Final answer:
The biases involved are confirmation bias and anchoring bias. Confirmation bias is the tendency to search for information that confirms prior beliefs, while anchoring bias refers to relying on initial values when estimating something. The gambler's fallacy is not relevant in this context.
Step-by-step explanation:
The bias involved in this question is confirmation bias. Confirmation bias is the tendency to search for, interpret, favor, and recall information that confirms or supports your prior beliefs. When you bet money on a tennis player to win a match, you are more likely to be confident in her win because you are seeking information that confirms your belief that she will win.
Another bias mentioned in the question is the anchoring bias. Anchoring bias refers to our tendency to rely on initial values, prices, or quantities when estimating the actual value, price, or quantity of something. In this case, the initial value of betting money on the tennis player winning anchors your subsequent estimates and makes you more confident in her win.
Finally, the gamber's fallacy is mentioned in the reference material, but it is not directly related to the question. The gambler's fallacy is the belief that future chance events will be more likely if they have not happened recently, which is not applicable to the question about betting on a tennis player to win.