1987 Blockbusters

[SamJ93]

On another message board run by the Wizard of Odds, an expert on all things gambling, there is an interesting thread about the '87 Blockbusters and how the tie-breaker round--which allegedly gave both players equal chances to win--is actually heavily biased in favor of the vertically-moving player.

I'm a bit mathematically challenged, so some of the explanation is hard to follow, but it does seem to make sense.  Any math-inclined posters here care to comment?

[Vahan_Nisanian]

For me, the only flaw with Blockbusters (both versions) is that the endgame was too easy.

[gameshowcrazy]

I don't remember why, but I do know from back then trying to figure that out and learning from elsewhere, perhaps a math teacher, that the vertical player had a 1/2 question advantage.

[dale_grass]

Just in terms of number of paths using the minimum number of questions (4), white has a whopping 20 possibilities (if I counted correctly) compared to red's measely 6.  I'll leave the rest of the analysis to someone else, since I never cared for the theme song.

[rjaguar3]

I ran a Python simulation of all 65536 positions and investigated how many of them resulted in a white-to-white path.

Of the 65536 positions, there were 36852 that saw a white-to-white connection.  This means that if the white and red players are equally skilled, the white player will win about 56.23% of the time.  So white does indeed have an advantage.

[rjaguar3]

Just in terms of number of paths using the minimum number of questions (4), white has a whopping 20 possibilities (if I counted correctly) compared to red's measely 4.  I'll leave the rest of the analysis to someone else, since I never cared for the theme song.

Red has 13 paths of minimum length; 4 of them are straight vertical paths, while there are 9 of them between adjacent "inside" hexes.

[dale_grass]

Just in terms of number of paths using the minimum number of questions (4), white has a whopping 20 possibilities (if I counted correctly) compared to red's measely 4.  I'll leave the rest of the analysis to someone else, since I never cared for the theme song.

Red has 13 paths of minimum length; 4 of them are straight vertical paths, while there are 9 of them between adjacent "inside" hexes.

Shoot, I thought that seemed low.  I went back and counted and only found 6.  I'll have to take my shoes off next time.

[Kevin Prather]

Shoot, I thought that seemed low.  I went back and counted and only found 6.  I'll have to take my shoes off next time.

Blockbusters-a-chow.

[dale_grass]

Shoot, I thought that seemed low.  I went back and counted and only found 6.  I'll have to take my shoes off next time.

Blockbusters-a-chow.

Quite the seductive hexagon dance.  And 13 it is.

[Joe Mello]

I ran a Python simulation of all 65536 positions and investigated how many of them resulted in a white-to-white path.

Of the 65536 positions, there were 36852 that saw a white-to-white connection.  This means that if the white and red players are equally skilled, the white player will win about 56.23% of the time.  So white does indeed have an advantage.

Few questions:

1) Is that 6.23% statistically significant? (I'm slightly inclined to say yes)
2) How does the standard 5x4 grid fare?
3) Can you lend me some of your free time? ;-)

[TLEberle]

1) Is that 6.23% statistically significant? (I'm slightly inclined to say yes)

I'd say no, because every question is a toss-up, and if you've let someone get three in a row with just the one more needed to peg into the base, that's your own fault, isn't it? They don't take turns, and the better player should pick up more of them, all else equal. I'd also argue that the better player would win two-nil making the tie-breaker moot.

[Unrealtor]

According to my numbers (which do vary in the number of total wins for each side), just a little more than half of the possible boards (50.05%) result in a 4-space win for white. 95% of white's winning combinations are in 4 moves vs. 78% of red's winning combinations. Also, there are substantially more 4-space wins for white than for red (32,801 vs 24,192).

At some point, I think one of those has to have some statistical significance, even if people being in control of what spaces are played in what order may counteract most of the disadvantage.