among gamblers than positive-progression strategies.

\[table:win-lose\]

Risk attitude {#risk-attitude .unnumbered}
-------------

We now turn to the following question: When a player is allowed to choose the odds themselves in a near-fair game, how would they balance the risk and potential return? Higher odds means a lower chance of winning and higher potential return, for example, setting odds of $10$ means that the winning chance is only $1/10$, but the potential winning payoff equals $9$ times the original wager. In our analysis, we can examine such behaviors based on the gambling logs from Crash and Satoshi Dice games. For the Crash game only CSGOFAST.COM provides the player-selected odds even when players lose that round, whereas for the Satoshi Dice game only Coinroll accepts player-selected odds. We will therefore focus on the data collected on these two websites. For the Crash game on CSGOFAST.COM, the odds can only be set as multiples of $0.01$, whereas for the Satoshi Dice game on Coinroll the odds can be set to $0.99 \cdot 65536/i$ where $i$ is a positive integer less than $64000$. To simplify our modeling work, we will convert the odds on Coinroll to be multiples of $0.01$ (same as for the Crash 