]

I think it is more fair to keep the SD low than to have 0 EV
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The real problem I have with nonzero EV methods is that they necessarily have an (albait small) impact on the game before the chip raise. Consider the blinds are 10-25 and about to increase to 25-50, you have 4 odds chips after posting your SB, there are some limpers but no raise. Now the decision whether to play that longshot offsuit one-gapper might very well depend on the procedure used for the chip raise. (The same holds true if you have one odd chip left after posting a 3 chip SB at 15-25, which might cause you to muck a hand you would otherwise play).
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One way to do this would be to remove the lowest 5-x cards when you give a chip to the player with x cards (assuming the new small chip equals 5 old small chips), though I expect to never see this.
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Could you elaborate on that? I would be nice to have a fair (i.e. zero-EV) and practical way to do the chip race which fits the "one chip to a player" restriction!

[Bozeman]

Oops, this is what I get for posting in the morning.
I didn't account for the non-independence of events when I thought I had a reasonable sol'n, it doesn't work.

If you divide it into separate matches where each match has 5 total chips, then it works, but you can't do it with everyone competing together. Also, in this case you'd have people arguing over whether the way of grouping is fair (and also problems when there are not a multiple of 5 odd chips).

I also don't like when proper poker play depends on the chip race, but because of variance and tourney nonlinearities of chip value, there are problems of this type with the 0 CEV sol'ns. In addition, it would be ideal to minimize the effect the chip race has on the tourney, since we would like to have tourneys decided 100% by poker.

For these reasons, I think the current method is good.

Another solution would be to have the chip denominations multiples of 2 so that each chip race only involves players with one odd chip.

We could also roll a 5 sided dice for each player.

Ugh,
Craig