Here's more analysis, this time for Tracy's game.
In the first half of the game, Tracy showed confidence and a willingness to play, as the offers were low. The next offer, changed things quickly.
Boxes: 11 (
0.10 5 10 250 500 750 5,000 15,000 20,000 100,000 250,000 )
Offer:
15,000 ( 42% )
Average:
35,592
Balance:
207 to
70,977
2-box average:
35% of time above current,
36% of time above offer.
This is a good offer for the board, the reason is two-fold.
First, a player is unlikely to deal here, because of the presence of 5 good reds, and has good possible expectations. What the banker is really looking for here, is information on whether she is willing to deal.
Secondly, the banker can tweak the offer percentage in the future, relative to the average, based on the above. This prevents the banker from making overly-generous offers when is not warranted.
The tactic worked so well here, that he became confident that she couldn't go all the way without a great board. And because this is unlikely to happen, he subsequently pegged the percentage for future offers around the same.
Boxes: 8 (
0.10 10 250 500 5,000 20,000 100,000 250,000 )
Offer:
20,001 ( 43% )
Average:
46,970
Balance:
190 to
93,750
2-box average:
46% of time above current,
46% of time above offer.
With the last offer, Tracy showed signs of weakness, and was a lot more tempted to deal here. The banker knows it is just a matter of time before she deals, so long as the board doesn't improve too much, he should be fine.
Boxes: 5 (
0.10 500 5,000 20,000 250,000 )
Offer:
22,000 ( 40% )
Average:
55,100
Balance:
1,200 to
109,000
2-box average:
40% of time above current,
40% of time above offer.
Why not offer £26,000 here, which would make a cast-iron deal? Because he doesn't need to.
The board looks strong, and I would be tempted to play on here. But as KP mentioned, the potential drop was just too great for her.
If we look at the balance in percentage terms, relative to the offer...
Balance:
5% to
495%
... and with at best a 1 in 5 chance of £250,000 even if you went all the way, then risking potentially 95% of the offer would enter gambling territory.
Boxes: 2 (
0.10 250,000 )
Proveout offer:
44,000 ( 35% )
Average:
125,000
In this scenario, one of ten possible, she would have dealt for £44,000. This is worse value than the offer before, but one which many here, including myself, would accept.
In the ten scenarios, she would needed to have won more than £220,000 total, to justify no dealing at 5-box. (Note: If a player no deals in a scenario, then the average amount is considered won.)
Of course, we can only guess what would have happened in the other nine. My guess is that there would be too little value for her playing on.
Have I really typed this much?! Well, I found it interesting. Just shows what the banker has up his sleeve, really.
Good game Tracy, enjoy the £22,000 with the family.