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Old 04-17-2007, 02:53 AM
qubits qubits is offline
Chip and a Chair
 
Join Date: Mar 2007
Posts: 7
Chips: 7
Rating: 0% (0)
Re: Color Up and Race

One aspect of this method that bothered me and my poker buddies is that players with two chips going into the race have less than twice the chance of winning a higher demonination over someone with just one small chip (and similar for three chips, etc.) Consider the following example:

Seat 1 - zero
Seat 2 - one T100 (desired chance 20%)
Seat 3 - two T100 (desired chance 40%)
Seat 4 - three T100 (desired chance 60%)
Seat 5 - four T100 (desired chance 80%)

Two T500 chips are to be awarded. Initially Seat 2 has a 20% chance of getting one of the top two cards. However, there is a 22% chance that Seat 3, 4, or 5 might get both high cards. When this happens, Seat 2 gets an additional chance at a T500 chip, beyond the target of 20%. Going through all the possible cases, the actual probabilities of receiving a T500 chip are:

Seat 1: 0%
Seat 2: 23.5% (+3.5%)
Seat 3: 44.1% (+4.1%)
Seat 4: 60.8% (+0.8%)
Seat 5: 71.6% (-8.4%)

Seats 2, 3, and 4 get extra benefit at the expense of seat 5. The difference grows as more chips are raced off. Example 2:

Seats 1 and 6: 0
Seats 2 and 7: one T100
Seats 3 and 8: two T100
Seats 4 and 9: three T100
Seats 5 and 10: four T100

And corresponding chances of getting a T500 chip:

Seats 2 and 7: 24.9% (+4.9%)
Seats 3 and 8: 44.8% (+4.8%)
Seats 4 and 9: 59.8% (-0.2%)
Seats 5 and 10: 70.5% (-9.5%)

To address this, we've tried two methods that are slight variants of the "official" race-off procedure:

Method #1 - Raffle
Shuffle and deal out cards as you work normally. However, allow a player to win multiple higher denomination chips if they are lucky enough to draw multiple top-ranked cards. It will be uncommon for a player to win two or more higher denomination chips in this manner. It will occur just often enough for the payouts to be "fair."

Method #2 - Stack the deck
Carefully stack a pile of cards so that the highest-ranked cards are as spread out as possible. For example, if four T500 chips are to be distributed in exchange for twenty T100 chips, arrange the pile like: AxxxxAxxxxAxxxxAxxxx, where "A" is an ace and "x" is any spot card. Then without shuffling the deck to disturb the order, have someone cut the stack. Finally, deal out the cards in order. If done correctly, no player should ever receive more than one ace, yet the payouts will be "fair."
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